Question

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below:
\(A(g) \rightleftharpoons B(g) + C(g)\)}

The magnitude of \(\frac{\Delta H^\circ}{R}\) calculated from the above data is ____. (Nearest integer)}

Answer 1

Correct Answer: 230

Step 1: Understanding the Question:
The variation of equilibrium constant with temperature is given by the van't Hoff equation. We need to find the enthalpy of reaction scaled by the gas constant.
Step 2: Key Formula or Approach:
The integrated form of the van't Hoff equation in terms of base-10 log is:
\[ \log_{10} K_p = -\frac{\Delta H^\circ}{2.303 RT} + \text{constant} \]
The slope of a plot of \(\log_{10} K_p\) versus \(\frac{1}{T}\) is \(-\frac{\Delta H^\circ}{2.303 R}\).
Step 3: Detailed Explanation:
Let's use two data points:
Point 1: \(\frac{1}{T_1} = 0.05, \log K_1 = 3.5\)
Point 2: \(\frac{1}{T_2} = 0.06, \log K_2 = 2.5\)
Slope = \(\frac{\Delta(\log K)}{\Delta(1/T)} = \frac{2.5 - 3.5}{0.06 - 0.05} = \frac{-1}{0.01} = -100\)
From the formula:
\[ -100 = -\frac{\Delta H^\circ}{2.303 R} \]
\[ \frac{\Delta H^\circ}{R} = 100 \times 2.303 = 230.3 \]
Rounding to the nearest integer, we get 230.
Step 4: Final Answer:
The magnitude of \(\frac{\Delta H^\circ}{R}\) is 230.