Question

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

Answer 1

The correct option is B first order

$\because Rate=\frac{-d\left[A\right]}{dt}=k\left[A\right]${By differential form of rate law}

$⟹\frac{d\left[A\right]}{\left[A\right]}=-kdt$

$⟹\ln \left[A\right]-\ln [A{]}_o=-kt${By integrating both sides}

$⟹\ln \left[A\right]=-kt+\ln [A{]}_o$

$⟹\log \left[A\right]=\log (a-x)=-\frac{kt}{2.303}+\log a$

Above expression is for a straight line with slope equal to $\frac{-k}{2.303}.$

So the reaction is of the first order.