JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Chemical Kinetics

Consider the following single step reaction in gas phase at constant temperature.

2 A_{(g)} + B_{(g)} \to C_{(g)}

The initial rate of the reaction is recorded as

r_{1}

when the reaction starts with 1.5 atm pressure of A and 0.7 atm pressure of B. After some time, the rate

r_{2}

is recorded when the pressure of

C

becomes 0.5 atm. The ratio

r_{1} : r_{2}

is ______

\times 1 0^{- 1}

.
(Nearest integer)

Answer: 315

Solution

Rate law for the elementary step:

r = k [P_{A}]^{2} [P_{B}]

.
Initially:

r_{1} = k (1.5)^{2} (0.7)

.
When

P_{C} = 0.5

atm has formed, by the stoichiometry

2 A + B \to C

P_{A}

has fallen by

2 (0.5) = 1.0

atm to

0.5

atm and

P_{B}

0.5

atm to

0.2

atm:

r_{2} = k (0.5)^{2} (0.2)

\frac{r _{1}}{r _{2}} = \frac{( 1.5 ) ^{2} ( 0.7 )}{( 0.5 ) ^{2} ( 0.2 )} = \frac{1.575}{0.05} = 31.5 = 315 \times 1 0^{- 1}

JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Integer answer