The value of K_a for nitrous acid (HNO₂) at 25 °C is given in Appendix D. (b) By using the value of Ka, calculate ΔG° for the dissociation of nitrous acid in aqueous solution.

Verified step by step guidance

1. Identify the relationship between the equilibrium constant (K_a) and the standard Gibbs free energy change (ΔG°) using the equation: ΔG° = -RT ln(K_a), where R is the universal gas constant and T is the temperature in Kelvin.
2. Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius (25 °C).
3. Look up the value of the gas constant R, which is 8.314 J/(mol·K).
4. Substitute the values of R, T, and K_a into the equation ΔG° = -RT ln(K_a) to calculate ΔG°.
5. Ensure that the units are consistent, particularly that the temperature is in Kelvin and the gas constant is in J/(mol·K), to obtain ΔG° in joules per mole.

Key Concepts

Acid Dissociation Constant (K_a)

The acid dissociation constant (K_a) quantifies the strength of an acid in solution. It is defined as the equilibrium constant for the dissociation of an acid into its conjugate base and a proton. A higher K_a value indicates a stronger acid, as it dissociates more completely in water.

Gibbs Free Energy (ΔG°)

Gibbs free energy (ΔG°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic process at constant temperature and pressure. For a reaction, a negative ΔG° indicates that the reaction is spontaneous, while a positive ΔG° suggests non-spontaneity. The relationship between ΔG° and K_a can be expressed using the equation ΔG° = -RT ln(K_a), where R is the gas constant and T is the temperature in Kelvin.

Equilibrium and Reaction Quotient

Equilibrium in a chemical reaction occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The reaction quotient (Q) compares the current concentrations of products and reactants to those at equilibrium. For weak acids like nitrous acid, understanding how to calculate Q and relate it to K_a is essential for determining the direction of the reaction and calculating ΔG°.