The rate law for the reaction $A + B \rightarrow \text{product}$ is given by $\text{rate} = k[A][B]$. Calculate $[A]$ if the rate of reaction and rate constant are $0.25 \ mol \ dm^{-3} \ s^{-1}$ and $6.25 \ mol^{-1} \ dm^3 \ s^{-1}$ respectively,and $[B] = 0.25 \ mol \ dm^{-3}$.

For the reaction $2N_2O_5 \to 4NO_2 + O_2$,the rate of reaction and rate constant are $1.02 \times 10^{-4} \ mol \ L^{-1} \ s^{-1}$ and $3.4 \times 10^{-5} \ s^{-1}$ respectively. The concentration of $N_2O_5$ at that time will be:

The rate law for the reaction $A + B \rightarrow \text{product}$ is $\text{rate} = k[A][B]$. When will the rate of reaction increase by a factor of $2$?

For a certain reaction $A_{(g)} \to B_{(g)}$,the half-life for different initial pressures of $A$ is given below:

$P_{A_0} \text{ (atm)}$	$0.1$	$0.025$
$t_{1/2} \text{ (sec)}$	$100$	$50$

The correct statement about the order of reaction is:

Write the differential rate expression for the following reactions and determine their order of reaction:
$1) \ 2 N_2O_5(g) \rightarrow 4 NO_2(g) + O_2(g)$
$2) \ C_4H_9Cl(aq) + OH^-(aq) \rightarrow C_4H_9OH(aq) + Cl^-(aq)$

Consider the following single step reaction in gas phase at constant temperature.
$2 \ A_{(g)} + B_{(g)} \rightarrow C_{(g)}$
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 $\qquad$ $\times 10^{-1}$.
(Nearest integer)