Rate of first order reaction $A \rightarrow \text{product}$ is $0.01 \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the concentration of the reactant is $0.2 \ M$. (in $s^{-1}$)

Time required to decompose $SO_{2}Cl_{2}$ to half of its initial amount is $60 \ minutes$. If the decomposition is a first order reaction,calculate the rate constant of the reaction.

$R \rightarrow P$ is a first order reaction. For this reaction,a graph of $\ln [R]$ (on $y$-axis) and time (on $x$-axis) gives a straight line with a negative slope. The intercept on the $y$-axis is equal to ($k =$ rate constant):

Derive the equation showing the relation between the concentration $[R]_1$ and $[R]_2$ at time $t_1$ and $t_2$ for a first-order reaction.

The reaction $X \rightarrow$ products is a first order reaction. In $40 \ min$,the concentration of $X$ changes from $1.0 \ M$ to $0.25 \ M$. What is the rate of reaction when $[X] = 0.1 \ M$? $(\log 4 = 0.60)$

Which of the following plots is(are) correct for the given reaction? $( [P]_0$ is the initial concentration of $P$ $)$