Using data from Appendix C, write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free-energy change for these reactions at 298 K: (a) NaHCO₃(s) ⇌ NaOH(s) + CO₂(g)

Verified step by step guidance

1. Write the equilibrium constant expression for the reaction. For the reaction NaHCO3(s) ⇌ NaOH(s) + CO2(g), the equilibrium constant expression (K) is defined by the concentrations of the products raised to their stoichiometric coefficients divided by the concentrations of the reactants raised to their stoichiometric coefficients. Since NaHCO3(s) and NaOH(s) are solids, their concentrations remain constant and do not appear in the expression. Thus, K = [CO2].
2. Look up the standard Gibbs free energy of formation (ΔG°f) for each species involved in the reaction at 298 K from Appendix C. You will need the values for NaHCO3(s), NaOH(s), and CO2(g).
3. Calculate the standard Gibbs free energy change for the reaction (ΔG°rxn) using the formula ΔG°rxn = ΣΔG°f(products) - ΣΔG°f(reactants). Here, you will substitute the ΔG°f values of NaOH(s) and CO2(g) as products and NaHCO3(s) as the reactant.
4. Use the relationship between the equilibrium constant and the Gibbs free energy change to find the equilibrium constant. The formula to use is ΔG°rxn = -RT ln(K), where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K). Solve for K by rearranging the formula to K = e^(-ΔG°rxn / (RT)).
5. Substitute the values of ΔG°rxn, R, and T into the formula to calculate the value of the equilibrium constant, K.

Key Concepts

Equilibrium Constant Expression

The equilibrium constant expression (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It is derived from the balanced chemical equation, where the concentrations of gaseous and aqueous species are included, while solids and liquids are omitted. For the reaction NaHCO3(s) ⇌ NaOH(s) + CO2(g), K would be expressed in terms of the partial pressure of CO2 since NaHCO3 and NaOH are solids.

Calculating Equilibrium Constant

To calculate the equilibrium constant, one must know the concentrations or partial pressures of the reactants and products at equilibrium. For the reaction in question, once the equilibrium concentrations are determined, K can be calculated using the formula K = [products]/[reactants]. This value provides insight into the extent of the reaction and its favorability under the given conditions.

Gibbs Free Energy Change

Gibbs free energy change (ΔG) indicates the spontaneity of a reaction at constant temperature and pressure. It is related to the equilibrium constant by the equation ΔG = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin. A negative ΔG suggests that the reaction is spontaneous, while a positive ΔG indicates non-spontaneity. This relationship helps in understanding the thermodynamic favorability of the reaction at 298 K.