Question

Which of the following graphs is correct for a first order reaction?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C), (D)

Analysing the graphs of $t\frac{1}{2}$ vs $[R{]}_0$

Half life of first order reaction is:

$t_{\frac{1}{2}}=\frac{0.693}{k}$

So, half-life for a first-order reaction is independent of the initial concentration of the reactant. The graph between half life and initial concentration of the reactant can be plotted as:


So, graph will be a horizontal straight line.

Hence, option $\left(A\right)$ is correct while option $\left(B\right)$ is incorrect.

Analyzing the graph of $\log \frac{\left[R_0\right]}{\left[R\right]}$ vs $t$

For the first-order reaction,

$t=\frac{2.303}{k}\log \frac{\left[R_0\right]}{\left[R\right]}$

$\log \frac{\left[R_0\right]}{\left[R\right]}=\frac{k}{2.303}t$

Comparing this equation with the equation of a straight line,

$y=mx$

The graph will be as given below:

Hence, option $\left(D\right)$ is correct.

Also, option $\left(C\right)$ is incorrect because the concentration of the product increases with time. But in the graph, it has been shown as decreasing.

Hence, options $\left(A\right)$ and $\left(D\right)$ are the correct answers.