1. Tardigrade
  2. Question
  3. Chemistry
  4. Rate constant (K) varies with temperature as given by equation log K( min -1)=5-(2000/T) Consider the following about this equation I. Pre exponential factor is 105. II. Ea is 9.212 kcal. III. Variation of log K with (1/T) is linear. Select the correct statement.

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Q. Rate constant $(K)$ varies with temperature as given by equation
$\log K\left(\min ^{-1}\right)=5-\frac{2000}{T}$
Consider the following about this equation
I. Pre exponential factor is $10^{5}$.
II. $E_{a}$ is $9.212\, kcal$.
III. Variation of $\log K$ with $\frac{1}{T}$ is linear.
Select the correct statement.

AIIMSAIIMS 2017

Solution:

Given,
$\log k\left(\min ^{-1}\right)=5-\frac{2000}{T}$ ...(i)
$\because \log _{10} k=\log _{10} A-\frac{E_{a}}{2.303 R T}$ ...(ii)
On comparing equations (i) and (ii)
I. $\log A=5$ or $A=10^{5}$
Thus, (i) is true
II. $\frac{E_{a}}{2.303 R}=2000$
$E_{a}=2.30 \times 2000 \times 0.002\, kcal$
$\therefore E_{a}=9.212\, kcal$
Thus (ii) is true.
III. From Eq. (ii) it is clear that, $\log k \propto \frac{1}{T}$
$\therefore $ Thus (III) is also false.