Agaseous reaction occurs and comes to equilibrium:
2hi(g) + cl2(g) > 2hcl(g) + i2(g) + energy
which of the following changes to the system will serve to increase the nuber of moles of i2 present at equilibrium?
a.) increasing the volume at constant temperature
b.) decreasing the volume at a constant temperature
c.) increasing the temperature at a constant volume
d.) decreasing the temperature at constant volume

d) Decreasing the temperature at constant volume

Explanation:

if we assume ideal gas behaviour, since the concentration of the gas is proportional to its pressure at constant temperature

(from the ideal gas law PV =nRT or P= CRT), the equilibrium constant in terms of pressure will be

Kp = (p² HCl *p² I2)/(p² HI *p² CL2)

from Dalton's law : pi = P*xi

Kp = (P²*x² HCl *P* x I2)/(P*x HI *P²x² CL2) =  (x² HCl * x I2)/(x HI *x² CL2)

since Kp does not change because the T is constant and it does not depend on pressure → the equilibrium will not change due to changes in pressure caused by reductions or increases in volume at constant pressure and composition

also since the reaction is exothermic → an increase in temperature will displace the equilibrium towards the reactants , and thus decreasing the moles of I2 at equilibrium

this can be seen from van't hoff equation :

d ln (K) /dT= ΔH/RT² , since ΔH>0 → K diminishes with increase in temperature

on the other hand, a decrease in temperature will displace the equilibrium towards the products , and thus increasing the moles of I2 at equilibrium