Question

For the reaction, \(N_{2}O_{4} \rightleftharpoons 2NO_{2}\) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is 5.40 kJ \(mol^{-1}\). 
B. As \(\Delta G\) in graph is positive, \(N_{2}O_{4}\) will not dissociate into \(NO_{2}\) at all. 
C. Reverse reaction will go to completion. 
D. When 1 mole of \(N_{2}O_{4}\) changes into equilibrium mixture, value of \(\Delta G = -0.84 \text{ kJ mol}^{-1}\). 
E. When 2 mole of \(NO_{2}\) changes into equilibrium mixture, \(\Delta G\) for equilibrium mixture is \(-6.24 \text{ kJ mol}^{-1}\). 

Choose the correct answer from the following.

• A. B and C only
• B. A and D only
• C. D and E only
• D. C and E only

Hint:

\(\Delta G^\circ\) determines the position of equilibrium (Ratio of Products/Reactants at minimum G), but \(\Delta G\) determines the spontaneity of moving towards equilibrium from a specific state.

Answer 1

The Correct Option is B

Step 1: Analysis of the Graph and Given Data

The graph represents Gibbs free energy (\(G\)) versus the fraction of \(N_2O_4\) dissociated.

• Point A (pure \(N_2O_4\)) corresponds to extent of dissociation \(\xi = 0\).

• Point B (pure \(2NO_2\)) corresponds to \(\xi = 1\).

• The minimum of the curve represents the equilibrium composition.

From the graph:

• Drop in Gibbs free energy from pure reactants to equilibrium: \(-0.84 \, \text{kJ mol}^{-1}\)

• Drop in Gibbs free energy from pure products to equilibrium: \(-6.24 \, \text{kJ mol}^{-1}\)

Step 2: Evaluation of Statement A

Standard Gibbs free energy change is defined as: \[ \Delta G^\circ = G^\circ(\text{products}) - G^\circ(\text{reactants}) \] Using the values obtained from the graph:

\[ G_{\text{products}} = G_{eq} + 6.24 \] \[ G_{\text{reactants}} = G_{eq} + 0.84 \] Therefore, \[ \Delta G^\circ = (G_{eq} + 6.24) - (G_{eq} + 0.84) \] \[ \Delta G^\circ = +5.40 \, \text{kJ mol}^{-1} \] Hence, Statement A is correct.

Step 3: Evaluation of Other Statements

• Statements B and C:
Since equilibrium occurs at an intermediate composition corresponding to minimum Gibbs free energy, the reaction neither goes to completion nor remains unreacted. Hence, statements B and C are incorrect.

• Statement D:
Free energy change when starting from 1 mole of reactants to reach equilibrium is \(-0.84 \, \text{kJ}\). Hence, statement D is correct.

• Statement E:
Free energy change when starting from products to reach equilibrium is \(-6.24 \, \text{kJ}\). Hence, statement E is also correct.

Step 4: Selection of Correct Option

Since Statements A and D are correct and correspond to Option 2, the correct answer is:

Final Answer: Option 2