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

Options

A. Increase the volume of `CoCl_(2)` 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 `Co(s)|CoCl_(2)(M_(2))||HCl(M_(2))||(H_(2),g)Pt`, we can analyze the effects of each proposed change on the EMF using the Nernst equation.

### Step-by-Step Solution:

1. **Identify the Cell Reaction**:
- The cell reaction involves cobalt being oxidized and hydrogen ions being reduced. The overall reaction can be represented as:
\[ Co(s) \rightarrow Co^{2+}(aq) + 2e^{-} \quad \text{(oxidation)} \]
\[ 2H^{+}(aq) + 2e^{-} \rightarrow H_{2}(g) \quad \text{(reduction)} \]

2. **Write the Nernst Equation**:
- The Nernst equation for this cell can be expressed as:
\[ E_{cell} = E^{\circ} - \frac{0.0592}{n} \log \left( \frac{[Co^{2+}]}{[H^{+}]^2 \cdot P_{H_{2}}} \right) \]
- Here, \( n = 2 \) (the number of electrons transferred).

3. **Analyze Each Change**:
- **Change A**: Increasing the volume of CoCl₂ from 100 mL to 200 mL.
- Increasing the volume decreases the concentration of \( Co^{2+} \) ions, which will increase the EMF since it appears in the numerator of the log term.
- **Conclusion**: This change will increase EMF.

- **Change B**: Increasing \( M_2 \) (the concentration of \( H^+ \)) from 0.1 M to 0.5 M.
- Increasing \( H^+ \) concentration decreases the denominator in the Nernst equation, which will also increase EMF.
- **Conclusion**: This change will increase EMF.

- **Change C**: Increasing the pressure of hydrogen gas from 1 atm to 2 atm.
- Increasing the pressure of \( H_2 \) increases the concentration of \( H_2 \) in the numerator, which will decrease EMF.
- **Conclusion**: This change will not increase EMF.

- **Change D**: Increasing \( M_1 \) (the concentration of \( Co^{2+} \)) from 0.01 M to 0.5 M.
- Increasing \( Co^{2+} \) concentration increases the numerator in the Nernst equation, which will decrease EMF.
- **Conclusion**: This change will not increase EMF.

4. **Final Answer**:
- The changes that will increase the EMF of the cell are:
- **Change A**: Increasing the volume of CoCl₂ from 100 mL to 200 mL.
- **Change B**: Increasing \( M_2 \) from 0.1 M to 0.5 M.

### Summary:
The correct options that will increase the EMF of the cell are **A and B**.

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