Chemistry Q74 – JEE-MAIN 2026

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below

A (g) ⇌ B (g) + C (g)

\begin{array}{cc} \frac{1}{T} (K^{- 1}) & \log_{10} K_{p} \\ 0.05 & 3.5 \\ 0.06 & 2.5 \\ 0.07 & 1.5 \end{array}

The magnitude of

\frac{Δ H^{\circ}}{R}

calculated from the above data is _______. (Nearest integer)

Enter Calculated Numerical Value:

The relationship between the equilibrium constant and temperature is described by the Van't Hoff equation.

Step 1: Identify the relevant equation✦ Active

The Van't Hoff equation relates the equilibrium constant $K_{p}$ to temperature $T$ and the standard enthalpy change $Δ H^{\circ}$ :

\ln K_{p} = - \frac{Δ H^{\circ}}{R} \frac{1}{T} + C

To use the given $\log_{10} K_{p}$ values, convert the equation:

2.303 \log_{10} K_{p} = - \frac{Δ H^{\circ}}{R} \frac{1}{T} + C

Dividing by $2.303$ gives:

\log_{10} K_{p} = - \frac{Δ H^{\circ}}{2.303 R} \frac{1}{T} + C^{'}

This equation is in the form $y = m x + c$ , where $y = \log_{10} K_{p}$ and $x = \frac{1}{T}$ . The slope $m = - \frac{Δ H^{\circ}}{2.303 R}$ .

Step 2: Calculate the slope from the given data○ Expand

Using two data points from the table, for example, $(x_{1}, y_{1}) = (0.05, 3.5)$ and $(x_{2}, y_{2}) = (0.06, 2.5)$ :

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{2.5 - 3.5}{0.06 - 0.05} = \frac{- 1.0}{0.01} = - 100

💡 Teacher's Secret Hint

Any pair of points from the table should yield the same slope.

Step 3: Calculate the magnitude of

\frac{Δ H^{\circ}}{R}

○ Expand

Equating the calculated slope with the theoretical slope from the Van't Hoff equation:

m = - \frac{Δ H^{\circ}}{2.303 R}

Substitute the calculated slope:

- 100 = - \frac{Δ H^{\circ}}{2.303 R}

Solve for $\frac{Δ H^{\circ}}{R}$ :

\frac{Δ H^{\circ}}{R} = 100 \times 2.303 = 230.3

The magnitude of $\frac{Δ H^{\circ}}{R}$ is $| 230.3 | = 230.3$ . Rounding to the nearest integer, the value is 230.

💡 Teacher's Secret Hint

Remember to take the magnitude as requested by the question.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Chemistry Question 74 – JEE-MAIN 2026