# Equilibrium constant from thermodynamic values

1. Mar 23, 2007

### ultimateguy

1. The problem statement, all variables and given/known data
Using information from tables, calculate the equilibrium constant K of the following reaction at 32 degrees C.

$$PCl_5 \rightarrow PCl_3 + Cl_2$$
$$\Delta H^0_{rxn} = 68.6kJ$$

a) $$4.62 \times 10^{-3}$$atm
b) 216 atm
c) $$7.81 \times 10^{-11}$$atm
d) 163 atm

2. Relevant equations

$$\Delta G^0 = -RT\ln{K_p}$$
$$\Delta G^0 = \Delta H^0 - T\Delta S^0$$

3. The attempt at a solution

First attempt:

Calculated the change in Gibbs energy using the energy of formation of the compounds, then plugged into the first equation to get Kp. Wrong answer.

$$\Delta G^0 = 0 + (-267.8\frac{kJ}{mol}) - (-305\frac{kJ}{mol}) = 37.2kJ$$
$$K_p = e^{\frac{-37200J}{8.3145(305K)}} = 4.289 \times 10^{-7}$$

Second attempt:

Calculated the change in entropy using values from tables, plugged into 2nd equation to get change in Gibbs, then plugged into first equation to get Kp. Wrong answer.

$$\Delta S^0 = 223.08\frac{J}{Kmol} + 311.78\frac{J}{Kmol} - 364.58\frac{J}{Kmol} = 170.28\frac{J}{K}$$
$$\Delta G^0 = 68600J - (305K)(170.28\frac{J}{K}) = 16664.6J$$
$$\Delta K_p = 1.4 \times 10^{-3}$$

As usual, I'm going nuts. Any help appreciated.

Last edited: Mar 23, 2007