Which of the following changes will increase the `EMF` of the cell `:`
`Co(s)|CoCl_(2)(M_(1))||HCl(M_(2))||(H_(2),g)Pt`

Options

A. Increae in the volume of `CoCl_(2)` solution from `100mL` to `200mL`.
B. Increase `M_(2)` from `0.1 M` to `0.50M`.
C. Increase the pressure of the `H_(2)(g)` from `1.0` to `2.0 atm`.
D. Increase `M_(1)` from `0.01M` to `0.50M`.

Explanation

To determine which changes will increase the EMF of the cell represented by the notation \( \text{Co(s)} | \text{CoCl}_2(M_1) || \text{HCl}(M_2) || (H_2, g) \text{Pt} \), we can analyze the effects of various changes on the cell's EMF.

### Step-by-Step Solution:

1. **Identify the Cell Reaction**:
The cell consists of cobalt (Co) being oxidized and hydrogen ions (H\(^+\)) being reduced. The overall cell reaction can be written as:
\[ \text{Co(s)} + 2\text{H}^+ \rightarrow \text{Co}^{2+} + \text{H}_2(g) \]

2. **Determine the Anode and Cathode Reactions**:
- **Anode (Oxidation)**:
\[ \text{Co(s)} \rightarrow \text{Co}^{2+} + 2e^- \]
- **Cathode (Reduction)**:
\[ 2\text{H}^+ + 2e^- \rightarrow \text{H}_2(g) \]

3. **Write the Nernst Equation**:
The EMF of the cell can be expressed using the Nernst equation:
\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.059}{n} \log Q \]
where \( n = 2 \) (number of electrons transferred), and \( Q \) is the reaction quotient given by:
\[ Q = \frac{[\text{Co}^{2+}]}{[H^+]^2 \cdot P_{H_2}} \]

4. **Analyze the Effect of Changes**:
- **Change A: Dilution of CoCl\(_2\)** (decrease in \([\text{Co}^{2+}]\)):
- If we dilute CoCl\(_2\), \([\text{Co}^{2+}]\) decreases, which increases \( E_{\text{cell}} \) because it reduces the numerator in \( Q \).
- **Conclusion**: This change **increases EMF**.

- **Change B: Increase in HCl concentration** (increase in \([\text{H}^+]\)):
- Increasing \([\text{H}^+]\) increases the denominator in \( Q \), which leads to a decrease in \( Q \) and thus increases \( E_{\text{cell}} \).
- **Conclusion**: This change **increases EMF**.

- **Change C: Increase in pressure of H\(_2\)**:
- Increasing the pressure of H\(_2\) increases \( P_{H_2} \) in the denominator of \( Q \), which increases \( Q \) and decreases \( E_{\text{cell}} \).
- **Conclusion**: This change **decreases EMF**.

- **Change D: Increase in concentration of CoCl\(_2\)** (increase in \([\text{Co}^{2+}]\)):
- Increasing \([\text{Co}^{2+}]\) increases the numerator in \( Q \), which increases \( Q \) and decreases \( E_{\text{cell}} \).
- **Conclusion**: This change **decreases EMF**.

5. **Final Answer**:
The changes that will increase the EMF of the cell are:
- **Change A**: Dilution of CoCl\(_2\) (decreases \([\text{Co}^{2+}]\))
- **Change B**: Increase in HCl concentration (increases \([\text{H}^+]\))