### Gibbs – Helmholtz EquationThe Gibbs – Helmholtz equation is expressed as:\[\left( \frac{\partial \left( \frac{\Delta G}{T} \right)}{\partial T} \right)_P = -\frac{\Delta H}{T^2}\]**Tasks:**a) Integrate this equation between \( T_1 \) and \( T_2 \) to obtain:\[\frac{\Delta G(T_2)}{T_2} = \frac{\Delta G(T_1)}{T_1} + \Delta H \left( \frac{1}{T_2} - \frac{1}{T_1} \right)\]b) Determine \( \Delta_r G^\circ \) and \( \Delta_r H^\circ \) for the reaction:\[ N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)\]Given:- \( \Delta_f H^\circ (NH_3) = -80.3 \, \text{kJ} \, \text{mol}^{-1} \)- \( \Delta_f G^\circ (NH_3) = -26.5 \, \text{kJ} \, \text{mol}^{-1} \)c) Calculate \( \Delta_r G \) at 500 K and 1000 K, assuming \( \Delta H \) is independent of \( T \).

In this question Gibbs-Helmholtz equation is given and we have to integrate this equation between T1 and T2 to obtain the following equation,

Answered: The Gibbs – Helmholtz equation is - T…

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The Gibbs – Helmholtz equation is - T ΔΗ ƏT T2 P a) Integrate this equation between T, and T2 and obtain AG(T2) AG(T,) + ΔΗ 1 T2 T1 T1

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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Question

### Gibbs – Helmholtz Equation

The Gibbs – Helmholtz equation is expressed as:

\[
\left( \frac{\partial \left( \frac{\Delta G}{T} \right)}{\partial T} \right)_P = -\frac{\Delta H}{T^2}
\]

**Tasks:**

a) Integrate this equation between \( T_1 \) and \( T_2 \) to obtain:

\[
\frac{\Delta G(T_2)}{T_2} = \frac{\Delta G(T_1)}{T_1} + \Delta H \left( \frac{1}{T_2} - \frac{1}{T_1} \right)
\]

b) Determine \( \Delta_r G^\circ \) and \( \Delta_r H^\circ \) for the reaction:

\[
N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)
\]

Given:
- \( \Delta_f H^\circ (NH_3) = -80.3 \, \text{kJ} \, \text{mol}^{-1} \)
- \( \Delta_f G^\circ (NH_3) = -26.5 \, \text{kJ} \, \text{mol}^{-1} \)

c) Calculate \( \Delta_r G \) at 500 K and 1000 K, assuming \( \Delta H \) is independent of \( T \).

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