A galvanic cell is composed of two hydrogen electrods, one of which is a standard one. In which of the following solutions should the other electrode be immersed to get maximum e.m.f:

Options

A. 0.1M HCl
B. 0.1 M `H_2SO_4`
C. 0.1 M `NH_4OH`
D. 0.01 M HCOOH

Answer

To solve the problem of determining the solution in which the other hydrogen electrode should be immersed to achieve maximum electromotive force (e.m.f.) in a galvanic cell composed of two hydrogen electrodes, we can follow these steps:

### Step 1: Understand the Components of the Galvanic Cell
- A galvanic cell consists of two electrodes: one is a standard hydrogen electrode (SHE) with a potential of 0 V, and the other is a hydrogen electrode whose potential we need to determine based on the solution it is immersed in.

### Step 2: Write the Nernst Equation
- The e.m.f. (E_cell) of the galvanic cell can be calculated using the Nernst equation:
\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.059}{n} \log \left( \frac{[\text{H}^+]_{\text{anode}}}{[\text{H}^+]_{\text{cathode}}} \right) \]
Here, \(E^\circ_{\text{cell}} = 0\) V for the standard hydrogen electrode, and \(n = 2\) for the reaction involving hydrogen.

### Step 3: Analyze the Solutions Given
- We need to analyze the H⁺ ion concentration in each of the provided solutions:
1. **0.1 M HCl**: This gives \([\text{H}^+] = 0.1 \, \text{M} = 10^{-1} \, \text{M}\)
2. **0.1 M H₂SO₄**: This dissociates to give \(2 \times 0.1 \, \text{M} = 0.2 \, \text{M} = 2 \times 10^{-1} \, \text{M}\)
3. **0.1 M NH₄OH**: The concentration of H⁺ can be calculated using the ion product of water:
\[ K_w = [\text{H}^+][\text{OH}^-] = 10^{-14} \]
Since \([\text{OH}^-] = 0.1 \, \text{M}\), we find:
\[ [\text{H}^+] = \frac{10^{-14}}{0.1} = 10^{-13} \, \text{M} \]
4. **0.01 M Oxalic Acid**: This gives \([\text{H}^+] = 0.01 \, \text{M} = 10^{-2} \, \text{M}\)

### Step 4: Compare H⁺ Concentrations
- Now we compare the H⁺ concentrations:
- HCl: \(10^{-1} \, \text{M}\)
- H₂SO₄: \(2 \times 10^{-1} \, \text{M}\)
- NH₄OH: \(10^{-13} \, \text{M}\)
- Oxalic Acid: \(10^{-2} \, \text{M}\)

### Step 5: Identify the Solution with Minimum H⁺ Concentration
- The solution with the lowest H⁺ concentration is **0.1 M NH₄OH**, which has a concentration of \(10^{-13} \, \text{M}\).

### Step 6: Conclusion
- To achieve the maximum e.m.f. in the galvanic cell, the other hydrogen electrode should be immersed in **0.1 M NH₄OH**.

### Final Answer
The correct answer is **0.1 M NH₄OH**.

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