Question

@empty I'm a noob at chem

Answer 1

Alright so let's learn how to balance a chemical equation with linear algebra! Do you happen to have one that looks difficult or should I just come up with something on my own?

Answer 2

Come up with one, but remember I'm in baby chem! lol

Answer 3

\[W \cdot C_6H_{12}O_6 + X \cdot O_2 \rightarrow Y \cdot H_2O+Z \cdot CO_2\] OK hopefully this isn't too crazy. This is the burning of sugar \(C_6H_{12}O_6\) with oxygen gas \(O_2\) to make steam \(H_2O\) and carbon dioxide gas \(CO_2\)

And W, X, Y, and Z are the coefficients we want to use to balance our equation. Everything seem pretty reasonable so far?

Answer 4

I can do an easier one first for an example if this seems too big and confusing.

Answer 5

That's fine, I like combustion :D

Answer 6

So we start out by seeing what all the atoms are in the reaction they will form our basis vectors! We only have Carbon, Hydrogen, and Oxygen, straight forward enough, so here we have our basis vectors:

B={C,H,O}

That means the vector \[\left[ \begin{array}c 6\\ 12\\ 6\\\end{array} \right]\] represents sugar, since we have 6 carbon, 12 oxygen and 6 hydrogen in it. What are the other 3 vectors?

Answer 7

Is that suppose to be 12 hydrogen or oxygen

Answer 8

12 hydrogen. I've just randomly decided the order should be from top to bottom the same as it is listed left to right in my basis {C, H, O} so that means the top is # of carbon, middle is # of hydrogen, and bottom is # of oxygen atoms. So the 12 is for hydrogen.

\(C_6H_{12}O_6\) the subscripts one each letter represent how much of that atom are in the molecule. So for instance \(H_2O\) means 2 Hydrogen and 1 Oxygen (the 1 is understood if it's not listed).

Answer 9

Ah ok, no I just looked at you said 6 carbon, 12 oxygen, and 6 hydrogen, and was just wondering, if it was an error or that's how it is

Answer 10

So for the second one don't know how to do linear algebra on LaTeX XD

Answer 11

Where did I say 12 oxygen and 6 hydrogen? haha I want to correct it so it's not confusing

Answer 12

http://assets.openstudy.com/updates/attachments/4dfe63b10b8bbe4f12e73631-amistre64-1308517305050-matrix.html

Answer 13

Also, that's correct for the second one :)

Answer 14

it's no big deal haha

Answer 15

Ahhh ok I see sorry about that haha.

Answer 16

Alright, so go ahead and try that link out, just press 3 and 1 and that'll make your vector to fill in, then copy paste in here the last two vectors. :)

Answer 17

Alright, cool haha \[X \[\left[ \begin{array}c 0\\ 0\\ 2\\\end{array} \right]\] -> Y \[\left[ \begin{array}c 0\\ 2\\ 1\\\end{array} \right]\] + Z\[\left[ \begin{array}c 1\\ 0\\ 2\\\end{array} \right]\] \]

Answer 18

Oh oops, that looks ugly, but I think that's the right idea

Answer 19

Yeah, here I'll help clean it up: \[ W \left[ \begin{array}c 6\\ 12\\ 6\\\end{array} \right] + X \left[ \begin{array}c 0\\ 0\\ 2\\\end{array} \right]=Y\left[ \begin{array}c 0\\ 2\\ 1\\\end{array} \right]+Z\left[ \begin{array}c 1\\ 0\\ 2\\\end{array} \right]\]

Answer 20

ah yeah