Chemistry - Electrochemistry Question with Solution | TestHub

Question Explanation:

Calculating heat of reaction $(\Delta \mathrm{H})$ using EMF temperature coefficient.

Concept:

Gibbs-Helmholtz Equation in Electrochemistry.

Solution:

The heat of reaction inside a cell is related to the cell potential (E) and its temperature coefficien $\left(\frac{\mathrm{dE}}{\mathrm{dT}}\right)$. We calculate the change in EMF over the change in temperature to find the entropy component, then solve for enthalpy.

$\Delta \mathrm{H}=\mathrm{nF}\left[\mathrm{T}\left(\frac{\mathrm{dE}}{\mathrm{dT}}\right)-\mathrm{E}\right]$

Given: $\mathrm{n}=1,\mathrm{E}=0.27\mathrm{V}$ at $\mathrm{T}=298\mathrm{K}\left(25^{\circ }\mathrm{C}\right),\mathrm{F}=96500\mathrm{C}/\mathrm{mol}$.

$$\begin{array}{rlrlr}& \frac{\mathrm{dE}}{\mathrm{dT}}=\frac{0.26-0.27}{35-25}=\frac{-0.01}{10}=-0.001\mathrm{V}/\mathrm{K}& & & \end{array}$$

$$\Delta \mathrm{H}=1\times 96500\times [298(-0.001)-0.27]$$

$$\Delta \mathrm{H}=96500\times [-0.298-0.27]=96500\times [-0.568]$$

$$\Delta \mathrm{H}\approx -54812\mathrm{J}\approx -54.8\mathrm{kJ}$$

Final Answer: Option (A)