The half-life of a first-order reaction is $20 \text{ minutes}$. What is the rate constant (in $\text{min}^{-1}$) for this reaction?

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

The degree of dissociation of a first-order reaction is

The rate constant for a first order reaction is $60 \text{ s}^{-1}$. How much time (in seconds) will it take to reduce the initial concentration of the reactant to its $1/16^{th}$ value?

If the half-life $(t_{1/2})$ of a first-order reaction is $20 \ minutes$,what fraction of the reactant remains after $40 \ minutes$?

Identify True $(T)$ and False $(F)$ statements for the following expressions regarding a first-order reaction $R \rightarrow P$:
Statement $I$: $\text{Rate} = -\frac{d[R]}{dt} = k[R]$
Statement $II$: $\text{Rate} = -\frac{d[R]}{dt} = -k[R]$