Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# A plot of log(a-x) against time ’t’ is a straight line. This indicates that the reaction is of:(A) Zero order(B) First order(C) Second order(D) Third order

Last updated date: 14th Sep 2024
Total views: 371.6k
Views today: 8.71k
Verified
371.6k+ views
Hint: Reaction in which the reaction rate is linearly dependent on the concentration of only one reactant is called a first order reaction.

We know that for a first order reaction,
${\text{ - }}\dfrac{{{\text{dC}}}}{{{\text{dt}}}}{\text{ = k}}{\text{.C}}$
On integrating we get, $\int\limits_{{{\text{C}}_{\text{0}}}}^{\text{C}} {\dfrac{{{\text{dC}}}}{{\text{C}}}} {\text{ = - k }}\int\limits_{\text{0}}^{\text{t}} {{\text{dt}}}$
Where, ${{\text{C}}_0}$ is the concentration of the reactant at time t = 0 and C is the concentration of the reactant at time t = t.
So, we get, ${\text{log C - log}}{{\text{C}}_0}{\text{ = - k}}{\text{. t}}$
${\text{log C = - k}}{\text{.t + log }}{{\text{C}}_0}$
But, ${\text{log }}{{\text{C}}_0}$ is the initial concentration of the reactant which will be constant. So, if ${{\text{C}}_0}$ i.e. initial concentration of the reactant is considered to be ‘a’ then C which is concentration at time t will be (a-x).
So, we write it as ${\text{log (a - x) = - k}}{\text{.t + log a}}$. This equation is of the form ${\text{y = mx + c}}$.
Thus, graph of log(a-x) against time ’t’ will look like –

Hence, option B is correct.