For a hypothetical reaction,$A \rightarrow C$. The mechanism is: $A \underset{k_2}{\stackrel{k_1}{\rightleftharpoons}} B$ (Fast),$A + B \xrightarrow{k_3} C$ (Slow). The rate law for this reaction is:

What is the unit of the rate constant for a $4^{th}$ order reaction?

Consider the reaction between chlorine and nitric oxide:
$Cl_{2(g)} + 2NO_{(g)} \rightarrow 2NOCl_{(g)}$
On doubling the concentration of both reactants,the rate of the reaction increases by a factor of $8$. However,if only the concentration of $Cl_2$ is doubled,the rate increases by a factor of $2$. The order of this reaction with respect to $NO$ is :

For a particular reaction,the rate expression is given as $r = k[A][B]^{0.5}$. If the volume of the vessel is reduced to one-fourth of the initial volume,the rate of reaction would

From the rate expression for the following reaction,determine its order of reaction and the dimensions of the rate constant.
$(iii)$ $CH_{3}CHO_{(g)} \rightarrow CH_{4(g)} + CO_{(g)} \quad$ Rate $= k[CH_{3}CHO]^{3/2}$

What is the time taken for the $3^{rd}$ half-life of a second-order decomposition reaction,given that its first half-life is $20 \ s$ (in $s$)?