For a certain reaction \(R \rightarrow\) Product, the plot of concentration \([R]\) vs time has a negative slope as shown. The order of reaction is :

(A) From the given graph, the plot of concentration \([R]\) versus time \(t\) is a straight line with a negative slope.
The equation for this straight line can be written as:
\(\begin{aligned}& y=m x+c \ 
{[R]=(\text { slope }) \times t+\text { intercept }}\end{aligned}\)
Given that the intercept is \(\left[R_0\right]\) and the slope is \(- k\), the equation becomes:
\([R]=-k t+\left[R_0\right]\)
This equation represents the integrated rate law for a zero-order reaction. For a zero-order reaction, the rate of reaction is independent of the concentration of the reactant:
\(\text { Rate }=-\frac{d[R]}{d t}=k[R]^0=k\)
Integrating both sides:
\(\int_{\left[R_0\right]}^{[R]} d[R]=-k \int_0^t dt\)
\({[R]-\left[R_0\right]=-k t}\)
\({[R]=-k t+\left[R_0\right]}\)
Since the graph matches this equation, the order of the reaction is 0 .