Rate law for a reaction between $A$ and $B$ is given by

$$\mathrm{r}=\mathrm{k}[\mathrm{~A}]^{\mathrm{n}}[\mathrm{~B}]^{\mathrm{m}}$$

If concentration of $A$ is doubled and concentration of $B$ is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{r_2}{r_1}\right)$ is

Consider the following statements related to temperature dependence of rate constants.

Identify the correct statements.

A. The Arrhenius equation holds true only for an elementary homogenous reaction.

B. The unit of $A$ is same as that of $k$ in Arrhenius equation.

C. At a given temperature, a low activation energy means a fast reaction.

D. A and Ea as used in Arrhenius equation depend on temperature.

E. When $\mathrm{Ea} \gg \mathrm{RT}, \mathrm{A}$ and Ea become interdependent.

Choose the correct answer from the options given below:

In a reaction $A+B \rightarrow C$, initial concentrations of $A$ and $B$ are related as $[A]_0=8[B]_0$. The half lives of $A$ and $B$ are 10 min and 40 min , respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

Reactant A converts to product D through the given mechanism (with the net evolution of heat):

A → B     slow;     ΔH = +ve

B → C     fast;     ΔH = -ve

C → D     fast;     ΔH = -ve

Which of the following represents the above reaction mechanism?