Permutations and Combinations

Right so apparently someone my mum knows needs some 3CD help, but I'm kinda worried that I might have forgotten half of it, so I'm going to blog to refresh my memory.

First up we have counting techniques, which is a relatively straightforward concept but sometimes the questions can be annoying (as with so many other areas of maths...). The main types of counting techniques you need to know for 3CD are permutations and combinations.

Permutations are basically about how many ways a group of objects can be arranged. For example, if you get three characters, say, Azizi, Bentley and Cynder, and put them in a line, in how many ways can they be arranged? You'll find that the answer is six:

ABC
ACB
BAC
BCA
CAB
CBA

It's easy to work that out when you've got so few people. But what if you have 100 people? How many ways can they be arranged? (Not that you'd ever need to know the answer to this question, but still.) This is where the concept of the factorial comes in.

Let's go back to our 3-character example. Instead of thinking about who's going to go where etc., let's slow right down and think of an empty space with 3 spots waiting to be filled with the three characters:
_ _ _

Now let's choose who's going to fit into the first slot. There's 3 options, since nobody's been picked yet.
3_ _

When we move over to the second slot, since one person has been taken, there's only 2 options left.
3 2 _

Finally, that leaves only one person to fill the last slot.
3 2 1

For each character that goes in the first slot, there are 2 different permutations, as there are 2 different characters who can fit in the second slot (the last slot is then a given since there's only 1 character left by that point). Since there are 3 characters who can go in the first slot, this gives us 3 characters x 2 permutations each = 6 total permutations.

Sorry if that wasn't a good explanation. Here's a tree diagram that might help:

There's a logical pattern that holds true no matter how many people you have to arrange. Let's say you have n people to arrange. Therefore there will be n possibilities for the first slot, (n - 1) for the second, (n - 2) for the third and so on. This gives you n(n - 1)(n - 2) x ... x 1 as the total number of permutations.

Thankfully, you don't have to write it all out in full, thanks to the handy dandy factorial symbol (which is just an exclamation mark: !)

Hence, the number of ways you can arrange 3 people is 3! (3 x 2 x 1)

The number of ways you can arrange 4 people is 4! (4 x 3 x 2 x 1)

and the number of ways you can arrange n people is n!

That's easy, isn't it?

Now on to combination!

Combinations is basically the number of different subsets you can get from one big set.

I'm going to use my year 10/11 maths teacher's example for this one, because it's so awesome. I'll just change the characters' names though since I don't remember what the original names were.

Darius, Ember, Flame, Gaul and Hunter all like earthworms, so they all decide to set up an Earthworm Appreciation Society. At first, they decide to create a subcommittee, with a president, vice-president and secretary, appointed in that order. This is where you draw on your permutations knowledge, as first you've got 5 options for president, then 4 for vice-president, then 3 for secretary, resulting in 5 x 4 x 3 = 60 ways in which the subcommittee members can be elected.

Later on, instead of having different ranks within the subcommittee, the Earthworm Appreciation Society members decide that they're going to make all 3 subcommittee members of equal rank (which leaves you wondering what happens to the other two... well, I guess all animals are equal, but some are more equal than others). How many ways can the subcommittee be selected?

No, the answer is not 60. Why? Because, this time, everyone's of equal rank, so Darius-Ember-Flame is the same subcommittee as Ember-Darius-Flame.

How do we get around this problem? you must be asking. Well, first consider how many ways each subset can be arranged. Each subset consists of 3 characters. From the previous thingo on permutations, we know that they can be arranged in 3! = 3 x 2 x 1 = 6 different ways. Hence the Darius/Ember/Flame subset appears 6 times:

DEF

DFE

EDF

EFD

FDE

FED

and each other subset would, likewise, appear 6 times. Hence, to get the number of possible subcommittees, you need to divide 60 by 6 in order to avoid counting subsets 6 times each. This leaves us with 10 possible subcommittees:

DEF

DFG

DGH

DEG

DEH

DFH

EFG

EFH

EGH

FGH

There's also a general rule for this too. Let's first take a look at why it works.

When working out the total number of permutations (remember, permutations is where order matters) for n objects in r [number of] slots, it's a case of multiplying n x (n - 1) x (n - 2) etc. all the way until you've filled up all r slots. An easy way to express this is n!/(n-r)!

I'm not sure how to explain this without being super confusing, but I'll try. n! is the product of all of the numbers from n all the way to 1. The thing is, you only need the product of r of these numbers, because you only need r slots. The remaining number of numbers that you have remaining (i.e. the numbers between 1 and n that don't need to be used) can be expressed by (n - r).

To find the product of just the numbers that you need, n!/(n-r)! works because n! is essentially n x (n - 1) x (n - 2) x ... x (n - r) x ... x 1 and (n - r)! is (n - r) x (n - r - 1) x ... x 1. Hence when you divide n! by (n - r)! you'll find that all of the terms from (n - r) and beyond cancel each other out, just leaving you with the product of the top r numbers. Nifty, right?

Now, as I stated before, working out the total number of permutations isn't enough- you have to then divide by the number of permutations within each subset of r objects, which is r!. This leaves us with a final equation of (drumroll):

The thingo on the left is the notation for combinations (well, one kind of notation anyway. You might see other notation involving P for permutations or C for combinations, with the two numbers on top left and bottom right). The number on the top is the total number of stuff you have to choose from, while the number on the bottom is the number of stuff you want in the subsets. Make sure that the brackets are roundish, otherwise it'll look like a matrix.

That's pretty much all the main basic stuff on permutations and combinations. Because I can be bothered, however, here's some pointers on how to tackle the problem solving varieties of these questions.

Problem Solving: Permutations and Combinations

The problems that you will encounter when it comes to permutations and stuff generally involve some restriction, such as that someone must be on the end of the line, or two people must stand together, or something. I'll show you some basic techniques for solving these, but some are a bit trickier. Just do as many as you can to develop that problem-solving brain of yours!

Oh yeah and, apart from reading the examples in the textbook to get a feel for the types of questions they might ask, I'm making up these questions on my own, which is why they're so weird.

Question 1

Eliona, Sharon, Karyn, Maria and Sarah are lining up for their flu jabs. In how many ways can they line up if:

a) Sarah must go first?

b) Sarah must go first and Karyn must go fourth?

c) Maria is behind Sharon? (Sarah doesn't necessarily have to be first this time)

Question 2

a) Out of 8 humans and 6 Vulcans, a crew consisting of 4 humans and 4 Vulcans is required. How many possible crews are there?

b) One of the humans is Captain James T. Kirk. How many of the crews contain Captain Kirk?

Question 3

Hienuri Kayleuetski is on a chat room with her friends, Diani, Ashleigh and Fiona, who are all using Ashleigh's computer together. To distinguish themselves, they refer to each other as "meep," "moop" and "murp" and encourage Kayleuetski to guess who is who. Kayleuetski's first guess is that Diani is "meep," Ashleigh is "moop" and Fiona is "murp," but is then informed that all of her guesses were wrong. How many possible combinations remain?

Question 4

Neisure has 10 uni books to arrange on her shelf, 4 Psychology, 3 Education and 3 Magic (she lives in an alternate universe where magic is possible!!). How many ways can she arrange them if:

a) they don't have to be arranged in any particular order?

b) books of the same subject are to be kept together?

c) the 3 Magic books must all be together on either end of the shelf, but the other 7 books can be arranged in any order?

Question 5

A TV talk show host wants to invite 3 characters to his upcoming show. His list of potential candidates consists of Alakazam, Blissey, Charizard, Loudred, Miltank, Seviper and Zangoose. How many possibilities are there if:

a) there are no restrictions?

b) he decides not to invite both Seviper and Zangoose (since they hate each other)?

c) he decides not to invite either Seviper or Zangoose, fearing that inviting either would just incite more rivalry?

d) he decides to invite both Seviper and Zangoose just to add some excitement to the show?

Answers

1a) Since Sarah must go first, that only leaves us with 4 characters in 4 possible positions. Hence the number of possible permutations is 4! = 24 ways in which they can line up.

1b) Since two positions are fixed, that only leaves us with 3 characters in 3 possible positions, leaving us with 3! = 6 ways in which they can line up.

1c) To do a problem like this, I generally split it up into different categories and then add them together: if Sharon is first, second, third or fourth (she can't be fifth since Maria has to be behind her). Then I draw boxes for each position and then write numbers in each box corresponding to how many options I have (see my explanation for permutations).

If Sharon is first, Maria will definitely be after her. And since Sharon's position is fixed, that leaves us with 4 characters in 4 possible positions, with 4! = 24 ways.

If Sharon is second, only 3 characters can be in front of her (Sarah, Karyn or Eliona). The other three can be arranged in any order.

[3][1][3][2][1] = 3 x 1 x 3 x 2 x 1 = 18

If Sharon is third, only 3 characters can be first (Sarah, Karyn or Eliona) and 2 characters can be second (those three minus whoever goes first). The other two can be arranged in any order.

[3][2][1][2][1] = 3 x 2 x 1 x 2 x 1 = 12

If Sharon is fourth, Maria must be last, and the other three can be arranged in any order, giving 3! = 6.

Hence the total number of ways in which they can be arranged is 24 + 18 + 12 + 6 = 30 + 30 = 60.

2a) Use the Combinations technique to "choose" 4 humans and to "choose" 4 Vulcans, then multiply the two together.

For humans: nCr(8, 4) (that's the notation used on many calculators) = 70

For Vulcans: nCr(6, 4) = 15

Hence total number of possible crews = 1050

The reason why this works is, for every subset of humans chosen, there are 15 Vulcan subsets that they could be partnered up with. Hence you need to multiply the 70 different groups of humans with the 15 different groups of Vulcans that they could be partnered up with.

2b) Since one of the humans has been "chosen," that leaves us with only 7 humans left to choose from and 3 slots left to fill. Hence, the number of human teams is nCr(7, 3) = 35 and the number of Vulcan teams remains the same (15) which gives us 35 x 15 = 525 different crews all containing Captain Kirk.

3. Yes, I actually did get given a similar problem in real life once, except I skimmed over the part where my friends said "all wrong" and then thought "there's 3! permutations, and I've already guessed one, leaving me with 5 more to go!" No, this is not the case. (I was told to "learn to math" at this point.) And yes, this was a bit of a trick question.

Since Diani is definitely not "meep," this leaves us with two other possibilities: Ashleigh or Fiona.

If Ashleigh is "meep," this leaves us with Fiona and Diani. Fiona can't remain "murp," hence there is only one other option for her: "moop." Diani then takes the last available slot.

If Fiona is "meep," this leaves us with Ashleigh and Diani. Ashleigh can't remain "moop," hence there is only one other option for her: "murp." Diani then takes the last available slot.

Hence there are only 2 possible permutations remaining.

4a) The answer's just 10! = 3 628 800.

4b) To do this, I prefer to think of all of the books of the same subject as just being one book, and then adjusting the number of "slots" accordingly. Therefore I would think of it as 3 books needing to be arranged in 3 different slots, which gives us 3! = 6 ways in which the subjects can be arranged.

After that, you have to multiply by the number of ways books of the same subject can be arranged amongst themselves. The four Psychology books can be arranged in 4! = 24 ways, and the Magic and Education books can be arranged in 3! = 6 ways each.

Then you need to multiply the lot together, to give 6 x 24 x 6 x 6 = 5 184 possibilities.

4c) As in 4b), just think of all three Magic books as simply being one book. This "book" must be at either end, leaving us with 7 slots in which the 7 other books can be arranged. The Magic books themselves can be arranged in 3! = 6 different ways. This leaves us with (7!)(3!)(2) ways in which the books can be arranged (the x2 is because the Magic books can be at either end). Total number of possibilities is 60 480.

5a) nCr(7, 3) = 35 different ways

5b) First see how many possibilities there are if Seviper is definitely coming and Zangoose is definitely not coming. Since Seviper takes up one slot, and Zangoose can't come, that leaves us with 5 potential characters remaining and 2 slots, or nCr(5, 2) = 10 ways. Multiply this by 2 to get the other possibility (i.e. Zangoose comes and not Seviper), and you've got 20 different ways in which to select 3 candidates.

5c) Since neither Seviper nor Zangoose can come, we only have 5 characters to fit into the 3 slots. nCr(5, 3) = 10 possibilities.

5d) Seviper and Zangoose fill up one slot each, so that leaves 5 potential characters and only 1 slot, so only 5 different ways in which to select 3 candidates by this criteria.

An egocentric-sounding passage from 秘密 (The Secret)

Last year, I stumbled across a copy of the Chinese version of The Secret in a university book store. Having never read The Secret, and being curious to know what exactly it's about, I bought the book. Later on, I stumbled across it again in the Self-Help section of a book store in Singapore, and upon opening it and finding out that The Secret is mainly just about positive thinking, my first thought was "This is just an example of very, very good marketing." Back home, curious as to whether people really believed stuff like the "Law of Attraction," I googled reviews of The Secret. Apparently at the end the whole book really does boil down to Byrne's commandment that we all "Feel good now," or something, which is all nice-sounding and stuff, but the truth is, I don't believe that we have that much control over how we feel, though we can control how we handle our feelings. I wanted to see what that looked like in the Chinese version, but on the last page (before the summary and background information on people referred to in the book), I instead found an even more egocentric passage. I couldn't understand all of it at first, but what I could understand made me raise my eyebrows until they'd practically rocketed off the top of my head (gee, I'm glad that my thoughts aren't going to manifest such an occurrence in real life). By the way, the emphasis is not added: the word "你" is actually written in bold print, just to drive the egocentric message even further.

地球为你而转动，海洋为你潮涨潮退，鸟儿为你唱歌，太阳为你朝升暮落，星星也是为了你而出现。你所看到的一切美丽事物，所体验到的一切美妙经验，都是为了你而存在的。看看周遭的一切，没有你，它们没有一个能存在。不论过去你认为自己是谁，现在，你知道真正的自己的真相了。你是你自己宇宙的主宰，你是你自己王国的继承者，你是生命的圆满。现在，你知道这秘密了。

Now, I'm not sure if I've translated this right, so I'll post my translation here just to make sure that I'm not imagining things (or "attracting" things!) and that this really is one of the most egocentric-inspiring passages that I've ever read.

"The world turns for you, the ocean tides rise and lower for you, the birds sing for you, the sun rises and sets for you, the stars also appear for you. Every beautiful thing that you can see, every wonderful experience you have had, all exist for you. Look at everything around you- if you didn't exist, these things also would not be able to. No matter who you thought you were in the past, now you know who you truly are. You are the master of your universe, the ruler of your kingdom, life's satisfaction. Now you know this Secret."

I don't know about you, but I do not necessarily want the birds to sing specifically for me. Let the birds sing for themselves, or for whoever they choose to sing for.

And that is my two cents into the matter.

EDIT: Wow, I was pretty much right about the translation. From http://www.shiningthelightonthesecret.com/whatpeoplearesaying.htm, the actual ending of the book is:

The earth turns on its orbit for You. The oceans ebb and flow for You. The birds sing for You. The sun rises and it sets for You. The stars come out for You. Every beautiful thing you see, every wondrous thing you experience, is all there, for You. Take a look around. None of it can exist, without You. No matter who you thought you were, now you know the Truth of Who You Really Are. You are the master of the Universe. You are the heir to the kingdom. You are the perfection of Life. And now you know The Secret.

Redox in Action: Some Batteries plus Corrosion

Now that we've learned a bit more about redox, let's see how the stuff we've learned applies to the world around us! Yay. Now I sound like an overenthusiastic presenter on a children's TV show.

Continuing with the overenthusiastic children's TV presenter theme (because I feel like I need a lame way to amuse myself today)...

Hey, kids! You know all those batteries that you use to power up all your favourite toys and gadgets? Well, we're going to learn allllllllll about batteries. Well, maybe not all about them, because there's just so much to learn! So, today, we're just going to learn the basics.

The most common kind of battery that you'll see around the shops and in your electronic gizmos is the dry cell. The dry cell is probably called the dry cell because it has a kind of paste, rather than a liquid, inside it.

Here's a picture of the cross-section of a dry cell. The cross-section is what you would see if you cut a dry cell in half, riiiiiight down the middle! But don't try this at home, because it is very very dangerous, and we wouldn't want anyone to get hurt, would we?

You know how the different ends of the batteries are labelled positive and negative? Well, they're named that way for a reason. At the anode, which is the negative side of the battery, the zinc casing undergoes a reaction that produces electrons needed for current to flow.

Zn_(s) à Zn²⁺_(aq) + 2e^-

But wait! If the casing is reacting, how come the casing doesn't corrode? Well, that's because the zinc doesn't just react on its own: it's actually reacting with another substance called magnesium dioxide which is normally found in a powdered form around the graphite rod in the middle of the battery. When they make the batteries, they make sure that there isn't enough magnesium dioxide to react with all of the zinc.

2MnO_2(s) + 2NH₄⁺_(aq) + 2e^- à Mn₂O_3(s) + 2NH_3(aq) + H₂O_(l)

After those two reactions happen, the zinc ions from the first reaction combines with the ammonia from the second to produce another ion- a complex ion this time! Ooh, how exciting!

Zn²⁺_(aq) + 4NH_3(aq) à [Zn(NH₃)₄]²⁺_(aq)

Now, eventually, the outer shell of the dry cell does corrode. That's why you sometimes get battery leakages, where the paste inside the battery comes out. This can be very dangerous, so try not to leave your batteries in your electronic devices (or anywhere, really) for so long that they start leaking!

Why does the dry cell corrode even though there isn't enough magnesium dioxide? Well, that paste inside the dry cell doesn't just contain magnesium dioxide- it contains other stuff too, like ammonium chloride and zinc chloride! Ammonium ions in solution can create an acidic environment, which makes the cell corrode after a while.

Since the zinc ions, once formed, are no longer where the original zinc was, dry cells can't be recharged by making the reactions reverse, and you shouldn't try to recharge them either, as that's also quite dangerous! This inability to recharge makes dry cells primary cells, as opposed to secondary cells, which can recharge.

There's also a very similar cell, called the silver oxide cell! These kinds of cells are also primary cells- that is, they can't recharge. They normally appear in button form, like the batteries in watches and in some calculators! They also use the same anode reaction- the conversion of zinc to zinc ions- but silver oxide, rather than magnesium oxide, is consumed at the cathode.

Ag₂O_(s) + H₂O_(l) + 2e^- à 2Ag_(s) + 2OH^-_(aq)

Apparently they've started developing rechargeable versions of these cells, but most silver oxide cells that you'll encounter at this point in time aren't rechargeable. Make sure to only recharge rechargeable batteries, kids!

The next type of cell that I'm going to tell you all about is the lead-acid accumulator! Unlike the dry cell or silver oxide cell, which produce relatively small currents of electricity, the lead-acid accumulator is created to produce lots and lots of current in a very short amount of time. It's often used in cars.

The lead-acid accumulator is actually made up of a bunch of different cells, each with an anode and a cathode. Each electrode has a lead alloy grid, but the anode's grid is packed with finely divided lead and the cathode's grid is divided with lead (IV) oxide powder. You see, when you finely divide something, it makes the reaction proceed much much faster than if you had it all in one single thick lump!

Anode: Pb_(s) + SO₄^2-_(aq) à PbSO_4(s) + 2e^-

Cathode: PbO_2(s) + SO₄^2-_(aq) + 4H⁺_(aq) + 2e^- à PbSO_4(s) + 2H₂O_(l)

Also, unlike the previous two batteries, these cells are secondary cells. They can recharge, which makes them much more useful for much longer! You can't recharge them too fast, though, or water might be electrolysed to hydrogen gas and oxygen gas, which would mean that you'd have to top up the battery with distilled water. Not only that, but it might explode and that would defeat the whole idea of the battery being useful for a long time!

2PbSO_4(s) + 2H₂O_(l) à Pb_(s) + PbO_2(s) + 4H⁺_(aq) + 2SO₄^2-_(aq)

There are many other kinds of batteries, but there's not enough time to cover them all in today's show. We might be able to talk about them in a future episode. So that's all for now, kids! Stay safe, and look after your batteries!

...

Whew. Now that the show's over, I can go back to being an obnoxious teenager.

By the way, one of my friends' older sisters was watching a whole bunch of kids' shows just to look out for any mistakes that the producers made. Once, she was watching Play School and, at the end, right before the camera was turned off, you could hear someone in the background say, "I hate my job!"

Just some random trivia for you. No, I don't know what episode that is, so I can't help you find it.

Anyway. I'm not going to talk about the other types of batteries, for now at least. Instead, I'm going to talk about corrosion. Yay?

Metals rust and corrode when they're exposed to water and oxygen. How so? you may ask. Well, if you have a look at your data sheet, you'll notice that water and oxygen can be reduced to form hydroxide ions!

O_2(g) + H₂O_(l) + 4e^- à 4OH^-_(aq)

And, as you probably already know if you've become familiar with the basics of redox, many metals can oxidise. Therefore, what we have here is a redox process of sorts, with the metal oxidising and the oxygen and water reducing.

Bear in mind, though, that those metals right at the bottom of the Standard Reduction Potentials table aren't likely to corrode in the same way. This is because these metals oxidise so readily they tend to react really violently with water to produce hydrogen gas, metal ions and hydroxide ions. Take potassium, for instance:

K_(s) + H₂O_(l) à K⁺_(aq) + OH^-_(aq) + H_2(g)

Also, some of the metals near the top of the table won't corrode simply because they're more likely to reduce than water and oxygen are. These metals include gold and silver.

Most other metals, like iron and zinc, will corrode. In fact, iron is very commonly referred to in corrosion questions and examples. My textbook only gives the equations for the rusting of iron. I highly doubt this is really breaching copyright, since you'd probably be able to find all the equations on Google anyway, so here they are:

1. Hydroxide ions produced from the reduction of water and oxygen and iron (II) ions produced by the oxidation of iron combine to produce iron (II) hydroxide: Fe²⁺_(aq) + 2OH^-_(aq) à Fe(OH)_2(s)
2. Iron (II) hydroxide is easily oxidised (more so than iron) to produce iron (III) oxide: Fe(OH)_2(s) + OH^-_(aq) à Fe(OH)_3(s) + e^-
3. The iron (III) hydroxide is then partially dehydrated to produce hydrated iron oxide, or Fe₂O₃·xH₂O. This is basically just rust, that flaky reddish stuff.

Also, as iron (II) ions are consumed to produce the two hydroxides, the reaction producing these ions is favoured in order to partially restore the number of ions- remember good ol' Châtelier? Since the reaction producing these ions also happens to be the oxidation of iron, the rusting process essentially speeds up the rusting process. Brilliant.

Now, we like our things to last, don't we? So, how can we stop our iron tidbits from corroding? Here are some ways we can prevent a metal from corroding:

1. We can coat it with a more reactive metal or connect it via a wire to another more reactive metal. This metal acts as a "sacrificial anode" and will rust instead of the iron or whatever metal that you're trying to protect. If you coat the metal with a less reactive metal, however, then any small scratch on the coating will cause the metal inside to corrode faster. Ditto with linking the metal up to a less reactive metal.
2. Cathodic protection: In cathodic protection, the metal to be protected is linked up to the negative terminal of a DC (direct current) power source, while some scrap metal is linked up to the positive terminal. The negative terminal of the power source provides all the electrons that the iron needs to stay as a metal- if any iron dares become an ion, it will simply collect the electrons being fed to it and become iron again.
3. Some metals are awesome and actually stop themselves from corroding in the long run. Take aluminium, for example. When aluminium oxidises, it forms aluminium oxide, which actually forms a protective coating that stops any further oxidation. Pretty handy, huh?

That's pretty much all from me on corrosion, unless you feel I haven't covered enough. I might do another post on the different kinds of cells if I can be bothered, but for now I'll just go on to thinking about writing posts about organic chemistry. (Actually writing them might be a little tougher.)

Redox reactions (including the T-word)

The first thing that you have to know is how to write equations for and interpret observations for redox reactions. But we've already done writing equations! you might say, and you're right, since I've already talked about them in my post aptly titled "Redox Equations."  We haven't done observations, though, because observations are totally a whole new ball game. Not.

Basically, the first thing that you need to do is write the equation. Then have a look to see if any of these things happen:

• Gases are bubbled through the liquid
• Gases are produced
• Solids dissolve
• Solids form
• The solution changes colour (use your data sheet to determine the colour of reactant and product ions)

Once you've determined these things, you need to make sure to provide detail. If a gas is bubbled through or if a gas is produced, what colour is the gas, and what does it smell like? Most gases are colourless and odourless, but some have a colour, like chlorine gas which is greenish-yellow. Additionally, most gases are odourless, but there are some that are considered to have a "pungent odour" like hydrogen sulfide (and maybe nitrogen dioxide, I can't remember). If a solid is dissolved or formed, what colour is the solid? (By the way, you have to use what the data sheet tells you. So yes, that means you have to say that copper is "salmon pink.") Also, generally, in a redox reaction, where one solid dissolves and another forms, you can just say that the first solid is coated with the second. I think.

A couple of common ion colours that you should know are the permanganate ion (purple) which can be reduced to manganese (II) ions (pink) and the dichromate ion (orange) which can be reduced to chromate ions (yellow). They're on the data sheet anyway, but they're so common in redox reactions that it's almost worth getting to know them.

What's next? Hm. Stoichiometry. Well, stoichiometry here works the same way as stoichiometry everywhere else, so if you need to brush up on that, head on over to the following posts:

• Simple Calculations Involving Moles
• Reactions and Equations, part deux
• Simple Chemistry Calculations
• Empirical Formulae and Limiting Reagents and Some Other Stuff

Next up: Explain the use of self-indicators in redox titrations. You know how you need an indicator of some kind in acid-base titrations? (If not, go to my post on titrations.) Well, in redox, you generally don't, because common oxidising agents used, like permanganate and dichromate ions, change colour when they're reduced anyway, and it's this colour change that helps you to work out an end point.

Redox titrations are a bit more complex than acid-base titrations because you normally have to go to all the work of sufficiently acidifying the permanganate or dichromate ion solutions otherwise you'll end up with manganese dioxide or chromate ions later on.

Now, a bit more about redox titrations. A primary standard needed here is something that's going to oxidise or reduce, otherwise you wouldn't end up with a redox reaction! Oxalic acid (H₂C₂O₄ , otherwise known as HOOCCOOH which is kinda like Ho-oh with some extra letters added in) is often used for redox titrations as a primary standard because it can be prepared to a high degree of purity and whatnot (my first post on titrations outlines the main characteristics of primary standards).

When using potassium permanganate solution, you have to take all kinds of precautions because it oxidises stuff easily and also decomposes in solution, especially in sunlight. When you prepare the solution, you sometimes have to cover the beaker and boil the solution before filtering it through glass wool into a dark storage bottle. Now, I'm not 100% sure on the science behind all of this, because we haven't really done a lot of redox titrations, but I think the boiling might be to get rid of stuff within the solution that the potassium permanganate might oxidise? I'm not sure exactly what stuff needs to be removed, but there you go. As for the glass wool, I have absolutely no idea whatsoever (and I'm feeling too lazy to look it up right now), so if someone could enlighten me, that would be great! If not, that's okay, you don't have to do all my dirty work for me.

The rest of the titration proceeds in pretty much the same way as an acid-base titration, except for a couple of differences:

1. You have to add sulfuric acid (NOT hydrochloric acid, as the chlorine ions will be oxidised by the permanganate ions) to the solution so that the permanganate or dichromate or whatever solution will form your desired products (i.e. manganese (II) ions rather than manganese dioxide).
2. You have to heat the conical flask before reaction because the reaction proceeds too slowly at room temperature. (Well, too slowly for our purposes, anyway.)
3. You don't have to add indicator because permanganate ions are purple and they should turn pink (or a murky brownish colour if you didn't add enough acid) and dichromate ions are orange and they should turn deep green (or yellow if you didn't add enough acid). However, I've also heard that occasionally the permanganate solution might turn clear instead of pink despite what it says on the data sheet.

Whew. That wasn't so bad. I guess it's easier talking about titrations than actually doing them.

Redox again- Electrolytic cells and some other stuff

(Lack of introduction here because I can't be bothered.)

Previous posts on redox:

• Basics of Redox
• Redox Equations
• Electrolysis
• Applications of Electrolysis
• Ways to Remember Oxidation and Reduction

As with pretty much every other topic we've done this year, the redox stuff this year pretty much takes off from what we did last year. The main difference is that we're going to be talking about electrolytic cells rather than electrolysis- rather than running an electric current through a substance to make a reaction occur, we're using the transfer of electrons in redox reactions to produce electricity. I think.

Anyway, let's take a look at what we need to know.

We still need to know basic stuff like oxidation numbers, as outlined in the Basics of Redox post. Additionally, we need to know how to balance redox equations in normal and in acidic conditions, both of which are outlined in Redox Equations.

By the way, I also know how to balance equations in alkaline conditions. Basically, what you do is you balance the equation as if it's in acidic conditions, then add OH- ions to both sides to turn all H+ into water. Just make sure that water's only left on one side of the equation afterwards.

As an example, let's take the acidic conditions example from the Redox Equations post:

MnO₄^- + 8H⁺ + 5e^- -> Mn²⁺ + 4H₂O

For alkaline conditions, there need to be OH- ions. Accordingly, I add 8OH- to each side (to get rid of H+):

MnO₄^- + 8H⁺ + 8OH^- + 5e^- -> Mn²⁺ + 4H₂O + 8 OH^-

Next I combine the H+ and OH- on the left hand side into water:

MnO₄^- + 8H₂O + 5e^- -> Mn²⁺ + 4H₂O + 8 OH^-

Finally, I cancel out 4 water molecules from each side, and I'm done!

MnO₄^- + 4H₂O + 5e^- -> Mn²⁺ + 8 OH^-

Hmm... what else... "Apply the table of Standard Reduction Potentials to determine the relative strength of oxidising and reducing agents to predict reaction tendency." This isn't too hard. Basically, the higher an element's reduction potential, the more likely it is to be reduced. This, conversely, makes the element a better oxidising agent. Hence, fluorine is a great oxidising agent, and potassium ions are pretty crap in comparison.

When strong oxidants get reduced, they become weak reductants. For example, fluorine, a strong oxidant, can be reduced to fluoride ions which are relatively weak reductants when compared to potassium (which is what you get when potassium ions are reduced).

Another way of thinking about this is by flipping around everything on the Standard Reduction Potentials table to essentially get a Standard Oxidation Potentials table. To get the oxidation potential of the reverse reaction for any reaction on the table, just change the positive or negative sign of the reduction potential.

Okay, I realise that that probably doesn't make sense, so here's an example.

The reduction potential of F₂ + 2e^- à 2F^- is 2.89V. Therefore, the oxidation potential of 2F^- à  F₂ + 2e^- is just -2.89V.

Similarly, if a reaction's reduction potential is negative, the reverse reaction's oxidation potential will be positive.

You might also need to know some of the common oxidants and reductants, though if you're studying Chemistry you'll probably know them already from encountering them often. Possibly the two most common oxidising agents that you'll encounter are the permanganate ion (MnO₄^-) and the dichromate ion (Cr₂O₇^2-), as these are commonly used in redox titrations (titrations AND redox... the two parts of Chemistry that I hate most combined into one... what could be better?).

Other common oxidising agents that you'll need to know, according to my course outline, are oxygen (!), chlorine, the hypochlorite ion (ClO^-- I love Google sometimes), the hydrogen ion, concentrated sulfuric acid and concentrated nitric acid. With regards to the latter two- I think that it's mainly the hydrogen ions in sulfuric acid that oxidise stuff, while that job's given to the nitrate ions in nitric acid, as nitrate ions are better oxidants than hydrogen ions. If you happen to be doing the same Chem course as me you'll notice that nitrate ions have conveniently been left off the data sheet, so here's an equation- two equations, in fact- showing how nitrate ions can be reduced:

NO₃^-_(aq) + 4H⁺_(aq) + 3e^- à NO_(g) + 2H₂O_{(l)     +0.96V}

NO₃^- _(aq) + 2H⁺_(aq) + e^- à NO_2(g) + H₂O_{(l)       +0.80V}

Now, you may ask, out of these two equations, which one will occur in a reaction? Well, judging by the reduction potentials, the top reaction is more likely to happen. I'm assuming that the lower reaction will probably only occur when there aren't enough hydrogen ions. Sorta like how the permanganate ion might reduce to manganese dioxide if the permanganate solution isn't acidified enough.

Due to the nitrate ions being more readily reduced than hydrogen ions in, say, hydrochloric acid, copper will react with concentrated nitric acid, but not with hydrochloric acid. Just some trivia for y'all.

Now let's have a quick look at common reducing agents that you'll need to know. Many metals are good reducing agents, like zinc and magnesium. Hydrogen gas is also a common reducing agent. Iron (II) ions also sometimes oxidise to iron (III) ions (though I'm fairly sure iron itself is a better reductant than its ions), and the chromate ion (C₂O₄^2-) can oxidise to the dichromate ion.

What's up next? Hmm... electrolytic cells! Yay.

Basically, an electrolytic cell is actually made up of two half-cells: one positive, one negative. Each cell consists of some kind of electrode in solution. These electrodes are joined together by a wire which allows for the flow of electrons when the redox reaction between different substances in the cell takes place. I *think* that it's this very flow of electrons that produces electricity. My vague understanding of current from not doing physics and hardly being able to understand the relief teacher/ not really paying attention in year 9 science is that current is basically just the flow of electrons. To complete the circuit, there must be something else connecting these two cells: in the lab, we can just use a salt bridge (a filter paper dipped in solution) with ions that won't react with the ions in either solution. A common solution used for creating a salt bridge is potassium nitrate because neither potassium nor nitrate ions will cause anything to precipitate out of solution.

Enough blabbering on, here's a diagram:

Just like in good ol' electrolysis, the anode is where oxidation takes place and the cathode is where reduction takes place. When stuff gets oxidised at the anode, electrons are removed from whatever is being oxidised and then travel down the wire to the cathode, where they reduce the other substance in question. The salt bridge completes the circuit by allowing charged particles like ions to move between the cells. Since stuff is being oxidised and is becoming more positive in the anode cell, negative ions will migrate towards the anode. Similarly, since stuff is being reduced and is becoming more negative in the cathode cell, positive ions will migrate there.

Also, I need someone to help me out here: is the anode the negative cell, as it produces electrons, while the cathode is the positive cell? This is where I always end up guessing on Chemistry tests. (Well, not always- we've only been asked a total of 2-3 questions about this- 1-2 on the redox test, and one on the exam.)

Sometimes, the electrode in each cell will be a metal and the electrolyte will simply be a solution containing ions of the metal used in the electrode. This, however, is not always the case. The only metal and metal ions that you really need are the ones that are going to take part in the reaction. For example, if you want to utilise a reaction between zinc and nickel (zinc being more likely to oxidise to zinc ions), you do need a zinc electrode in one cell and a nickel ion electrolyte in the other, but you get some degree of choice in the rest. In the zinc cell, the electrolyte can be any solution containing ions (I think that you need ions to help with the flow of electricity- maybe water will suffice in some cases?) that won't react with the zinc. Normally, it's easiest just to use a solution with zinc ions, but I think (I'm not sure) that you can use a solution with manganese or aluminium ions which won't react with the zinc. In the nickel cell, the electrode can be any metal that won't react with the nickel ions- normally graphite or platinum are used as they are inert substances.

What happens if you want to use a gas, like hydrogen gas, as an electrode? Well, that's possible too. What you do is you bubble the gas over a platinum (or carbon, since platinum and carbon are inert) wire/mesh electrode. The wire serves to carry the electrons and the mesh is probably there to increase surface area. I dunno. 

Speaking of hydrogen, there's actually a very special half-cell called the hydrogen half cell which has been assigned a standard reduction potential of 0V. (Did you think that that was an awesome coincidence? I might have. Actually, I can't really remember if I even gave two hoots about it back in Year 11.) All of the other half-cells have had their standard reduction potentials assigned by comparing them to the hydrogen half cell. Here is the hydrogen half-cell, in only some of its glory (well? It's a bit hard for something to maintain its full glory after I've mutilated it on Paint!):

Note that the pressure of the gas, the concentration of the acid and the temperature are all controlled. This is because the standard reduction potentials can change depending on temperature, pressure and concentration. That's right: those Standard Reduction Potentials aren't set in stone. I think most tables show them for 1 mol/L solutions (for substances that are in solutions) at 25 degrees Celsius. (As for gaseous substances, I'm not sure, but I think that they're probably for 101.3kPa, or 1atm. Or 760mmHg if you're that way inclined.)

To work out the standard reduction potentials of other standard cells (cells at 25 degrees C and whatever pressure/concentration is considered "standard"), the other standard cells are hooked up to a standard hydrogen half cell and the voltage recorded. The positive and negative values are assigned depending on what direction the electrons are flowing: if they're going from the hydrogen half cell to the other cell, the values are positive, whereas if they're going from the other cell to the hydrogen half cell, then the values are negative.

Oh, silly me. I've forgotten to tell you all how to calculate the electrical potential of a cell using the table!

Basically, write down the oxidation and reduction half-reactions taking place in the cell (or don't, if you prefer to work mentally). Add the reduction potential for the reduction half-reaction and the oxidation potential for the oxidation half-reaction together to get the electrical potential of the cell. Yay! (I briefly outlined how to work out the oxidation potential earlier in this post.)

By the way, if you get a negative value, you might want to check that you've got your anode and cathode reactions the right way around. Electrical potential values should be positive.

That's pretty much the main stuff covered on redox. Next up will probably be stuff on dry cells (batteries, yay) and corrosion. Oh, and redox titrations, if I can bring myself to write about them.

I still hate redox. And I still hate titrations. They make me really angry for some reason.

Anyway.

TTFN!

The Lit Formula: Playing the Game of Lit- Part 2

(Part 1 can be found at http://year11misadventures.blogspot.com.au/2013/09/the-lit-formula-playing-game-of-lit.html)

In Part 1, I talked about answering the question and structuring your essay. Now I'm going to talk about a few other little details that you might need to know.

A Very Quick Word on Course Concepts

Course concepts are all hidden in the educational waffle in the syllabus. Yes, that thing that hardly anyone reads. If you do read it, I'd recommend that you only read the 3B one or the condensed one with both units- the 3B syllabus has a couple more dot points than the 3A one and, apart from that, there's only a one word difference between the two so it's not worth wasting your time reading both.

The long and short of it is, there's only a limited amount of stuff that they can ask you about. This helps when studying, because then you could just look at how each text addresses each course concept. Of course, not every text is geared to address every single one, but it's nice to see how many different ways you can look at a text (or at least I find that it helps me to feel reasonably confident in the exam room).

Some more reasons why you'll need to know the course concepts are a) because they give you something to write about in your thesis statements and b) they give you something to look for in your Close Readings. If you can't find anything to write about, just think, "Hmm, is there any way I could tie this to genre? Context? Intertextuality?"

Anyway, without further ado, here is a condensed list of course concepts that could be thrown at you. Make sure to get yourself familiarised with them.

• Genres and generic conventions
• Language
• Context- social, historical, cultural, reader's own context
• Values and ideologies
• Aesthetic functions
• Reading intertextually
• Discourses- different ways of thinking and talking about the world
• How nations recognise themselves through their literary texts (an example of a question that asks this is "How might literary works help us to recognise ourselves as Australians?")
• Reading practices- feminism, Marxism, new-historicism, post-colonialism etc.

More Big Words

Sometimes the idea that you want to talk about involves some other big word, like postmodernism, determinism and so on. If you are going to use these words, make sure that 1) you make sure to tie your reading to those course concepts and 2) you ensure that you fully understand whatever term that you're trying to use. I tend to stray away from big words so my advice here would be to write some practice essays and show your teacher so that at least you know whether you're on the right track or whether you should avoid using these terms until you learn more.

Using Quotes, or "[Making] Strategic and Cticial Use of Supporting Evidence Including Quotes and/or Examples"

As I've stated previously, you need to back up all your points with evidence. To assist you there, I'm now going to explain how to integrate your evidence.

Most of your evidence will probably come in the form of quotes. Therefore, it helps to use quotes fluently. It's a bit hard to explain this, but I'll have a go. Basically, only use the part of the quote that you really need, and try and make it flow into the sentence as much as possible, such that the sentence would make sense even without the quotation marks. You shouldn't have to use the word "quote" to talk about quotes. In a take-home essay, you need to put the page number of the quote in brackets (parentheses for any US folks out there reading this) after the quote. If you're referencing a scholarly article, you need to put the author's surname in the brackets too. Here's some examples of using quotes:

• Huberto initially "[scratches] a living through hustling and petty thievery" (62), and Eva is tossed from employer to employer to earn money for her madrina.
• He refers to Claudius, his uncle who has become king so soon after his father's death, as "a little more than kin, and less than kind."
• Not knowing what to do or say, to have lines "not simply forgotten but never learned" is an "actor's traditional nightmare" (Zeifman 205).

You might also notice that I've used square brackets in the first quote. Square brackets are used if you need to alter a verb tense or a pronoun to fit your sentence. They can also be used if you need to change a lowercase letter to uppercase (but I don't think it's absolutely necessary to use square brackets here). In the first quote, I think that it was originally "scratching," but it wouldn't make sense to say "Huberto initially scratching a living." Thus, I had to change the verb tense to let the sentence flow.

Another use of square brackets in quotes that you might have seen is the word [sic]. You probably won't have to use this yourself, unless you're quoting something from the first part of Flowers for Algernon or another text with deliberate spelling and grammar errors. Simply put, if what you're quoting has spelling or grammatical errors, you can use [sic] to show that you are simply keeping the original spelling and grammar intact.

We're nearly there. Just one more quick point!

Expression of Ideas

Expression of ideas isn't something that I can just explain. Everyone has their own unique writing styles and it is up to you to develop yours. Reading and writing are probably the two best ways to help you achieve this. Your teachers will probably also be willing to help if you show them essay drafts.

I wish you luck on your adventures studying Lit!

For fellow Year 12s: Just two more Lit exams EVER (unless you fail and have to sit the sup- apparently the sup's really easy though, which is good). Yay! No more timed Lit essays EVER after these two last exams!

The Lit Formula: Playing the Game of Lit- Part 1

I'm one of those people who just wants to pass Lit, but I seem to be doing pretty well in it lately so I think I might actually be in a reasonable position to give pointers to other people who just want to pass.

One of the most frustrating things with Lit is that it's not that obvious what it is that you need to do to pass and what you can do to improve. With maths and science subjects, you can always just do more questions to help build your understanding and in some cases just rote-learn the content that you need (the latter doesn't really work for me as I'm blessed with a terrible memory for rote-learning- yes, I mostly see it as a blessing- but it might work for some other people). Lit seems rather subjective, though, and sometimes the comments you get only really seem relevant to that one particular essay. So how does one improve their Lit marks?

Well, in Lit, just like any other subject, if your aim is simply to pass, then it helps to just learn the rules of the game and work from there. Normally I condone this somewhat reductionist approach to learning- you should be learning to learn, not just for the Curriculum Council's stupid little game- but an approach like this might be what you need to jump-start your understanding and increase your capacity to learn this subject.

That's enough waffling. Now for actual content.

First up: what are the rules of the game?

Let's look at the marking key. It's divided into 5 sections: quality of reading, engagement with task, expression of ideas, use of key concepts/literary terms and use of supporting evidence.

• Quality of reading is all about "[presenting] a detailed and critical reading of the text" and " [commenting] astutely on language and/or generic conventions and/or context." This is where the bulk of the marks lies. I'm not 100% sure what all this educational gobbledygook means (wow, Google Chrome doesn't mark "gobbledygook" as being incorrectly spelled), but I think it's all about content: how detailed and insightful is your response, and how much does it tie to relevant features of the text, like language, generic conventions and context?
• Engagement with task: This one is kind of weirdly worded. I think all they want here is for you to answer the question, or, as my maths teacher puts it, ATBQ (Answer The Bloody Question). Your essay also needs to have "focus and direction" to get a good mark in this category- I guess this means that your entire essay needs to be relevant (focus) and well-structured (direction).
• Expression of ideas: This is basically about how well you can get your ideas onto paper and how clear you can make them. You can get the full 6 marks of this category if you can write in a "sophisticated and lucid style" but if you, like me, like to play it safe and just be clear and simple, you can still net 4-5 marks here. Structure also helps here too.
• Use of key concepts/literary terms: This is where you get marks for using fancy terms. But you can't just use fancy terms- you have to use them well, and at least look like you know what you're talking about. (Unfortunately, it's not so easy to bluff in Lit if you don't know what you're talking about. English teachers are very good at reading between the lines. That's why they're English teachers.)
• Use of supporting evidence: Quotes! Quotes galore! And also other relevant examples and stuff too. When you use supporting evidence, however, you need to make sure that it fits in to what you are talking about and that the quote kind of "flows" in with everything else you are writing.

So to recap: Answer the question with the most insightful response you can muster, put in some quotes and literary terms and try and express all your ideas clearly if not in a "sophisticated and lucid manner" and then you'll be on the road to some good marks in Lit!

Of course, it's not that easy, which is why I'm going to break things down even further.

Engaging with the Task: Answering the Bloody Question

Answering the question sounds like such a simple task, but it's something so often forgotten about in the quest to write a good essay. Remember that you're not just writing an essay: you're providing an answer or a response to whatever's being asked of you. Sometimes, though, the question isn't all too easy to understand, or it's written in such academic gobbledygook discourse (a key Lit term!) that the question is obscured. Let's take a look at how to dissect these questions.

The first step is finding the 2 or 3 main parts to the question. Nearly all questions have a few main parts: one relating to course concepts like genre or intertextuality, and another relating to ideas. Normally the questions are broad- the exam writers don't know what texts you've studied, after all. Normally the question will point to a specific convention, or a specific idea, or occasionally both. (Of course, some questions don't point to anything specific, but most questions of this type that I've seen are better left avoided unless you have a text that really matches the question.)

The first sample question in my course handbook is "How can knowledge of the context of a text's production help readers to make meanings from it?" This question relates to the specific course concept of context, and then points towards the broad idea of the making of meaning. In answering this question, you would have to talk mainly about context, but then you would be able to (read: have to) push context towards whatever meanings you want to make. When planning, you could perhaps go paragraph by paragraph according to different meanings made, or you could go paragraph by paragraph according to different contextual influences on the text.

A question in my course handbook of the opposite type is "Literature may be read as a form of social and/or cultural history. Discuss, referring to one or more literary texts you have studied." Here, course concepts aren't mentioned at all, but remember this- you ALWAYS have to talk about them, regardless of whether the question mentions them or not. In other words, while you must talk about the social and/or cultural history, you cannot just talk about the social and/or cultural history on its own without talking about how it relates to the text, otherwise what would be the point of Literature as a subject?

And of course sometimes you get questions that specify both course concept and idea, like, "How do intertextual readings contribute to the circulation or construction of value systems in a society?" Here you have your specific course concept- intertextuality- and your specific idea- the circulation or construction of value systems.

(And then there are horrible questions like the 2012 paper's "Works of literature invite us to experience the lives of others. Discuss with reference to one or more works you have studied." My suggestion is to run far away from these questions as it's pretty iffy. Whatever you do, though, don't do what the weakest students did, which was simply write essays fantasising about themselves as handmaids or whatever.)

So, in a nutshell: find out what 1 or 2 specific things they're asking you to address, and make sure you address those things all throughout your essay. Also, make sure that you talk about course concepts like genre, intertextuality, language and generic conventions, regardless of whether the question specifically asked for them or not.

Structure and Logic: They Have Their Place in Lit Too

Structure is pretty important in an essay. It helps organise your ideas and make your essay easier for your marker to follow, which in turn leads to better marks. Yay!

Essays are pretty structured pieces of writing, and they're all held together by a single thread: your thesis. A thesis statement is a sentence or two that sums up pretty much everything that you're going to talk about. In your body paragraphs, you expand on whatever it was that you were talking about in your thesis. Finally, your conclusion reiterates what you were talking about in your essay. Yes, it sounds like you're repeating yourself a lot, but it helps to get your point across.

Here's a brief stupid example to explain the structure of an essay. Let's say that I want to argue that clarinets are wonderful musical instruments. To do so, I'd have to come up with a few reasons why clarinets are so amazing:

1. They have a large pitch and dynamic range.
2. They are versatile and can play a wide variety of musical styles.
3. They are very portable.

Then I would incorporate all of this into my thesis: "I believe that clarinets are wonderful musical instruments due to their large pitch and dynamic range, their ability to play a wide variety of musical styles and their portability."

The thesis would normally be part of an introduction paragraph rather than just a stand-alone sentence, but if you are struggling to find something to write in a 60 minute close reading, or if you are writing an extended response for another subject that doesn't require a lot of eloquence, writing the thesis alone might suffice. (You can always write a proper introduction later if you have time- just make sure that it's clearly marked.) An introduction paragraph should just introduce what you are talking about, including uncommon key terms (i.e. not in the course syllabus) relevant to your subject matter. For example, in this particular non-essay about clarinets, you could introduce the clarinet by providing basic facts (e.g. it's a woodwind instrument, it has a single reed, it came into use in the Classical period) before launching into the thesis. I personally like to have the thesis at the end of the introduction paragraph because it comes as a sort of "climax" to the intro, but you can always have the thesis at the beginning if that floats your boat. Just make sure your thesis statement is obviously a thesis statement.

In each body paragraph, I would then expand on each of the points. For example, for the first point, I could provide the following expansion:

1. Clarinets have a large pitch range. They can play from a low E below the treble stave to a high G on several leger lines above the treble stave (standard range). It is possible to make the clarinet play even higher.
2. Clarinets have a large dynamic range. They can go from being very soft such that they can be used in "fading away" effects like in Frank Ticheli's Sanctuary, or they can be loud enough to play solos in orchestral music.

Note that for each point, I've provided my statement, plus some evidence and explanation. There's an acronym for this: SEE, or Statement, Evidence, Explanation. An alternative acronym is PEE, or Point, Evidence, Explanation. As one of my Year 10 English teachers put it, "Try and PEE several times in each paragraph!" (And make sure you have a basin or something beneath you. Umm.) Seriously, though, just make sure that you go into as much detail as need be, and back up everything you say with concrete evidence.

So how does this tie into a Lit essay? Well, that's easy. Your thesis will obviously be different because it'll be all about generic conventions and how they do this or that or the other, and then all throughout your body paragraphs you'll be breaking down your argument and providing evidence and explanations for everything. I'm not the best Lit student so I feel kind of tentative providing a Lit example of my own, but here's an example from my Close Reading on the Semester 1 exam.

Remember what I said before about each question having 2 parts: generic conventions and ideas? Well, make sure to address both of those parts in your thesis statement, even if the question was as vague as the good ol' Close Reading "present a reading." Here is the thesis statement from my Close Reading:

"The extract from Bereft can be read as a Romantic text exploring the beauty and power of nature as well as a Realist text that provides the truth "as it is" and comments on different societal issues through the use of imagery, structure and intertextuality."

Yes, it's kind of long-winded and maybe I should have broken it down into two sentences. But hey, it does the job... somewhat.

Stuff to notice here:

• "can be read"- in this Lit course you have to use words like "can be read," "may be read," "can be seen" etc. as a way of letting the markers know that you know that there's more than one correct way to read a text, because there is. (Why else would people complain about the subjectivity of English so much?)
• Generic conventions- as you can see, I pointed my thesis directly towards imagery, structure and intertextuality.
• Ideas- the ideas I pointed towards are Romanticism and Realism.

So basically, when you write your thesis statement, you have to make sure that you make your reading contingent (for lack of a better word) and you have to include both generic conventions and ideas. Try and tie your reading to one of the course concepts because the markers like that.

As for the body paragraphs, you can divide them up in different ways: you might choose to have a paragraph on each of the generic conventions, or a paragraph on each idea, depending on what best fits your argument. Sometimes it might even be best to talk about the text chronologically (e.g. stanza by stanza in the case of a poem). No matter which structure you choose, however, you have to stay close to the text and talk about those generic conventions! After all, this is an essay primarily about literature and not an essay primarily about determinism or Romanticism or whatever ideas you're talking about.

In this particular case, I divided my essay up by ideas, writing a couple of paragraphs about Romantic ideas and a couple of paragraphs about Realist ideas.

Which reminds me. Each paragraph should start with a topic sentence that sums up what that particular paragraph is going to be about. (Yes, you do a hell of a lot of summing up stuff in essays.) Making a topic sentence is just like making a thesis statement except it's a bit narrower because you're only talking about one of the points that you made in your thesis. For example, in my first paragraph about Romantic ideas, my topic sentence is "The extract can be read as a Romantic text portraying the beauty and power of nature through imagery and structure." Once again, it's tying to generic conventions and ideas- but only one particular idea in this case, since we're trying to narrow things down a bit so that we can go into further detail.

That topic sentence was my statement. Now I need some evidence and explanation for how structure and imagery help to portray Romantic ideas about the beauty and power of nature. Here is an example of evidence and explanation for each point:

• (Structure)
  Evidence: A whole paragraph near the beginning of the extract is dedicated to simply discussing the myriad of creatures that live in the ocean.
  Explanation: This highlights the importance of nature through this paragraph's prominent place in the text.
• (Imagery)
  Evidence: Visual imagery- "Birds [bathing] in the rainbows"
  Explanation: This is a peaceful and beautiful image as bathing is a calming task, as well as one that cleanses and makes one more beautiful, while rainbows have connotations of beauty and happiness.

I have several other examples in my paragraph. What ties them together is, of course, the way I choose to express my ideas- I'll briefly talk about this later.

After writing several body paragraphs detailing pretty much everything you wish to say, it's now time to write a conclusion summing up everything that you have written. I'll be honest with you here- I have no idea how to write conclusions. They always end up looking like my introductions. I think what you're meant to do is mainly just sum up everything that you've said, but at the same time you could hint at how your argument could be applicable to the real world (e.g. if you're talking about the patriarchal society as portrayed in Ibsen's A Doll's House you could argue that some elements of this society can still be seen in parts of the world today). You just have to be careful that you don't introduce too much new stuff. In any case I'm not very good at writing conclusions so I can't give too much advice here.

This post is getting quite long, so I'm going to round it off here and write a Part 2 about key terms and how to use quotes, among other things.