JEE Main 2025 Apr 7 Shift 1, Chemistry Q3: Reactions of Various Orders

JEE Main2025Apr 7, Shift 1Chemistry

Reaction A(g) $\to$ 2B(g) + C(g) is a first order reaction. It was started with pure A

t/min	Pressure of system at time t/mm Hg
10	160
$\infty$	240

Which of the following option is incorrect ?

A
Initial pressure of A is 80 mm Hg
B
The reaction never goes to completion
C
Rate constant of the reaction is 1.693 min $^{- 1}$
D
Partial pressure of A after 10 minute is 40 mm Hg

Solution

Let the initial pressure of A be $P_{0}$ . Set up the pressure book-keeping:

	A	B	C
$t = 0$	$P_{0}$	0	0
$t = \infty$	0	$2 P_{0}$	$P_{0}$

At $t = \infty$ : $P_{total} = 3 P_{0} = 240 \Rightarrow P_{0} = 80$ mm Hg. So option (1) is correct.

Finding the rate constant: At $t = 10$ min, $P_{total} = 160$ . Using $P_{0} = 80$ and the integrated first-order form in terms of total pressure,

$k = \frac{1}{t} ln (\frac{P _{\infty} - P _{0}}{P _{\infty} - P _{t}}) = \frac{1}{10} ln (\frac{240 - 80}{240 - 160}) = \frac{ln 2}{10} \approx 0.0693 min^{- 1}$

The value claimed in option (3), 1.693 min $^{- 1}$ , is wrong by more than an order of magnitude. So option (3) is the incorrect statement.

For completeness: a first-order decay only reaches zero concentration asymptotically, so option (2) is true. And at $t = 10$ min, partial pressure of A is $P_{0} \cdot \frac{1}{2} = 40$ mm Hg (since exactly one half-life has elapsed), so option (4) is true.

$∴$ The incorrect option is (3).

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JEE Main 2025 Apr 7 Shift 1, Chemistry Q3: Reactions of Various Orders

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