Estimate the standard reaction Gibbs energy of the following reaction:

In summary, the task is to estimate the standard reaction Gibbs energy of N2 + 3H2 -> 2NH3 at 100K and 1000K using the equations ΔS(T2) = S°(T1) + ∫ nCp dT/T and ΔG = ΔH - TΔS. The given data for ΔfHm° and ΔSm° needs to be used. The calculations involve finding ΔS at 100K for NH3, H2, and N2 separately, and then using ΔrG = ΔprodG - ΔreacG. The equation H(T2) = H°(T1) + ∫ nCp d
  • #1
Jormungandr
30
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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 Cp 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 Cp 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 ΔrG = ΔprodG ‒ ΔreacG. I had to obtain values for Cp, ΔfHm°, and ΔSm° from a table in the back of my textbook.
Here's my math:

ΔrH = 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!
 
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  • #2
You could also use H(T2) = H°(T1) + ∫ n Cp dT.
 
  • #3
DrDu said:
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.
 
  • #4
Jormungandr said:
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.
 
  • #5
The easiest way to do this problem is to use the equation:

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

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
 

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

1. What is the standard reaction Gibbs energy?

The standard reaction Gibbs energy is a measure of the change in free energy that occurs during a chemical reaction under standard conditions (25°C, 1 atm pressure, and 1 M concentrations of all reactants and products). It represents the maximum amount of useful work that can be obtained from a reaction.

2. How is the standard reaction Gibbs energy calculated?

The standard reaction Gibbs energy is calculated using the equation ΔG° = ΣΔG°f(products) - ΣΔG°f(reactants), where ΔG°f represents the standard molar Gibbs energy of formation for each species involved in the reaction. This value can be found in thermodynamic tables or calculated using thermodynamic data for each individual species.

3. What are the units of standard reaction Gibbs energy?

The units of standard reaction Gibbs energy are kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).

4. How does the standard reaction Gibbs energy relate to equilibrium?

The standard reaction Gibbs energy is directly related to the equilibrium constant (K) of a reaction. The equilibrium constant can be calculated using the equation K = e^(-ΔG°/RT), where R is the gas constant and T is the temperature in Kelvin. A negative value for ΔG° indicates a spontaneous reaction and a positive value indicates a non-spontaneous reaction.

5. How does the standard reaction Gibbs energy change with temperature?

The standard reaction Gibbs energy is temperature-dependent. As the temperature increases, the value of ΔG° becomes more negative for exothermic reactions and more positive for endothermic reactions. This is because the change in entropy (ΔS°) also plays a role in the calculation of ΔG°, and entropy generally increases with temperature.

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