JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Chemical Kinetics

For the reaction

aA + bB \to cC + dD

, the plot of

lo g K

\frac{1}{T}

is given below :
The temperature at which the rate constant of the reaction is

1 0^{- 4} s^{- 1}

is ____ K.
(Rounded - off to the nearest integer)
[ Given : The rate constant of the reaction is

1 0^{- 5} s^{- 1}

at 500 K ]

Answer: 526

Solution

Taking logarithms of the Arrhenius equation,

lo g k = lo g A - \frac{E _{a}}{2.303 R T}

so a plot of

lo g k

against

\frac{1}{T}

is a straight line whose slope is

- \frac{E _{a}}{2.303 R}

; the graph gives that slope as

- 10000

K, and the line is therefore

lo g k = lo g A - \frac{10000}{T}

. At 500 K the rate constant is

1 0^{- 5} s^{- 1}

, so

- 5 = lo g A - \frac{10000}{500} \Rightarrow lo g A = 15

For

k = 1 0^{- 4} s^{- 1}

- 4 = 15 - \frac{10000}{T} \Rightarrow \frac{10000}{T} = 19 \Rightarrow T = 526.3 K

The rate constant reaches

1 0^{- 4} s^{- 1}

at 526 K.

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Integer answer