The molarity (concentration) of the NiSO4 solution should be approximately 14.77 M for the nickel electrode to show a potential of -0.2842 V with respect to a standard hydrogen electrode at 25°C.
To determine the molarity (concentration) of the NiSO4 solution when a nickel electrode shows a potential of -0.2842 V with respect to a standard hydrogen electrode, we can use the Nernst equation. The Nernst equation relates the electrode potential (E) to the concentrations of the ions involved in the electrochemical reaction. Here are the steps to calculate the molarity:
1. Write the Electrochemical Half-Reaction:
- The half-reaction for the nickel electrode immersed in a NiSO4 solution is:
Ni²⁺(aq) + 2e⁻ ⇌ Ni(s)
2. Nernst Equation:
- The Nernst equation is given as:
E = E° - (0.0592 / n) * log(Q)
Where:
- E is the measured electrode potential (-0.2842 V in this case).
- E° is the standard electrode potential for the half-reaction.
- n is the number of electrons transferred in the half-reaction.
- Q is the reaction quotient, which can be expressed in terms of the concentrations of reactants and products.
3. Determine E° and n:
- E° for the half-reaction is the standard electrode potential for the nickel half-cell, which is a tabulated value.
- In this case, E° for the reduction of Ni²⁺ to Ni is -0.25 V.
- The number of electrons transferred (n) is 2, as shown in the half-reaction.
4. Rearrange the Nernst Equation:
- Rearrange the Nernst equation to solve for log(Q):
log(Q) = (E° - E) * (n / 0.0592)
5. Calculate log(Q):
- Plug in the values:
log(Q) = (-0.25 V - (-0.2842 V)) * (2 / 0.0592)
log(Q) = 0.0342 * 33.78
log(Q) ≈ 1.1598
6. Calculate Q:
- Take the antilogarithm of both sides to find Q:
Q = 10^1.1598
Q ≈ 14.77
7. Calculate Molarity (Concentration):
- Q for the half-reaction is equal to the concentration of Ni²⁺ ions, so:
[Ni²⁺] = Q
[Ni²⁺] ≈ 14.77