Use the data in Appendix B to calculate ∆G for the decom-position of nitrosyl chloride at 25 °C when the partial pressures are 2.00 atm of NOCl, 1.00 * 10^-3 atm of NO, and 1.00 * 10^-3 atm of Cl2: Is the reaction spontaneous in the forward or the reverse direction under these conditions?

Verified step by step guidance

1. Identify the balanced chemical equation for the decomposition of nitrosyl chloride: 2 NOCl(g) \rightarrow 2 NO(g) + Cl_2(g).
2. Use the standard Gibbs free energy of formation values (\( \Delta G_f^\circ \)) from Appendix B to calculate the standard Gibbs free energy change (\( \Delta G^\circ \)) for the reaction: \( \Delta G^\circ = \sum \Delta G_f^\circ (\text{products}) - \sum \Delta G_f^\circ (\text{reactants}) \).
3. Calculate the reaction quotient \( Q \) using the given partial pressures: \( Q = \frac{(P_{NO})^2 (P_{Cl_2})}{(P_{NOCl})^2} \).
4. Apply the equation \( \Delta G = \Delta G^\circ + RT \ln Q \) to find the Gibbs free energy change under the given conditions, where \( R \) is the gas constant (8.314 J/mol·K) and \( T \) is the temperature in Kelvin.
5. Determine the spontaneity of the reaction by analyzing the sign of \( \Delta G \): if \( \Delta G < 0 \), the reaction is spontaneous in the forward direction; if \( \Delta G > 0 \), it is spontaneous in the reverse direction.

Key Concepts

Gibbs Free Energy (∆G)

Gibbs Free Energy (∆G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is used to predict the spontaneity of a reaction: if ∆G is negative, the reaction is spontaneous in the forward direction; if positive, it is spontaneous in the reverse direction.

Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is related to Gibbs Free Energy by the equation ∆G = ∆G° + RT ln(Q), where Q is the reaction quotient. Understanding K helps determine the direction of spontaneity based on the current conditions.

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative amounts of products and reactants present in a reaction at any point in time, calculated using the same expression as K but with current concentrations or partial pressures. Comparing Q to K allows us to predict the direction in which a reaction will proceed to reach equilibrium, indicating whether the forward or reverse reaction is favored.