The emf of cells `Zn| ZnSO_(4)||CuSO_(4), Cu" at "25^(@)C` is 0.03 V and temperature coefficient of emf is `1.4 xx 10^(-4) V` per degree. Calculate the heat of reaction for the change taking place inside the cell.

Answer

To calculate the heat of reaction for the electrochemical cell `Zn | ZnSO4 || CuSO4 | Cu`, we will follow these steps:

### Step 1: Identify the Given Data
- EMF of the cell (E0) = 0.03 V
- Temperature coefficient of EMF (dE/dT) = 1.4 x 10^(-4) V/°C
- Temperature (T) = 25°C = 298 K

### Step 2: Calculate the Change in Gibbs Free Energy (ΔG)
The relationship between Gibbs free energy change (ΔG), number of moles of electrons (N), Faraday's constant (F), and EMF (E0) is given by the equation:
\[ \Delta G = -NFE_0 \]
Here, for the reaction:
- Zinc (Zn) is oxidized to Zn²⁺, losing 2 electrons.
- Copper (Cu²⁺) is reduced to Cu, gaining 2 electrons.

Thus, N = 2 (moles of electrons).

Using Faraday's constant (F = 96500 C/mol), we can substitute the values:
\[ \Delta G = -2 \times 96500 \, \text{C/mol} \times 0.03 \, \text{V} \]
Calculating this:
\[ \Delta G = -5790 \, \text{J} \]

### Step 3: Calculate the Change in Entropy (ΔS)
The change in entropy (ΔS) can be calculated using the formula:
\[ \Delta S = N \frac{dE}{dT} \]
Substituting the known values:
\[ \Delta S = 2 \times 1.4 \times 10^{-4} \, \text{V/K} \times 96500 \, \text{C/mol} \]
Calculating this:
\[ \Delta S = 2 \times 1.4 \times 10^{-4} \times 96500 = 27.02 \, \text{J/K} \]

### Step 4: Calculate the Enthalpy Change (ΔH)
Using the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
Rearranging for ΔH:
\[ \Delta H = \Delta G + T \Delta S \]
Substituting the values:
\[ \Delta H = -5790 \, \text{J} + 298 \, \text{K} \times 27.02 \, \text{J/K} \]
Calculating:
\[ \Delta H = -5790 + 8051.96 = 2261.96 \, \text{J} \]

### Step 5: Convert ΔH to kJ
To convert joules to kilojoules:
\[ \Delta H = \frac{2261.96}{1000} = 2.26196 \, \text{kJ} \]

### Final Answer
The heat of reaction for the change taking place inside the cell is approximately:
\[ \Delta H \approx 2.26 \, \text{kJ} \]

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