For the reaction ,
`2AgCl(s)+H_(2)(g)(1" atm")to2Ag(s)+2H^(+)(0.1 M)+2Cl^(-)(0.1 M),DeltaG^(@)=-43600" J at "25^(@)C`.
Calculate e.m.f. of the cell.

Explanation

To calculate the e.m.f. (electromotive force) of the cell for the given reaction, we can follow these steps:

### Step 1: Understand the relationship between ΔG° and e.m.f.
The relationship between the standard Gibbs free energy change (ΔG°) and the standard electromotive force (E°) of a cell is given by the equation:
\[ \Delta G° = -nFE° \]
where:
- \( n \) = number of moles of electrons transferred in the reaction
- \( F \) = Faraday's constant (approximately \( 96500 \, \text{C/mol} \))
- \( E° \) = standard e.m.f. of the cell

### Step 2: Rearrange the equation to solve for E°
From the equation above, we can rearrange it to find \( E° \):
\[ E° = -\frac{\Delta G°}{nF} \]

### Step 3: Substitute the known values
We are given:
- \( \Delta G° = -43600 \, \text{J} \)
- \( n = 2 \) (since the reaction involves the transfer of 2 electrons)
- \( F = 96500 \, \text{C/mol} \)

Now, substituting these values into the equation:
\[ E° = -\frac{-43600 \, \text{J}}{2 \times 96500 \, \text{C/mol}} \]

### Step 4: Calculate E°
Calculating the above expression:
\[ E° = \frac{43600}{193000} \approx 0.226 \, \text{V} \]

### Step 5: Use the Nernst equation to find the e.m.f. of the cell
The Nernst equation relates the e.m.f. of the cell (E) to the standard e.m.f. (E°) and the concentrations of the reactants and products:
\[ E = E° - \frac{RT}{nF} \ln \left( \frac{[products]}{[reactants]} \right) \]
Where:
- \( R = 8.314 \, \text{J/(K mol)} \)
- \( T = 298 \, \text{K} \) (25°C)
- Concentrations: \([H^+] = 0.1 \, \text{M}\), \([Cl^-] = 0.1 \, \text{M}\), and \([H_2] = 1 \, \text{atm}\)

### Step 6: Substitute values into the Nernst equation
Substituting the known values:
\[ E = 0.226 - \frac{(8.314)(298)}{(2)(96500)} \ln \left( \frac{(0.1)^2(0.1)^2}{1} \right) \]

### Step 7: Calculate the logarithm term
Calculating the logarithm:
\[ \ln \left( \frac{(0.1)^4}{1} \right) = \ln(0.0001) = -9.2103 \]

### Step 8: Calculate the second term in the Nernst equation
Calculating the second term:
\[ \frac{(8.314)(298)}{(2)(96500)} \approx 0.0591 \]

### Step 9: Substitute and calculate E
Now substitute back:
\[ E = 0.226 - (0.0591)(-9.2103) \]
\[ E = 0.226 + 0.543 \]
\[ E \approx 0.769 \, \text{V} \]

### Final Answer
The e.m.f. of the cell is approximately **0.769 V**.

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