Which of the following changes will increase the emf of the cell :
`Co(s)| CoCl_(2) (M_1) || HCl(M_2) | pt(H_(2), g)`

Options

A. Increase the volume of `COCl_(2)` solution from 100mL to 200 mL by adding water
B. Increase M2 from 0.01 M to 0.50 M
C. Increase the pressure of the `H_(2)` from 1.0 to 2.0 atm
D. Increase `M_(1)` from 0.01 M to 0.50 M

Explanation

To determine which changes will increase the EMF (electromotive force) of the cell represented by the reaction:

\[ \text{Co(s)} | \text{CoCl}_2 (M_1) || \text{HCl}(M_2) | \text{pt}(\text{H}_2, g) \]

we need to analyze the effects of each proposed change on the cell's EMF using the Nernst equation.

### Step-by-Step Solution:

1. **Identify the half-reactions**:
- At the anode (left side), cobalt is oxidized:
\[ \text{Co(s)} \rightarrow \text{Co}^{2+} + 2e^- \]
- At the cathode (right side), hydrogen ions are reduced:
\[ 2\text{H}^+ + 2e^- \rightarrow \text{H}_2(g) \]

2. **Write the overall cell reaction**:
\[ \text{Co(s)} + 2\text{H}^+ \rightarrow \text{Co}^{2+} + \text{H}_2(g) \]

3. **Use the Nernst equation**:
The Nernst equation is given by:
\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n} \log \left( \frac{[\text{Co}^{2+}][P_{\text{H}_2}]}{[\text{H}^+]^2} \right) \]
where \( n = 2 \) (number of electrons transferred).

4. **Analyze the options**:
- **Option 1**: Increase the volume of CoCl₂ solution from 100 ml to 200 ml by adding water.
- This decreases the concentration of \([\text{Co}^{2+}]\), which will decrease the log term, making \(E_{\text{cell}}\) increase. **(Correct)**

- **Option 2**: Increase \(M_2\) from 0.01 molar to 0.5 molar (concentration of \(H^+\)).
- Increasing \([\text{H}^+]\) decreases the log term, leading to an increase in \(E_{\text{cell}}\). **(Correct)**

- **Option 3**: Increase the pressure of \(H_2\) from 1 to 2 atm.
- Increasing the pressure of \(H_2\) increases the log term, which decreases \(E_{\text{cell}}\). **(Incorrect)**

- **Option 4**: Increase \(M_1\) from 0.01 molar to 0.5 molar (concentration of \([\text{Co}^{2+}]\)).
- Increasing \([\text{Co}^{2+}]\) increases the log term, which decreases \(E_{\text{cell}}\). **(Incorrect)**

5. **Conclusion**:
The changes that will increase the EMF of the cell are:
- Option 1: Increase the volume of CoCl₂ solution.
- Option 2: Increase \(M_2\) from 0.01 molar to 0.5 molar.

### Summary of Correct Options:
- **Correct Options**: 1 and 2
- **Incorrect Options**: 3 and 4