JEE Main 2026 Apr 8 Shift 2, Chemistry Q7: Factors Affecting The Rate of a Chemical Reaction

JEE Main2026Apr 8, Shift 2Chemistry

Given below are two statements :

$R = 8.314$ J K $^{- 1}$ mol $^{- 1}$ and $1$ cal $= 4.2$ J

Statement I : When $E_{a} = 12.6$ kcal/mol, the room temperature rate constant is doubled by a $10^{\circ}$ C increase in temperature ( $298$ K to $308$ K).

Statement II : For a first order reaction $A \to B$ . Here $[A]_{0}$ is the initial concentration of $A$ and $t_{1/2}$ is half-life of reaction.

In the light of the above statements, choose the correct answer from the option given below :

A
Both Statement I and Statement II are true
B
Both Statement I and Statement II are false
C
Statement I is true but Statement II is false
D
Statement I is false but Statement II is true

Solution

Statement I. Apply the Arrhenius equation in ratio form:

$ln (\frac{K _{2}}{K _{1}}) = \frac{E _{a}}{R} (\frac{T _{2} - T _{1}}{T _{1} T _{2}})$

Convert $E_{a} = 12.6$ kcal/mol $= 12.6 \times 1 0^{3} \times 4.2 = 52920$ J/mol. With $R = 8.314$ , $T_{1} = 298$ , $T_{2} = 308$ :

$ln (\frac{K _{2}}{K _{1}}) = \frac{52920}{8.314} \cdot \frac{10}{298 \times 308} \approx 6365 \cdot 1.089 \times 1 0^{- 4} \approx 0.693$

So $K_{2} / K_{1} = e^{0.693} = 2$ . Statement I is true.

Statement II. For a first-order reaction, $t_{1/2} = \frac{ln 2}{k}$ , which is independent of $[A]_{0}$ . The graph should be a horizontal line, not a sloped one through the origin. Statement II is false.

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JEE Main 2026 Apr 8 Shift 2, Chemistry Q7: Factors Affecting The Rate of a Chemical Reaction

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