Week 1 Problem 10

[Karla Baltierra Zamora 3C]

Hello,
I was wondering how you would set up the equation in the form of ax^2 + bx + c = 0 to solve for x. Specifically, what would you add to get "bx" and "c".

[Lindsey_Tran_3I]

I'm not sure what numbers you have for this problem since Achieve changes it up for every student, but this is just the general way to get to the point of
ax^2 + bx +c = 0:

1. Set up and fill out your (R)ICE table.
2. Plug in your "E" values into the formula for the equilibrium constant: K = [P]/[R].
3. The problem should have provided you with a K, so set K = [P]/[R] equal to the equilibrium constant they give you.
4. From here, you should be able to rearrange this equation into the form of ax^2 + bx +c = 0 by multiplying the denominator on both sides of the equation and then moving all values onto one side (by adding and subtracting) to make the other side equal to 0.
5. Once this is in the form of ax^2 + bx +c = 0, you can use the quadratic formula to find x, and then you can use x to find the concentration of each compound.

[joselle barnoya 1k]

Also of note-- there are different ways to end up getting a quadratic equation when solving for x. It partially depends on the combination of stoichiometric coefficients on each term in the reaction (this will cause you to raise that concentration to the coefficient-- for example, if the ice table gave you (0.5-x) for that term and it had a 2 in front of it in the reaction, for k you would put (0.5-x)², getting you than ax² term). Additionally, since in the equation for k you are multiplying reactants and multiplying products, the more of either you have, the more x terms you may end up multiplying, leading to that ax² term. If the reaction has two products each being (0.5-x) on the ice table, though their stoichiometric coefficients in the reaction may be one, since they are both products you have to multiply them by each other, leading to that ax² term again. Sorry if this is confusing sounding at all!!