For a given reaction $\mathrm{R} \rightarrow \mathrm{P}$, $\mathrm{t}_{1 / 2}$ is related to $[\mathrm{A}]_{0}$ as given in table : | $[\mathrm{A}]_{0} / \mathrm{molL}^{-1}$ | $\mathrm{t}_{1 / 2} / \mathrm{min}$ | |---|---| | 0.100 | 200 | | 0.025 | 100 | Given : $\log 2$ = 0.30 Which of the following is true? A. The order of the reaction is $\frac{1}{2}$. B. If $[\mathrm{A}]_{0}$ is 1 M , then $\mathrm{t}_{1 / 2}$ is $200 \sqrt{10} \mathrm{~min}$ C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100 M to 0.500 M . D. $\mathrm{t}_{1 / 2}$ is 800 min for $[\mathrm{A}]_{0}=1.6 \mathrm{M}$ Choose the correct answer from the options given below:

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Chemical Kinetics

For a given reaction

R \to P

t_{1/2}

is related to

[A]_{0}

as given in table :

$[A]_{0} / molL^{- 1}$	$t_{1/2} / min$
0.100	200
0.025	100

Given :

lo g 2

= 0.30
Which of the following is true?
A. The order of the reaction is

\frac{1}{2}

.
B. If

[A]_{0}

is 1 M , then

t_{1/2}

20010 min

C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100 M to 0.500 M .
D.

t_{1/2}

is 800 min for

[A]_{0} = 1.6 M

Choose the correct answer from the options given below:

(A)A and C only
(B)A and B only
(C)A, B and D only✓ Correct
(D)C and D only

Answer: (C)

Solution

Between the two data points,

[A]_{0}

drops by a factor of 4 (0.100 to 0.025 M) while

t_{1/2}

drops by a factor of 2 (200 to 100 min). Since

t_{1/2} \propto [A]_{0}^{1 - n}

(1/4)^{1 - n} = 1/2

gives

1 - n = 1/2

, so

n = 1/2

— statement A is true. Because

t_{1/2} \propto [A]_{0}

t_{1/2} = 200 [A]_{0} /0.1

; at

[A]_{0} = 1

M this gives

t_{1/2} = 20010

min (statement B true), and at

[A]_{0} = 1.6

t_{1/2} = 20016 = 800

min (statement D true). The order of a reaction is a fixed property of its rate law and does not change with the concentration used, so statement C, which claims the order shifts to 1 at higher concentration, is false. The true statements are A, B and D.

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Chemical Kinetics

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