Which of the following graphs is correct for | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For a first order reaction,the integrated rate equation is $\ln[R] = -kt + \ln[R]_0$,which can be rearranged as $\ln(\frac{[R]_0}{[R]}) = kt$.
Thi

Vedclass · Accepted Answer

Vedclass · Answer

(A) For a first order reaction,the integrated rate equation is $\ln[R] = -kt + \ln[R]_0$,which can be rearranged as $\ln(\frac{[R]_0}{[R]}) = kt$.
This implies that $\ln(\frac{[R]_0}{[R]})$ versus time $(t)$ is a straight line passing through the origin.
However,the graph of $\frac{[R]_0}{[R]}$ versus time $(t)$ is an exponential curve,not a straight line.
For a first order reaction,the half-life $t_{1/2} = \frac{0.693}{k}$ is independent of the initial concentration $[R]_0$.
Therefore,the graph of $t_{1/2}$ versus $[R]_0$ is a horizontal straight line parallel to the $[R]_0$ axis.
None of the provided graphs correctly represent the standard linear relationships for a first order reaction.
If we consider the plot of $\ln(\frac{[R]_0}{[R]})$ versus time,it is linear.
Given the options,if the question intended to ask for a plot that is $NOT$ linear or if there is a typo in the axis labels,the standard textbook graphs for first order are:
$1$. $\ln[R]$ vs $t$ (linear with negative slope)
$2$. $[R]$ vs $t$ (exponential decay)
$3$. $t_{1/2}$ vs $[R]_0$ (horizontal line).
Since none of the provided images match these,and assuming the question implies a specific relationship,the most common correct graph for first order kinetics is the linear plot of $\ln(\frac{[R]_0}{[R]})$ vs $t$.

Which of the following graphs is correct for a first order reaction $R \rightarrow P$?

Similar Questions

The effect of $pH$ on the rate constant for the hydrolysis of an ester is given by:

The reaction $A \xrightarrow{K} \text{Product}$ is zero order while the reaction $B \xrightarrow{K} \text{Product}$ is first order. For what initial concentration of $A$,the half-lives of the two reactions will be equal?

Which of the following statements is correct?

Which of the following statement$(s)$ is (are) correct?

Write the half-life $({t_{1/2}})$ equation and its unit for the following reactions:
$(i)$ Zero order reaction
$(ii)$ First order reaction

Vedclass Test Series

Exam Paper Generator

Online Exam Module