The value of K_a for nitrous acid (HNO₂) at 25 °C is given in Appendix D. (d) What is the value of ΔG when [H⁺] = 5.0⨉10^-2 M, [NO₂^-] = 6.0⨉10^-4 M, and [HNO₂] = 0.20 M?

Verified step by step guidance

1. Identify the reaction for the dissociation of nitrous acid: \( \text{HNO}_2 \rightleftharpoons \text{H}^+ + \text{NO}_2^- \).
2. Write the expression for the reaction quotient \( Q \): \( Q = \frac{[\text{H}^+][\text{NO}_2^-]}{[\text{HNO}_2]} \).
3. Substitute the given concentrations into the expression for \( Q \): \( Q = \frac{(5.0 \times 10^{-2})(6.0 \times 10^{-4})}{0.20} \).
4. Use the relationship between \( \Delta G \), \( \Delta G^\circ \), and \( Q \): \( \Delta G = \Delta G^\circ + RT \ln Q \).
5. Calculate \( \Delta G^\circ \) using the formula \( \Delta G^\circ = -RT \ln K_a \), where \( K_a \) is the acid dissociation constant for nitrous acid.

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium involves the balance between an acid and its conjugate base in solution. For weak acids like nitrous acid (HNO2), this equilibrium can be described by the dissociation constant (Ka), which quantifies the extent of ionization. Understanding this concept is crucial for calculating concentrations of species in solution and predicting the behavior of acids in various conditions.

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) 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; a negative ΔG indicates a spontaneous process. In the context of acid-base reactions, ΔG can be calculated using concentrations of reactants and products, reflecting the system's favorability.

Reaction Quotient (Q)

The reaction quotient (Q) is a ratio that compares the concentrations of products to reactants at any point in a reaction, not necessarily at equilibrium. It is calculated using the same expression as the equilibrium constant (K) but with current concentrations. By comparing Q to K, one can determine the direction in which a reaction will proceed to reach equilibrium, which is essential for calculating ΔG in the given scenario.