JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Chemical Kinetics

Given below are two statements :

R = 8.314 J K^{- 1} mol^{- 1}

and

1 cal = 4.2 J

Statement I : When

Ea = 12.6 kcal / mol

, the room temperature rate constant is doubled by a

1 0^{\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 are false✓ Correct
(D)Statement I is false but Statement II are true

Answer: (C)

Solution

By the Arrhenius equation,

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

. With

E_{a} = 12.6 kcal mo l^{- 1} = 12.6 \times 1 0^{3} \times 4.2 J mo l^{- 1}

ln \frac{k _{2}}{k _{1}} = \frac{12.6 \times 1 0 ^{3} \times 4.2}{8.314} \cdot \frac{10}{298 \times 308} = 0.693

, so

\frac{k _{2}}{k _{1}} = 2

and the rate constant does double over the ten-degree rise; the first statement is true. For a first-order reaction

t_{1/2} = \frac{ln 2}{k}

, which is independent of the initial concentration, so a plot of

t_{1/2}

against

[A]_{0}

is a horizontal line, not the straight line through the origin shown; the second statement is false. The first statement is true and the second is false.

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Chemical Kinetics

Solution

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