Question:
For a certain decomposition
\[
X_2 Y_4 (g) \rightleftharpoons 2 XY_2 (g)
\]
Degree of dissociation of \( X_2 Y_4 \) is 75% at 1 bar and 600K. Find \( \Delta G^\circ \) of reaction in kJ/mol\(^{-1}\).
For a certain decomposition
\[ X_2 Y_4 (g) \rightleftharpoons 2 XY_2 (g) \] Degree of dissociation of \( X_2 Y_4 \) is 75% at 1 bar and 600K. Find \( \Delta G^\circ \) of reaction in kJ/mol\(^{-1}\).
\[ X_2 Y_4 (g) \rightleftharpoons 2 XY_2 (g) \] Degree of dissociation of \( X_2 Y_4 \) is 75% at 1 bar and 600K. Find \( \Delta G^\circ \) of reaction in kJ/mol\(^{-1}\).
Show Hint
When calculating \( \Delta G^\circ \) for reactions involving dissociation, first determine the equilibrium constant \( K \) using the degree of dissociation and then apply the formula \( \Delta G^\circ = -RT \ln K \).
Updated On: Apr 7, 2026
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Verified By Collegedunia
Correct Answer: 8.169
Solution and Explanation
Step 1: Expression for \( k_p \).
The expression for \( k_p \) is given as:
\[ k_p = \frac{4P_0 \alpha^2}{1 - \alpha^2} = \frac{36}{7} \]
Step 2: Formula for \( \Delta G^\circ \).
The formula for \( \Delta G^\circ \) is:
\[ \Delta G^\circ = -RT \ln k_p \]
Step 3: Substituting the value of \( k_p \).
Substituting the value of \( k_p = \frac{36}{7} \) into the equation:
\[ |\Delta G^\circ| = 8.314 \times 600 \ln \left( \frac{36}{7} \right) \]
Step 4: Calculate the value.
Now, calculating the natural logarithm:
\[ \ln \left( \frac{36}{7} \right) = \ln(5.1429) = 1.636 \]
Step 5: Final calculation.
Now, substituting this value back into the equation:
\[ |\Delta G^\circ| = 8.314 \times 600 \times 1.636 = 8169.5 \, \text{J mol}^{-1} \]
Step 6: Convert to kJ/mol.
Since the value is in J/mol, we convert it to kJ/mol:
\[ = 8.169 \, \text{kJ/mol} \] Final Answer: 8.169 kJ/mol
The expression for \( k_p \) is given as:
\[ k_p = \frac{4P_0 \alpha^2}{1 - \alpha^2} = \frac{36}{7} \]
Step 2: Formula for \( \Delta G^\circ \).
The formula for \( \Delta G^\circ \) is:
\[ \Delta G^\circ = -RT \ln k_p \]
Step 3: Substituting the value of \( k_p \).
Substituting the value of \( k_p = \frac{36}{7} \) into the equation:
\[ |\Delta G^\circ| = 8.314 \times 600 \ln \left( \frac{36}{7} \right) \]
Step 4: Calculate the value.
Now, calculating the natural logarithm:
\[ \ln \left( \frac{36}{7} \right) = \ln(5.1429) = 1.636 \]
Step 5: Final calculation.
Now, substituting this value back into the equation:
\[ |\Delta G^\circ| = 8.314 \times 600 \times 1.636 = 8169.5 \, \text{J mol}^{-1} \]
Step 6: Convert to kJ/mol.
Since the value is in J/mol, we convert it to kJ/mol:
\[ = 8.169 \, \text{kJ/mol} \] Final Answer: 8.169 kJ/mol
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