Delta G and equalibrium constant question

[paulnz]

Homework Statement

The equation and data to which the question refers is in the attachment. I am just trying to do part (a) of the question at the moment:

Calculate ΔG and K, the equilibrium constant, for this reaction at 298 K.

Homework Equations

I would have thought that I would need to use the equation ΔG=-RTln K, but I am unsure how to find K, the equilibrium constant, because I am not given the amounts of the reactants or products.

The Attempt at a Solution

Perhaps there is a way to solve the problem using an equation I am not aware of? And I am not sure how to use the data given to solve the problem, if in fact it is needed for question (a) I have no idea.

 

[Chestermiller]

How is the standard free energy of formation of a species related to its standard enthalpy of formation, standard entropy of formation, and standard temperature 298? If you know the free energy of formation of each reactant and each product, how do you calculate the standard free energy change for the reaction?

If you can't answer these two questions, you need to go back to your textbook and find out.

Chet

 

[paulnz]

Thanks, that gave me the direction I needed to go in.

I believe that I use the equation:
$$\Delta _{f}G^{o}=\Delta _{r}H^{o} - T\Delta _{r}S^{o}$$

and take the reactant values from the product? ie:

$$\Delta _{r}G^{o}=\Delta _{f}G^{o}(CuO)-(\Delta _{f}G^{o}(Cu)+\frac{1}{2}\Delta _{f}G^{o}(\frac{1}{2}O_{2}))$$

 

[Chestermiller]

Thanks, that gave me the direction I needed to go in.

I believe that I use the equation:
$$\Delta _{f}G^{o}=\Delta _{r}H^{o} - T\Delta _{r}S^{o}$$

and take the reactant values from the product? ie:

$$\Delta _{r}G^{o}=\Delta _{f}G^{o}(CuO)-(\Delta _{f}G^{o}(Cu)+\frac{1}{2}\Delta _{f}G^{o}(\frac{1}{2}O_{2}))$$

You have the right idea. Just one thing: lose the Δ's in your first equation, and, on the right hand side of your second equation.

Chet

 

[DeeNos]

To calculate ΔG and K for this reaction at 298 K, you will indeed need to use the equation ΔG = -RTlnK. However, as you mentioned, you do not have the exact amounts of reactants and products, so you cannot calculate K directly. In this case, you can use the data given to you to determine K indirectly.

First, you can use the equation ΔG = ΔG° + RTlnQ, where Q is the reaction quotient. Since the reaction is at equilibrium, Q = K, and ΔG = 0. You can then rearrange the equation to solve for K:

K = e^(-ΔG°/RT)

Next, you will need to use the data given to calculate ΔG°. Since this is a standard state, you can use the standard enthalpy and entropy values for each component to calculate ΔG° using the equation ΔG° = ΔH° - TΔS°. Once you have calculated ΔG°, you can plug it into the equation above to solve for K.

I hope this helps. Let me know if you need further clarification or assistance.