What is a zero order reaction? Determine the integrated rate equation for a zero order reaction $R \to P$.

$A$ zero order reaction is a reaction in which the rate of reaction is proportional to the zero power of the concentration of reactants.
$\therefore \text{Rate} \propto [R]^{0}$
For the given reaction $R \to P$,which is a zero order reaction,the differential rate expression is:
$\text{Rate} = -\frac{d[R]}{dt} = k[R]^{0}$
Since $[R]^{0} = 1$,we have:
$-\frac{d[R]}{dt} = k \quad \dots (i)$
Rearranging the equation:
$d[R] = -k dt \quad \dots (ii)$
Integrating both sides:
$[R] = -kt + I \quad \dots (iii)$
where $I$ is the constant of integration.
At $t = 0$,the concentration of the reactant $[R] = [R]_{0}$,where $[R]_{0}$ is the initial concentration.
Substituting these values into equation $(iii)$:
$[R]_{0} = (-k \times 0) + I$
$\therefore I = [R]_{0} \quad \dots (iv)$
Substituting the value of $I$ back into equation $(iii)$:
$[R] = -kt + [R]_{0}$
Rearranging to solve for $k$:
$kt = [R]_{0} - [R]$
$\therefore k = \frac{[R]_{0} - [R]}{t}$