Consider the first order reaction $R \to P$. The fraction of molecules decomposed in the given first order reaction can be expressed as:

What is the value of the rate constant of a first-order reaction if the slope of the graph between $\log_{10} \frac{[A]_0}{[A]_t}$ ($y$-axis) and time ($x$-axis) is $1 \times 10^{-3}$?

For a certain first order reaction,$32 \%$ of the reactant is left after $570 \ s$. The rate constant of this reaction is ........... $\times 10^{-3} \ s^{-1}$. (Round off to the Nearest Integer).
$[$Given: $\log_{10} 2 = 0.301, \ln 10 = 2.303]$

The decomposition of $N_2O_5$ occurs as $2N_2O_5 \to 4NO_2 + O_2$ and follows first-order kinetics. Hence,

At $500\,^oC$,cyclopropane isomerizes to propene. This reaction is first order with a rate constant of $6.7 \times 10^{-4}\,s^{-1}$. If the initial concentration of cyclopropane is $0.05\, M$,what will be the molarity of cyclopropane after $30\, min$ (in $, M$)?

Time required to decompose $SO_2Cl_2$ to half of its initial amount is $40 \ minutes$. If the decomposition is a first order reaction,what will be the rate constant of the reaction?