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 reactions A $\rightarrow$ B, ![JEE Main 2026 Chemistry, Chemical Kinetics — question figure](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Chemistry/images/Chemical_Kinetics/69d8073b81239f6567c4f354/question_1__q_69d8073b81239f6567c4f354__cdn-question-pool.getmarks.app__08APRS2__q57_d1__be3a412c2c_final_ppt_sync.jpg) Here $[A]_o$ 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 options given below:

JEE Main 2026 — Chemistry Physical Chemistry

2026mcqmedium

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 reactions A $\rightarrow$ B,

JEE Main 2026 Chemistry, Chemical Kinetics — question figure

Here $[A]_o$ 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 options given below:

Official previous-year question

Held on 8 Apr 2026 · Verified 6 Jul 2026.

Options

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

Did you get this right?

Solution

For Statement I:

According to the Arrhenius equation:

$\log \left( \dfrac{k_2}{k_1} \right) = \dfrac{E_a}{2.303 R} \left( \dfrac{T_2 - T_1}{T_1 T_2} \right)$

Given that the rate constant doubles, $k_2 = 2k_1$ . The temperatures are $T_1 = 298$ K and $T_2 = 308$ K.

The gas constant $R = 8.314$ J K $^{-1}$ mol $^{-1} = \dfrac{8.314}{4.2}$ cal K $^{-1}$ mol $^{-1} \approx 1.98$ cal K $^{-1}$ mol $^{-1}$ .

Substituting the values:

$\log(2) = \dfrac{E_a}{2.303 \times 1.98} \left( \dfrac{308 - 298}{298 \times 308} \right)$

$0.301 = \dfrac{E_a}{4.56} \left( \dfrac{10}{91784} \right)$

$E_a = \dfrac{0.301 \times 4.56 \times 91784}{10} \approx 12598$ cal/mol $\approx 12.6$ kcal/mol.

Thus, Statement I is true.

For Statement II:

For a first order reaction, the half-life is given by:

$t_{1/2} = \dfrac{0.693}{k}$

This indicates that the half-life of a first order reaction is independent of the initial concentration $[A]_o$ . The graph of $t_{1/2}$ versus $[A]_o$ should be a horizontal line parallel to the concentration axis.

The given graph shows $t_{1/2}$ directly proportional to $[A]_o$ , which corresponds to a zero order reaction ( $t_{1/2} = \dfrac{[A]_o}{2k}$ ).

Thus, Statement II is false.

Therefore, Statement I is true but Statement II is false.

Answer: Statement I is true but Statement II is false

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Solution

For Statement I:

According to the Arrhenius equation:

$\log \left( \dfrac{k_2}{k_1} \right) = \dfrac{E_a}{2.303 R} \left( \dfrac{T_2 - T_1}{T_1 T_2} \right)$

Given that the rate constant doubles, $k_2 = 2k_1$ . The temperatures are $T_1 = 298$ K and $T_2 = 308$ K.

The gas constant $R = 8.314$ J K $^{-1}$ mol $^{-1} = \dfrac{8.314}{4.2}$ cal K $^{-1}$ mol $^{-1} \approx 1.98$ cal K $^{-1}$ mol $^{-1}$ .

Substituting the values:

$\log(2) = \dfrac{E_a}{2.303 \times 1.98} \left( \dfrac{308 - 298}{298 \times 308} \right)$

$0.301 = \dfrac{E_a}{4.56} \left( \dfrac{10}{91784} \right)$

$E_a = \dfrac{0.301 \times 4.56 \times 91784}{10} \approx 12598$ cal/mol $\approx 12.6$ kcal/mol.

Thus, Statement I is true.

For Statement II:

For a first order reaction, the half-life is given by:

$t_{1/2} = \dfrac{0.693}{k}$

The given graph shows $t_{1/2}$ directly proportional to $[A]_o$ , which corresponds to a zero order reaction ( $t_{1/2} = \dfrac{[A]_o}{2k}$ ).

Thus, Statement II is false.

Therefore, Statement I is true but Statement II is false.

Answer: Statement I is true but Statement II is false

JEE Main 2026 — Chemistry Physical Chemistry

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JEE Main 2026 — Chemistry Physical Chemistry

Options

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Solution

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JEE Main Physical Chemistry in other years

More JEE Main Physical Chemistry questions

Other Chemistry topics for JEE Main

Organic Chemistry

Inorganic Chemistry

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