Estimate the standard reaction Gibbs energy of the following reaction:

[Jormungandr]

Homework Statement

"Estimate the standard reaction Gibbs energy of the following reaction:

N₂ + 3 H₂ ‒‒> 2 NH₃

at 100K and at 1000K."

Homework Equations

ΔS(T2) = S°(T1) + ∫ n C_p dT/T
ΔG = ΔH ‒ TΔS

Given data: http://imgur.com/MBakUEB (may need to right-click and select "Open in new tab")

The Attempt at a Solution

So, I realize that we likely have to use the formula ΔS(T2) = S°(T1) + ∫ n C_p dT/T in our calculations to find the ΔS at the different temperatures. What I did was I calculated the ΔS at 100K for NH3, H2, and N2 separately, then did Δ_rG = Δ_prodG ‒ Δ_reacG. I had to obtain values for C_p, Δ_fH_m°, and ΔS_m° from a table in the back of my textbook.
Here's my math:

Δ_rH = 2 mol × ‒46.11 kJ/mol, because it is 0 for hydrogen and nitrogen.

http://imgur.com/TV8cfmB

Forgive the non-matching formatting. I found it was easier to go into Word and use its equation editor than to try and learn LaTEX, as time is somewhat of the essence here.

So is my work for the 100K case correct? I just realized that I may have needed to also convert my H value from the 273K to 100K, because the book gave standard enthalpies of reaction, and not that at 100K... Would I use the Kirchoff equation for that, then?

Thanks for the help!

 

[DrDu]

You could also use H(T2) = H°(T1) + ∫ n Cp dT.

 

[Jormungandr]

You could also use H(T2) = H°(T1) + ∫ n Cp dT.

That was the equation that I ended up using when I revised my answer. In the end, I got that at 100 K, ΔG = –68.6 kJ. Our professor also had us approximate the value using the Gibbs-Helmholtz equation, which gave me –72.6 kJ. It makes sense for the two values to be off, because I know the Gibbs-Helmholtz equation assumes that the process is isenthalpic.

 

[DrDu]

T It makes sense for the two values to be off, because I know the Gibbs-Helmholtz equation assumes that the process is isenthalpic.

No, if it were isenthalpic, Delta G won't depend on T at all. It is rather that you probably neglected the T dependence of Delta H in solving the Gibbs-Helmholtz equation. From your calculations you see that this is usually a good approximation.

 

[Chestermiller]

The easiest way to do this problem is to use the equation:

$$\frac{d(ΔG^0/RT)}{dT}=-\frac{ΔH^0}{RT^2}$$

This way, you don't have to mess with the entropy changes with temperature, and only need to take into account the changes in enthalpies with temperature.

Chet