For the reaction: Mg(s)+ AgNO₃(aq)→ Ag(s)+ Mg(NO₃)₂(aq) Ag⁺(aq)+ e^- → Ag(s)E° = 0.800 V Mg²⁺(aq)+ 2 e^- → Mg(s)E° = -2.356 V Estimate K_eq at 25 °C.

Question

Quizplus · Accepted Answer

The equilibrium constant (K_eq) for the reaction can be calculated using the Nernst equation and the standard electrode potentials (E°) given for the half-reactions. The overall cell potential (E°_cell) is the difference between the reduction potential of silver ion (Ag^+) and the oxidation potential of magnesium (Mg), which is the negative of the given E° for Mg. Thus, E°_cell = 0.800 V - (-2.356 V) = 3.156 V. The relationship between E°_cell and K_eq at 25 °C (298 K) is given by the equation ΔG° = -nFE°_cell = -RTlnK_eq, where n is the number of moles of electrons transferred (2 in this case), F is the Faraday constant (96485 C/mol), R is the gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin. Rearranging for K_eq gives K_eq = e^(-ΔG°/(RT)) = e^((nFE°_cell)/(RT)). Substituting the values and calculating gives a K_eq of approximately 5.7 × 10^110, which matches choice A.

For the Reaction: Mg(s)+ AgNO3(aq)→ Ag(s)+ Mg(NO3)2(aq)

For the Reaction: Mg(s)+ AgNO₃(aq)→ Ag(s)+ Mg(NO₃)₂(aq)