Question

For reaction \( A \rightleftharpoons B + C \) \[ \begin{array}{|c|c|c|c|} \hline \log K_p & 3.5 & 2.5 & 1.5 \\ \hline \frac{1}{T}\,(\text{K}^{-1}) & 0.04 & 0.05 & 0.06 \\ \hline \end{array} \] Calculate \( \dfrac{\Delta H}{R} \) (in Kelvin) based on above data. (Nearest integer)

Answer 1

Correct Answer: 230

Concept:
The relation between equilibrium constant and temperature is given by the Van’t Hoff equation: \[ \log K_2 - \log K_1 = \frac{\Delta H}{2.303R} \left(\frac{1}{T_1}-\frac{1}{T_2}\right) \] Step 1: Substitute given values. Using first two data points: \[ \log K_2 = 3.5, \quad \log K_1 = 2.5 \] \[ \frac{1}{T_1}=0.05, \quad \frac{1}{T_2}=0.04 \] \[ 3.5-2.5= \frac{\Delta H}{2.303R} (0.05-0.04) \] Step 2: Simplify the equation. \[ 1= \frac{\Delta H}{2.303R}(0.01) \] \[ \frac{\Delta H}{R}= \frac{2.303}{0.01} \] \[ \frac{\Delta H}{R}=230.3 \] \[ \boxed{\frac{\Delta H}{R}\approx230} \]