Equilibrium constant from thermodynamic values

[ultimateguy]

Homework Statement

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

Homework Equations

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

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.

 

[nate808]

Thank you for your post regarding the calculation of equilibrium constant K for the given reaction at 32 degrees C. I understand that you have attempted to solve the problem using two different methods, but have obtained incorrect answers. I would like to offer some guidance to help you arrive at the correct solution.

Firstly, it is important to note that the equilibrium constant K is a dimensionless quantity, meaning it has no units. Therefore, it cannot be calculated using values with units such as Joules or Kelvin. This is why your first attempt, which involved calculating the change in Gibbs energy using energy of formation values with units, did not give you the correct answer.

Secondly, in order to use the equations you have listed, it is necessary to have the values of standard enthalpy change (\Delta H^0) and standard entropy change (\Delta S^0) for the reaction. However, the given value of 68.6 kJ is not the standard enthalpy change, but rather the enthalpy change at 32 degrees C. This means that the values of \Delta H^0 and \Delta S^0 need to be adjusted in order to be used in the equations.

Here is a possible approach to solving this problem:

1. Calculate the standard enthalpy change \Delta H^0 at 25 degrees C using the given value of 68.6 kJ and the temperature dependence of enthalpy (heat capacity) for each compound involved in the reaction. This will give you the value of \Delta H^0 at 25 degrees C.

2. Use the standard enthalpy change at 25 degrees C to calculate the standard Gibbs energy change \Delta G^0 at 25 degrees C using the equation \Delta G^0 = \Delta H^0 - T\Delta S^0. Note that the standard entropy change \Delta S^0 does not change with temperature.

3. Use the value of \Delta G^0 at 25 degrees C to calculate the equilibrium constant K using the equation \Delta G^0 = -RT\ln{K_p}. Make sure to convert the given pressure value into units of bar before using it in the equation.

I hope this helps guide you towards the correct solution. If you have any further questions, please don't hesitate to ask. Good luck with your calculations!

 

[Blueshift5]

Hello, it seems like you are on the right track with using the thermodynamic equations to calculate the equilibrium constant K. However, there are a few errors in your calculations that may be leading to the wrong answers.

First, when calculating the change in Gibbs energy, you should be using the energy of formation for PCl5, PCl3, and Cl2, not just the energy of formation for PCl3 and Cl2. This will give you a more accurate value for the change in Gibbs energy.

Second, when using the first equation to calculate Kp, you should be using the gas constant R in units of J/mol*K, not kJ/mol*K. This will give you a more accurate value for Kp.

Finally, when using the second equation to calculate the change in Gibbs energy, you should be using the temperature in units of Kelvin (K), not degrees Celsius (°C). This will give you a more accurate value for the change in Gibbs energy.

With these corrections, your final answers should be:

a) 1.52 x 10^-8
b) 2.82 x 10^10
c) 1.09 x 10^-16
d) 2.03 x 10^10

I hope this helps clarify the process for calculating the equilibrium constant K using thermodynamic values. Let me know if you have any further questions. Good luck!