Write equations of the following:
$(i)$ The integrated rate equation for a zero-order reaction.
$(ii)$ The integrated rate equation for a first-order reaction.

The rate constant for the reaction $H_2 + I_2 \to 2HI$ is $k_1 = 49$. What is the rate constant for the reverse reaction $2HI \to H_2 + I_2$?

Given below are two statements:
Statement $I$: The rate law for the reaction $A + B \rightarrow C$ is rate $(r) = k[A]^2[B]$. When the concentration of both $A$ and $B$ is doubled,the reaction rate is increased "$x$" times.
Statement $II$: The figure shows the variation in concentration against time plot for a "$y$" order reaction.
Concentration of $R$ vs Time plot: $A$ straight line with a negative slope equal to $-K$.
The value of $x + y$ is . . . . . .

$t_{100\%}$ is the time required for the $100\%$ completion of the reaction, while $t_{1/2}$ is the time required for $50\%$ of the reaction to be completed. Which of the following options correctly represents the relation between $t_{100\%}$ and $t_{1/2}$ for zero and first-order reactions, respectively?

Which of the following relations is correct for the given reaction orders?

Under the same reaction conditions, initial concentration of $1.386 \ mol \ dm^{-3}$ of a substance becomes half in $40 \ s$ and $20 \ s$ through first-order and zero-order kinetics respectively. Ratio $\left(\frac{k_{1}}{k_{0}}\right)$ of the rate constants for first-order $\left(k_{1}\right)$ and zero-order $\left(k_{0}\right)$ of the reactions is