For a chemical reaction,$m A \rightarrow x B$,the rate law is $r = k[A]^{2}$. If the concentration of $A$ is doubled,the reaction rate will be,

Which function of $[X]$ plotted against time will give a straight line for a second order reaction? $X \to \text{Product}$

For a reaction $A + B \to$ product,it was found that the rate of reaction increases four times if the concentration of $A$ is doubled,but the rate of reaction remains unaffected if the concentration of $B$ is doubled. Hence,the rate law for the reaction is

Write the unit of the rate constant for the following reactions:
$1.$ Fourth order
$2.$ Third order

$A$ bacterial infection in an internal wound grows as $N(t) = N_0 \exp(t)$,where the time $t$ is in hours. $A$ dose of antibiotic,taken orally,needs $1 \ hour$ to reach the wound. Once it reaches there,the bacterial population decreases as $\frac{dN}{dt} = -5N^2$. What will be the plot of $\frac{N_0}{N}$ vs. $t$ after $1 \ hour$?

For the reaction $2A + 2B \rightarrow 2C + D$,the rate law is expressed as $\text{rate} = k[A]^2[B]$. Calculate the rate constant if the rate of reaction is $0.24 \ mol \ dm^{-3} \ s^{-1}$ where $[A] = 0.5 \ M$ and $[B] = 0.2 \ M$.