Unit 7: Topic 4 - Calculating the Equilibrium Constant

Question 1

What are some things to be careful about when calculating the equilibrium constant?

Answer 1

Recall that for a reaction aA + bB <–> cC + dD, Kc = ([C]^c * [D]^d) / ([A]^a * [B]^b) and Kp =((P_C)^c * (P_D)^d ) / ( (P_A) ^ a * (P_B)^b )
- The most important aspect of these formulas is that the concentrations and partial pressures that you plug in have to be at equilibrium. Plugging in the concentrations or partial pressures at any other point will only give you the reaction quotient (which would only provide the relative amounts of products and reactants present in the reaction at a particular time), and not the equilibrium constant.
- Make sure the values you plug in are in the right units. For example, if you were given the number of moles for each substance and asked to calculate Kc, you would first want to convert it into units of molarity(mol / L) before performing the calculation.

Question 2

2CO(g) <–> CO2(g) + C(s)

The reaction above takes place at 300K and is allowed to reach equilibrium. It has been experimentally determined that the partial pressures of CO2 and CO are 2.50 atm and 0.35 atm, respectively.
1. Write the equilibrium expression, Kp, for this reaction.
2. Calculate the value of Kp at 300K.

Answer 2

1. K = (P_CO2) / (P_CO) ^2
2. P_CO2 = 2.50 atm, and P_CO = 0.35 atm
   Kp = (2.50) / (0.35) ^2 = 20.4

Remember that the equilibrium constant is constant given constant temperature, and it is an unitless quantity.

Question 3

Consider the following reaction CO2(g) + H2(g) <–> CO(g) + H2O(g) at 300K.
If it has been discovered that 0.1908 moles of CO2, 0.0908 moles of H2, 0.0092 moles of CO, and 0.0092 moles of H2O vapor were present in a 2.0 L reaction vessel at equilibrium, calculate the equilibrium constant, Kc, for this system at the aforementioned temperature(300K).

Answer 3

First step: Write the equilibrium expression for this reaction
Kc = ([CO] * [H2O]) / ([CO2] * [H2])
Second step: Calculate the equilibrium concentrations, in molarity, for each substance.
CO: 0.0092mol / 2L = 0.0046M
H2O: 0.0092mol / 2L = 0.0046M
CO2: 0.1908mol /2L = 0.0954M
H2: 0.0908mol / 2L = 0.0454M

Finally, we can now plug these concentrations in the formula to find that:
Kc = ([CO] * [H2O]) / ([CO2] * [H2]) = [0.0046][0.0046] / [0.0954][0.0454] = 4.9 * 10^(-3)