$A $ gaseous hypothetical chemical equation $2A$ $ \rightleftharpoons  $ $4B + C$ is carried out in a closed vessel. The concentration of $ B$  is found to increase by $5 \times {10^{ - 3}}mol\,\,{l^{ - 1}}$ in $10 $ second. The rate of appearance of $B$  is

In a chemical reaction $A$ is converted into $B$ . The rates of reaction, starting with initial concentrations of $A$ as $2 \times {10^{ - 3}}\,M$ and $1 \times {10^{ - 3}}\,M$ , are equal to $2.40 \times {10^{ - 4}}\,M{s^{ - 1}}$ and $0.60 \times {10^{ - 4}}\,M{s^{ - 1}}$ respectively. The order of reaction with respect to reactant $A$ will be

For a reaction $2NO(g) + C{l_2}(g)$ $\rightleftharpoons$ $\,2NOCl(g)$. When concentration of $C{l_2}$ is doubled, the rate of reaction becomes two times of the original. When the concentration of $NO$  is doubled the rate becomes four times. What is the order of the reaction

The half-life of $2 $ sample are $0.1 $ and $ 0.4 $ seconds. Their respective concentration are $200 $ and  $ 50 $ respectively. What is the order of the reaction

The mechanism of the reaction $A + 2B \to  D$ is

$2B\xrightarrow{k}{B_2}\,\left[ {Slow} \right]$

${B_2} + A \to D\,\left[ {Fast} \right]$

The rate law expression, order with respect to $A$, order with respect to $'B'$ and overall order of reaction are respectively

The experimental data for decomposition of $N _{2} O _{5}$

$\left[2 N _{2} O _{5} \rightarrow 4 NO _{2}+ O _{2}\right]$

in gas phase at $318 \,K$ are given below:

$(i)$ Plot $\left[ N _{2} O _{5}\right]$ against $t$

$(ii)$ Find the half-life period for the reaction.

$(iii)$ Draw a graph between $\log \left[ N _{2} O _{5}\right]$ and $t$

$(iv)$ What is the rate law $?$

$(v)$ Calculate the rate constant.

$(vi)$ Calculate the half-life period from $k$ and compare it with $(ii)$.