Final answer:
To find E°, ΔG°, and K for the overall reaction, combine the half-reactions and use the standard reduction potentials to calculate the overall E°. Then, use the number of moles of electrons transferred and the Faraday constant to find ΔG°, and the relationship between ΔG° and K to calculate the equilibrium constant.
Step-by-step explanation:
To determine E°, ΔG°, and K for the overall reaction, we first need to combine the given half-reaction equations and their standard reduction potentials (E°) to get the overall balanced equation and overall E°.
The half-reactions are:
Co3+ + e- ⇌ Co2+ (E° = 1.92 V)
H3AsO3 + 2H+ + 2e- ⇌ H3AsO2 + H2O (E° = 0.575 V)
The overall reaction is:
2Co3+ + H3AsO3 + H2O ⇌ 2Co2+ + H3AsO2 + 2H+
The overall E° for the reaction can be calculated by adding the E° for the reduction of Co3+ to Co2+, which is given as 1.92 V, to the E° for the oxidation, which is the reverse of the second half-reaction, so its E° value would be -0.575 V.
The resulting equation for the overall E° is:
E° = 1.92 V - 0.575 V
E° = 1.345 V
Once we have E°, we can find ΔG° using the equation ΔG° = -nFE°, where n is the number of moles of electrons transferred and F is the Faraday constant (96,485 C/mol e-). For the reaction, n = 2, as there are 2 moles of electrons transferred in the balanced overall equation.
The equilibrium constant K can be calculated using the relationship between ΔG° and K, which is ΔG° = -RTlnK, where R is the gas constant (8.314 J/mol K) and T is the temperature in Kelvin. With ΔG° determined, K can be calculated at a given temperature.