Consider the following voltaic cell:

Ni(s)Ni2+(aq)Cl2(g)Cl–(aq)Pt(s)

If the standard potentials of the Ni2+/Ni and Cl2/Cl– couples are –0.23 V and +1.36 V, respectively, at 25 °C calculate the voltage of this cell when {Ni2+] = 0.100 M, [Cl–] = 0.100 M, and the pressure of Cl2(g) = 1.50 atm.

Question

Consider the following voltaic cell:

Ni(s)Ni2+(aq)Cl2(g)Cl–(aq)Pt(s)

If the standard potentials of the Ni2+/Ni and Cl2/Cl– couples are –0.23 V and  +1.36 V, respectively, at 25 °C calculate the  voltage of this cell when {Ni2+] = 0.100 M, [Cl–] = 0.100 M, and the  pressure of Cl2(g) = 1.50 atm.

BlackTom AI · Accepted Answer

We start by clearly noting the given cell and data.
The half-reactions are Ni2+ + 2e- -> Ni(s) with E° = -0.23 V and Cl2(g) + 2e- -> 2Cl- with E° = +1.36 V.
To determine the standard cell potential, identify the cathode (the reduction with the higher E°) and the anode (the oxidation of Ni). The Cl2/Cl- couple serves as the cathode, and Ni is oxidized, so:
E°cell = E°cathode - E°anode = 1.36 - (-0.23) = 1.59 V.
Next, balance the overall reaction and express the reaction quotient Q. The balanced equation is Ni(s) + Cl2(g) -> Ni2+(aq) + 2Cl-(aq).
Thus, Q = [Ni2+][Cl-]^2 / p(Cl2).
Plug in the given concentrations/pressure: [Ni2+] = 0.100 M, [Cl-] = 0.100 M, p(Cl2) = 1.50 atm. So Q = (0.100)(0.100)^2 / 1.50 = (0.100)(0.010) / 1.50 = 0.001 / 1.50 = 6.666... × 10^-4.
Now apply the Nernst equation at 25 °C. Using the common form with natural logarithm: E = E°cell - (RT/nF) ln Q. Alternatively, using the base-10 form: E = E°cell - (0.05916/n) log10 Q. Here n = 2.
Using the base-10 form for convenience: log10 Q = log10(6.666... × 10^-4) = log10(6.666...) + log10(10^-4) ≈ 0.824 - 4 = -3.176. So:
E = 1.59 - (0.05916/2)(-3.176) = 1.59 - 0.02958 × (-3.176) ≈ 1.59 + 0.0939 ≈ 1.684 V.
Rounding to two decimals, the cell potential is approximately 1.68 V.

Summary of key steps:
- Determine E°cell from the given standard potentials: E°cell ≈ 1.59 V.
- Compute Q from given concentrations/pressure: Q ≈ 6.666 × 10^-4.
- Apply the Nernst equation with n = 2 to find E ≈ 1.68 V.

Note: The provided answer options field appears empty in the data given, so no option-by-option analysis can be performed here. All calculations above assume standard conditions for temperature (25 °C) and activity-based approximations where concentrations are used directly as activities for dilute solutions.

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