The standard emf for the cell cell reaction ` Zn + Cu^(2+) rarr Zn^(2+) + Cu ` is 1.10 volt at ` 25^@ C`. The emf for the cell reaction when ` 0.1 M Cu^(2+)` and ` 0.1 M ZN^(2+)` solutions are used at `25^@ =C` is .

Options

A. ` 1.10` volt
B. `0. 110` volt
C. `- 1.10 `volt
D. `-0 . 110` volt

Explanation

To solve the problem, we will use the Nernst equation, which relates the cell potential (E_cell) under non-standard conditions to the standard cell potential (E°_cell) and the concentrations of the reactants and products.

### Step-by-Step Solution:

1. **Identify the Standard EMF (E°_cell)**:
The standard EMF for the cell reaction is given as:
\[ E°_{cell} = 1.10 \, \text{V} \]

2. **Write the Cell Reaction**:
The cell reaction is:
\[ Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu \]

3. **Determine the Number of Electrons Transferred (N)**:
In this reaction, one zinc atom is oxidized to Zn²⁺ and one copper ion is reduced to copper. Therefore, the number of electrons transferred (N) is:
\[ N = 2 \]

4. **Concentrations of Reactants and Products**:
The concentrations given are:
- \([Cu^{2+}] = 0.1 \, \text{M}\)
- \([Zn^{2+}] = 0.1 \, \text{M}\)

5. **Set Up the Nernst Equation**:
The Nernst equation is given by:
\[ E_{cell} = E°_{cell} - \frac{0.0591}{N} \log \left( \frac{[products]}{[reactants]} \right) \]
In this case, the products are Zn²⁺ and Cu, and the reactants are Zn and Cu²⁺. Therefore, we can express the equation as:
\[ E_{cell} = E°_{cell} - \frac{0.0591}{2} \log \left( \frac{[Zn^{2+}]}{[Cu^{2+}]} \right) \]

6. **Substituting the Concentrations**:
Substitute the concentrations into the equation:
\[ E_{cell} = 1.10 - \frac{0.0591}{2} \log \left( \frac{0.1}{0.1} \right) \]

7. **Calculate the Logarithm**:
Since \(\frac{0.1}{0.1} = 1\), we have:
\[ \log(1) = 0 \]

8. **Final Calculation**:
Substitute back into the equation:
\[ E_{cell} = 1.10 - \frac{0.0591}{2} \times 0 \]
\[ E_{cell} = 1.10 - 0 \]
\[ E_{cell} = 1.10 \, \text{V} \]

### Conclusion:
The EMF for the cell reaction when using 0.1 M Cu²⁺ and 0.1 M Zn²⁺ solutions at 25°C is:
\[ E_{cell} = 1.10 \, \text{V} \]