If the relation between half-life time $(t_{1/2})$ and initial concentration $[R]_0$ is given by $t_{1/2} \propto \frac{1}{[R]_0^{n-1}}$,what is the order of the reaction?

If a reaction has the experimental rate expression $\text{rate} = K [A]^2[B]$,what happens to the reaction rate if the concentration of $A$ is doubled and the concentration of $B$ is halved?

$A$ 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 $1 \ hour$?

The three experimental data sets for determining the differential rate of the reaction $2 NO_{(g)} + Cl_{2_{(g)}} \rightarrow 2 NOCl_{(g)}$ at a definite temperature are given below. (Note: The data table was missing in the input,assuming standard values for this reaction: $Exp 1: [NO]=0.1, [Cl_2]=0.1, Rate=0.18$; $Exp 2: [NO]=0.1, [Cl_2]=0.2, Rate=0.36$; $Exp 3: [NO]=0.2, [Cl_2]=0.1, Rate=0.72$).
$(a)$ Derive the differential rate law of the reaction.
$(b)$ Calculate the order of the reaction.
$(c)$ Calculate the value of the rate constant.

The rate constant for the reaction $2N_2O_5 \to 4NO_2 + O_2$ is $3.0 \times 10^{-5} \, sec^{-1}$. If the rate is $2.40 \times 10^{-5} \, M \, sec^{-1}$,then the concentration of $N_2O_5$ (in $M$) is?

Half-life periods for a reaction at initial concentrations of $0.1 \ M$ and $0.01 \ M$ are $5$ and $50$ minutes,respectively. The order of reaction is