Juan M. answered • 04/30/23
Professional Math and Physics Tutor
The cell potential, E, can be calculated using the Nernst equation:
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 electrons transferred in the balanced redox equation, F is the Faraday constant, and Q is the reaction quotient.
In this case, the balanced redox equation is:
2Co3+(aq) + 2Cl−(aq) → 2Co2+(aq) + Cl2(g)
The number of electrons transferred is 2.
The reaction quotient, Q, can be expressed as:
Q = ([Co2+]^2 [Cl2]) / ([Co3+]^2 [Cl^-]^2)
Substituting the given concentrations and partial pressure into the equation, we get:
Q = ([0.444 M]^2 * [4.50 atm]) / ([0.713 M]^2 * [0.434 M]^2)
= 8.61
Substituting the given values into the Nernst equation, we get:
E = 0.483 V - (0.0257 V/K) * ln(8.61/2)
= 0.483 V - 0.0515 V
= 0.4315 V
Therefore, the cell potential at 25°C is 0.4315 V.
Juan M.
I apologize for the confusion in the previous response. You are correct that the number of electrons transferred (n) was not properly explained, and it's also important to note that mixing pressures and concentrations in the Nernst equation is not appropriate. Let's reevaluate the problem. First, we need to determine the balanced redox half-reactions and find the number of electrons transferred (n): Oxidation half-reaction: Co^3+ (aq) → Co^2+ (aq) + e^- Reduction half-reaction: Cl^-(aq) + e^- → 1/2 Cl2 (g) To balance the electrons, we'll multiply the oxidation half-reaction by 1 and the reduction half-reaction by 2: Oxidation half-reaction: Co^3+ (aq) → Co^2+ (aq) + e^- Reduction half-reaction: 2Cl^-(aq) + 2e^- → Cl2 (g) Now the balanced redox equation is: Co^3+ (aq) + 2Cl^-(aq) → Co^2+ (aq) + Cl2 (g) The number of electrons transferred (n) in the balanced equation is 1 for the oxidation half-reaction and 2 for the reduction half-reaction. The overall n is 2. Now, let's address the issue of mixing pressures and concentrations in the Nernst equation. We should not mix them directly. However, we can convert the partial pressure of Cl2 to concentration using the ideal gas law: PV = nRT Rearrange to solve for concentration (n/V): C = P / (RT) For Cl2 at 25°C (298K), the conversion is: C_Cl2 = P_Cl2 / (R * T) = (4.50 atm) / (0.0821 L atm/mol K * 298 K) = 0.183 M Now we can properly calculate the reaction quotient, Q: Q = ([Co^2+]^1 [Cl2]^1) / ([Co^3+]^1 [Cl^-]^2) Substituting the given concentrations, we get: Q = ([0.444 M]^1 * [0.183 M]^1) / ([0.713 M]^1 * [0.434 M]^2) = 0.173 Now we can use the Nernst equation: E = E° - (RT / nF) * ln(Q) At 25°C (298 K), the Nernst equation becomes: E = E° - (0.0592 V / n) * log(Q) Substituting the values, we get: E = 0.483 V - (0.0592 V / 2) * log(0.173) E ≈ 0.483 V + 0.051 V ≈ 0.534 V Therefore, the cell potential at 25°C is approximately 0.534 V.05/02/23
J.R. S.
05/01/23