If `E^(Theta` for copper electrode is 0.34 V, how will you calculate its e.m.f. value when the solution in contact with it is 0.1M in copperions? How does e.m.f.for copper electrode changes when concentration of `Cu^(2+)` ions in the solution is decreased ?

Explanation

To calculate the electromotive force (e.m.f.) value of the copper electrode when the solution is 0.1 M in copper ions, we will use the Nernst equation. The Nernst equation relates the electrode potential under non-standard conditions to the standard electrode potential and the concentrations of the reactants and products involved in the electrochemical reaction.

### Step-by-Step Solution:

1. **Identify the Standard Electrode Potential (E°)**:
The standard electrode potential for the copper electrode (E°) is given as 0.34 V.

2. **Write the Half-Cell Reaction**:
The half-cell reaction for the copper electrode can be represented as:
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \]

3. **Use the Nernst Equation**:
The Nernst equation is given by:
\[ E = E° + \frac{0.059}{n} \log \frac{[\text{Ox}]}{[\text{Red}]} \]
where:
- \(E\) = cell potential (e.m.f.)
- \(E°\) = standard electrode potential
- \(n\) = number of moles of electrons transferred in the reaction (for copper, \(n = 2\))
- \([\text{Ox}]\) = concentration of the oxidized form (Cu²⁺)
- \([\text{Red}]\) = concentration of the reduced form (Cu)

4. **Substitute the Values**:
For the given problem:
- \([\text{Cu}^{2+}] = 0.1 \, \text{M}\)
- \([\text{Cu}] = 1 \, \text{(since it's a pure solid, its activity is 1)}\)

Substituting these values into the Nernst equation:
\[ E = 0.34 + \frac{0.059}{2} \log \frac{0.1}{1} \]

5. **Calculate the Logarithm**:
\[ \log(0.1) = -1 \]

6. **Calculate the Nernst Equation**:
Now substituting the logarithm value:
\[ E = 0.34 + \frac{0.059}{2} \times (-1) \]
\[ E = 0.34 - 0.0295 \]
\[ E = 0.3105 \, \text{V} \]

7. **Conclusion**:
The e.m.f. value of the copper electrode when the solution is 0.1 M in copper ions is **0.3105 V**.

### Effect of Decreasing Concentration of Cu²⁺ Ions:
As the concentration of Cu²⁺ ions in the solution decreases, the logarithmic term in the Nernst equation becomes less negative (since \(\log\) of a smaller number is more negative), which results in an increase in the e.m.f. value. Therefore, as the concentration of Cu²⁺ ions decreases, the e.m.f. for the copper electrode will increase.