Question

Calculate the minimum (least negative) cathode potential (versus SHE) needed to begin electroplating nickel from 0.250 M Ni2+ onto a piece of iron. Assume that the overpotential for the reduction of Ni2+ on an iron electrode is negligible (The reduction potential of Ni2+ vs. SHE is –0.257 V).

Answer 1

The minimum cathode potential needed to begin electroplating nickel onto a piece of iron can be calculated by subtracting the standard electrode potential of Ni2+ from the standard hydrogen electrode potential.

Step-by-step explanation:

The minimum (least negative) cathode potential needed to begin electroplating nickel from 0.250 M Ni2+ onto a piece of iron can be calculated by subtracting the standard electrode potential for the oxidation of Ni2+ from the standard hydrogen electrode potential. The reduction potential of Ni2+ versus SHE is -0.257 V. Since we are asked for the potential for the oxidation of Ni to Ni2+ under standard conditions, we must reverse the sign of the reduction potential. Thus, E° oxidation = -(-0.257 V) = 0.257 V. Therefore, the minimum cathode potential needed for the electroplating process is 0.257 V.

Answer 2

The minimum cathode potential needed is simply the reduction potential of Ni2+ itself is -0.221 V vs. SHE.

How to find minimum cathode potential?

The electroplating of nickel onto a piece of iron involves the reduction of Ni²⁺ ions. The overall cell reaction for this process can be represented as follows:

`\[ \text{Ni}^(2+)(aq) + 2e^- \rightarrow \text{Ni}(s) \]`

The standard reduction potential (E°) and the actual cell potential (
`\(E_{\text{cell}}\)`) are related by the Nernst equation:

`\[ E_{\text{cell}} = E^\circ - (RT)/(nF) \ln\left(\frac{[\text{Ni}^(2+)]}{[\text{Ni}]} \right) \]`

In this case, since the concentration of nickel metal (
`\([\text{Ni}]\)`) is solid and constant, simplify the equation to:

`\[ E_{\text{cathode}} = E^\circ - (RT)/(nF) \ln[\text{Ni}^(2+)] \]`

Given that

`\(E^\circ\)` (reduction potential of Ni²⁺ versus SHE) = -0.257 V,

the temperature T = 298 K,

the Faraday constant F = 96,485 C/mol, and

the number of electrons transferred (n) in the reaction = 2.

`\[ E_{\text{cathode}} = -0.257 \, \text{V} - \frac{(8.314 \, \text{J/mol}\cdot\text{K})(298 \, \text{K})}{(2)(96485 \, \text{C/mol})} \ln(0.250 \, \text{M}) \]`

`\[ \frac{(8.314 \, \text{J/mol}\cdot\text{K})(298 \, \text{K})}{(2)(96485 \, \text{C/mol})} \approx 0.0257 \, \text{V} \]`

Now, substitute this value into the equation:

`\[ E_{\text{cathode}} = -0.257 \, \text{V} - 0.0257 \, \text{V} \ln(0.250 \, \text{M}) \]`

`\[ E_{\text{cathode}} \approx -0.257 \, \text{V} - 0.0257 \, \text{V} \cdot (-1.386) \]`

`\[ E_{\text{cathode}} \approx -0.257 \, \text{V} + 0.0357 \, \text{V} \]`

`\[ E_{\text{cathode}} \approx -0.221 \, \text{V} \]`

So, the minimum (least negative) cathode potential needed to begin electroplating nickel from 0.250 M Ni²⁺ onto a piece of iron is approximately -0.221 V versus the standard hydrogen electrode (SHE).