Question

The standard enthalpy and standard entropy of decomposition of \( N_2O_4 \) to \( NO_2 \) are 55.0 kJ mol\(^{-1}\) and 175.0 J/mol respectively. The standard free energy change for this reaction at 25°C in J mol\(^{-1}\) is  (Nearest integer)

Hint:

Remember to always convert units when necessary. In this case, converting the enthalpy from kJ to J helped to maintain consistency in the units for entropy (J/mol).

Answer 1

The dissociation of \(N_2O_4\) into \(NO_2\) is represented by the equilibrium:

\[ N_2O_4(g) \rightleftharpoons 2NO_2(g) \]

1. Provided Thermodynamic Information:

• Standard enthalpy change: \(\Delta H^\circ = 55.0 \, \text{kJ mol}^{-1} = 55000 \, \text{J mol}^{-1}\)
• Standard entropy change: \(\Delta S^\circ = 175.0 \, \text{J mol}^{-1} \text{K}^{-1}\)
• Temperature: \(T = 25^\circ \text{C} = 298 \, \text{K}\)

2. Gibbs Free Energy Equation:

The standard Gibbs free energy change is computed using the formula:

\[ \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \]

3. Calculation:

Substituting the given values into the equation:

\[ \Delta G^\circ = 55000 \, \text{J mol}^{-1} - (298 \, \text{K}) (175.0 \, \text{J mol}^{-1} \text{K}^{-1}) \] \[ \Delta G^\circ = 55000 - 52150 = 2850 \, \text{J mol}^{-1} \]

4. Concluding Statement:

At 25°C, the standard free energy change for this reaction is \(2850 \, \text{J mol}^{-1}\).

Final Answer:

The final answer is $\boxed{2850}$.