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 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 `Co(s)| CoCl_(2) (M_1) || HCl(M_2) | pt(H_(2), g)`, we need to analyze the effect of different changes on the cell's reaction quotient and the Nernst equation.

### Step-by-Step Solution:

1. **Understand the Cell Reaction**:
The cell reaction involves the oxidation of cobalt (Co) to cobalt ions (Co²⁺) and the reduction of hydrogen ions (H⁺) to hydrogen gas (H₂). The half-reactions can be represented as:
- Oxidation: Co(s) → Co²⁺ + 2e⁻
- Reduction: 2H⁺ + 2e⁻ → H₂(g)

2. **Write the Nernst Equation**:
The Nernst equation relates the emf of the cell to the concentrations of the reactants and products:
\[ E_{cell} = E^\circ_{cell} - \frac{0.059}{n} \log Q \]
where \( n \) is the number of electrons transferred (which is 2 in this case), and \( Q \) is the reaction quotient.

3. **Identify the Reaction Quotient (Q)**:
For the given cell:
\[ Q = \frac{[Co^{2+}]}{[H^+]^2 \cdot P_{H_2}} \]
where \([Co^{2+}]\) is the concentration of cobalt ions, \([H^+]\) is the concentration of hydrogen ions, and \(P_{H_2}\) is the partial pressure of hydrogen gas.

4. **Analyze the Changes**:
- **Option A**: Increase the volume of CoCl₂ solution (dilution).
- Dilution decreases the concentration of Co²⁺, which decreases \( Q \). A decrease in \( Q \) will make the logarithmic term negative, thus increasing \( E_{cell} \).
- **Conclusion**: This option will increase the emf.

- **Option B**: Increase \( M_2 \) from 0.01 M to 0.50 M (increase [H⁺]).
- Increasing the concentration of H⁺ increases \( Q \). An increase in \( Q \) will make the logarithmic term positive, thus decreasing \( E_{cell} \).
- **Conclusion**: This option will not increase the emf.

- **Option C**: Increase \( M_1 \) from 0.01 M to 0.001 M (decrease [Co²⁺]).
- Decreasing the concentration of Co²⁺ (M₁) will also decrease \( Q \), which will increase \( E_{cell} \).
- **Conclusion**: This option will increase the emf.

5. **Final Conclusion**:
The changes that will increase the emf of the cell are:
- Option A: Increase the volume of CoCl₂ solution (dilution).
- Option C: Decrease the concentration of Co²⁺ from 0.01 M to 0.001 M.

### Summary of Correct Options:
- **Correct Options**: A and C will increase the emf of the cell.