Question

Consider the following reaction and associated equilibrium constant:
aA(g)+bB(g)⇌cC(g), Kc = 4.0

Find the equilibrium concentrations of A, B, and C for a=1, b=1, and c=2. Assume that the initial concentrations of A and B are each 1.0 M and that no product is present at the beginning of the reaction.

Answer 1

As we know equilibrium constant Kc, we can find equilibrium conc. Of A,B and C

	[A]	[B]	[C]
Initial	1.0	1.0	0
Change	- x	- x	+ 2x
Equilibrium

The minus sign comes from the fact that the A and B amounts are going to go down as the reaction proceeds.

x signifies that we know some A and B get used up, but we don't know how much. What we do know is that an EQUAL amount of each will be used up. We know this from the coefficients of the equation. For every one A used up, one B is used up also.

The positive signifies that more C is being made as the reaction proceeds on its way to equilibrium.

The two is important. C is being made twice as fast as either A or B are being used up.

In fact, always use the coefficients of the balanced equation as coefficients on the "x" terms.

In problems such as this one, never use more than one unknown. Since we have only one equation (the equilibrium expression) we cannot have two unknowns.

The equilibrium row should be easy. It is simply the initial conditions with the change applied to it:

	[A]	[B]	[C]
Initial	1.0	1.0	0
Change	- x	- x	+ 2x
Equilibrium	1.0 - x	1.0 - x	2x

Now we are are ready to put values into the equilibrium expression. For convenience, here is the equation again:

aA(g)+bB(g)⇌cC(g)

The equilibrium expression is:

K_c = [C]² / ([A] [B])

Plugging values into the expression gives:

4.0 = (2x)² / ((1.0 - x) (1.0 - x))

Two points need to be made before going on:

1) Where did the 4.0 value come from? It was given in the problem.
2) Make sure to write (2x)² and not 2x². As you well know, they are different. This mistake happens a LOT!!

Both sides are perfect squares (done so on purpose), so we square root both sides to get:

2.00 = (2x) / (1.0 - x)

From there, the solution should be easy and results in x = 0.5 M.

This is not the end of the solution since the question asked for the equilibrium concentrations, so:

[A] = 1.0 - 0.5 = 0.5 M
[B] = 1.0 - 0.5 = 0.5 M
[C] = 2 (0.5) = 1 M

You can check for correctness by plugging back into the equilibrium expression:

x = (1)² / ((0.5) (0.5))

Since x = 4.0. we know that the problem was correctly solved.