JEE Main 2025 Jan 24 Shift 2, Chemistry Q2: Reactions of Various Orders

JEE Main2025Jan 24, Shift 2Chemistry

Given below are two statements :

Statement (I) :

Statement (II) :

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

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

Solution

For a first order reaction the half-life depends only on the rate constant:

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

Since $t_{1/2}$ is independent of the initial concentration $[R]_{0}$ , the plot of $t_{1/2}$ against $[R]_{0}$ is a horizontal line. Statement I is correct.

The integrated rate law for a first order reaction is:

$lo g \frac{[ R ] _{0}}{[ R ]} = \frac{k}{2.303} t$

This means a plot of $lo g \frac{[ R ] _{0}}{[ R ]}$ versus $t$ is a straight line through the origin with slope $\frac{k}{2.303}$ . The plot drawn in Statement II uses $lo g \frac{[ R ]}{[ R ] _{0}}$ instead, which would give a line of slope $- \frac{k}{2.303}$ , not $+ \frac{k}{2.303}$ . Statement II is incorrect.

Correct option: (4)

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JEE Main 2025 Jan 24 Shift 2, Chemistry Q2: Reactions of Various Orders

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