Using the standard reduction potentials listed in Appendix E, calculate the equilibrium constant for each of the following reactions at 298 K: (a) Cu(s) + 2 Ag+(aq) → Cu2+(aq) + 2 Ag(s) (b) 3 Ce4+(aq) + Bi(s) + H2O(l) → 3 Ce3+(aq) + BiO+(aq) + 2 H+(aq) (c) N2H5+(aq) + 4 Fe(CN)6^3- (aq) → N2(g) + 5 H+(aq) + 4 Fe(CN)6^4-(aq)

Verified step by step guidance

1. Step 1: Identify the half-reactions for each redox reaction and write their standard reduction potentials (E°) from Appendix E.
2. Step 2: For each reaction, determine the oxidation and reduction half-reactions and calculate the standard cell potential (E°cell) using the formula: E°cell = E°(reduction) - E°(oxidation).
3. Step 3: Use the Nernst equation to relate the standard cell potential to the equilibrium constant (K) at 298 K: E°cell = (RT/nF) * ln(K), where R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is Faraday's constant (96485 C/mol).
4. Step 4: Rearrange the Nernst equation to solve for the equilibrium constant (K): K = exp((nFE°cell)/(RT)).
5. Step 5: Substitute the values for n, F, R, T, and E°cell into the equation to calculate the equilibrium constant (K) for each reaction.

Key Concepts

Standard Reduction Potentials

Standard reduction potentials are measured voltages that indicate the tendency of a chemical species to gain electrons and be reduced. Each half-reaction has a specific potential, and these values are typically listed in a standard table. The more positive the potential, the greater the species' ability to be reduced. These values are crucial for calculating the overall cell potential and determining the direction of electron flow in redox reactions.

Nernst Equation

The Nernst equation relates the cell potential of an electrochemical reaction to the concentrations of the reactants and products at non-standard conditions. It is expressed as E = E° - (RT/nF) ln(Q), where E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient. This equation is essential for calculating the equilibrium constant from the standard potentials.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is derived from the relationship between the standard cell potential and the Gibbs free energy change. A larger K value indicates a greater tendency for the reaction to favor products, while a smaller K suggests a preference for reactants. Understanding K is vital for predicting the extent of reactions and their favorability.