For the decomposition of A to B and C, A (s) ⇌B (g) + C (g) how will the reaction respond to each of the following changes at equilibrium?

a. double the concentrations of both products and then double the container volume

b. double the container volume

c. add more A

d. double the concentration of B and halve the concentration of C

e. double the concentrations of both products

f. double the concentrations of both products and then quadruple the container volume

a. No change.

b. The equilibrium will shift to the right.

c. No change

d. No change

e. The equilibrium will shift to the left

f. The equilibrium will shift to the right

Explanation:

We are going to solve this question by making use of Le Chatelier's principle which states that any change in a system at equilibrium will react in such a way as to attain qeuilibrium again by changing the equilibrium concentrations attaining Keq again.

The equilibrium constant for A (s) ⇌B (g) + C (g)

Keq = Kp = pB x pC

where K is the equilibrium constant (Kp in this case) and pB and pC are the partial pressures of the gases. (Note A is not in the expression since it is a solid)

We also use Q which has the same form as Kp but denotes the system is not at equilibrium:

Q = p'B x p'C where pB' and pC' are the pressures not at equilibrium.

a. double the concentrations of Q which has the same form as Kp but : products and then double the container volume

Effectively we have not change the equilibrium pressures since we know pressure is inversely proportional to volume.

Initially the system will decrease the partial pressures of B and C by a half:

Q = pB'x pC' (where pB'and pC'are the changed pressures)

Q = (2 pB) x (2 pC) = 4 (pB x PC) = 4 Kp ⇒ Kp = Q/4

But then when we double the volume, the sistem will react to double the pressures of A and B. Therefore there is no change.

b. double the container volume

From part a we know the system will double the pressures of B and C by shifting to the right (product) side since the change reduced the pressures by a half:

Q = pB'x pC' = (1/2 pB) x (1/2 pC) = 1/4 pB x pC = 1/4 Kp

c. add more A

There is no change in the partial pressures of B and C since the solid A does not influence the value of kp

d. doubling the concentration of B and halve the concentration of C

Doubling the concentrantion doubles the pressure which we can deduce from pV = n RT = c RT (c = n/V), and likewise halving the concentration halves the pressure. Thus, since we are doubling the concentration of B and halving that of C, there is no net change in the new equilibrium:

Q = pB'x pC' = (2 pB) x (1/2 pC) = K

e. double the concentrations of both products

We learned that doubling the concentration doubles the pressure so:

Q = pB'x pC' = (2 pB) x (2 pC) = 4 Kp

Therefore, the system wil reduce by a half the pressures of B and C by producing more solid A to reach equilibrium again shifting it to the left.

f. double the concentrations of both products and then quadruple the container volume

We saw from part e that doubling the concentration doubles the pressures, but here afterward we are going to quadruple the container volume thus reducing the pressure by a fourth:

Q = pB'x pC' = (2 pB / 4) x (2 pC / 4) = 4/16 Kp = 1/4 Kp

So the system will increase the partial pressures of B and C by a factor of four, that is it will double the partial pressures of B and C shifting the equilibrium to the right.

If you do not see it think that double the concentration and then quadrupling the volume is the same net effect as halving the volume.