For the first order reaction $\mathrm{A}\to \mathrm{B}$  the half life is $30 \min$. The time taken for $75\%$ completion of the reaction is mm. (Nearest integer)

Given : $\log 2=0.3010$

$\log 3=0.4771$

$\log 5=0.6989$

A first order reaction has the rate constant,  $\mathrm{k}=4.6\times {10}^{-3} {\mathrm{s}}^{-1}$. The number of correct statement/s from the following is/are Given: $\log 3=0.48$.

A. Reaction completes in $1000 \mathrm{s}$.
B. The reaction has a half-life of $500 \mathrm{s}$.
C. The time required for $10\%$ completion is 25 times the time required for 90% completion.
D. The degree of dissociation is equal to $\left(1-{\mathrm{e}}^{-\mathrm{kt}}\right)$.
E. The rate and the rate constant have the same unit.

For certain chemical reaction $\mathrm{X}\to \mathrm{Y}$, the rate of formation of product is plotted against the time as shown in the figure. The number of Correct statement/s from the following is _____ 

(A) Over all order of this reaction is one
(B) Order of this reaction can't be determined
(C) In region-I and III, the reaction is of first and zero order respectively
(D) In region-II, the reaction is of first order
(E) In region-II, the order of reaction is in the range of $0.1$ to $0.9$.

An organic compound undergoes first order decomposition. If the time taken for the $60\%$ decomposition is $540 \mathrm{s}$, then the time required for $90\%$ decomposition will be is _____ s. (Nearest integer).

Given : $\ln 10=2.3;\log 2=0.3$

$\mathrm{A}\to \mathrm{B}$

The rate constants of the above reaction at $200 \mathrm{K}$ and $300 \mathrm{K}$ are $0.03 {\min }^{-1}$ and $0.05 {\min }^{-1}$ respectively. The activation energy for the reaction is $\mathrm{J}$ (Nearest integer)

(Given : In $10=2.3$

$\mathrm{R}=8.3 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$

$\log 5=0.70$

$\log 3=0.48$

$\log 2=0.30$