JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Chemical Kinetics

Consider the following first order gas phase reaction at constant temperature

A (g) \to 2 B (g) + C (g)

If the total pressure of the gases is found to be 200 torr after 23 sec . and 300 torr upon the complete decomposition of A after a very long time, then the rate constant of the given reaction is ____

\times 1 0^{- 2} s^{- 1}

(nearest integer)
[Given :

lo g_{10} (2) = 0.301

]

Answer: 3

Solution

A (g) \to 2 B (g) + C (g)

: total moles triple on complete decomposition, so

3 P_{0} = 300 ⟹ P_{0} = 100

torr.

At

t = 23

s, if

x

is the pressure of A reacted, total pressure

= P_{0} + 2 x = 200 ⟹ x = 50

; remaining

P_{A} = P_{0} - x = 50

torr.

For a first-order reaction:

k = \frac{1}{t} ln \frac{P _{0}}{P _{A}} = \frac{1}{23} ln \frac{100}{50} = \frac{2.303 \times 0.301}{23} \approx 0.0301 s^{- 1} = 3.01 \times 1 0^{- 2} s^{- 1} \approx 3 \times 1 0^{- 2} s^{- 1}

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Integer answer

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JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Chemical Kinetics

Solution

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