Consider the following reaction

$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$

The time taken for A to become $1 / 4^{\text {th }}$ of its initial concentration is twice the time taken to become $1 / 2$ of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis.

The overall order of the reaction is ________.

<p>To determine the overall order of the reaction given by $\mathrm{A} + \mathrm{B} \rightarrow \mathrm{C}$, we can derive the information based on the given details about the kinetics of reactant A and the graphical behavior of reactant B.</p> <p>The first piece of information tells us that the time for the concentration of A to reduce to $1/4$ of its initial concentration ($[A]_0/4$) is twice the time it takes to reduce to half of its initial concentration ($[A]_0/2$). This characteristic is a hallmark of first-order reactions. In first-order reactions, the time it takes for the concentration of the reactant to reduce to half of its initial value (known as the half-life, $t_{1/2}$) is constant and does not depend on the initial concentration. Specifically, the fact that the concentration decreases by a factor of 4 (to $1/4$ its initial value) in twice the time it takes to decrease by a factor of 2 (to $1/2$ its initial value) indicates a constant half-life, consistent with first-order kinetics for reactant A.</p> <p>As for reactant B, the information provided is that a plot of its concentration change over time is a straight line with a negative slope and a positive intercept on the concentration axis. This description matches the behavior of a reactant in a reaction of zero-order kinetics with respect to B, where the rate of reaction is constant and independent of the concentration of B. In zero-order reactions, the concentration of the reactant decreases linearly over time, since the rate of decrease is constant.</p> <p>Therefore, considering the kinetics of both A and B:</p> <ul> <li>Reactant A shows first-order kinetics.</li> <li>Reactant B shows zero-order kinetics.</li> </ul> <p>The overall order of the reaction is the sum of the individual orders with respect to each reactant, which gives us:</p> <p>$$\text{Overall order} = \text{Order with respect to A} + \text{Order with respect to B} = 1 (A) + 0 (B) = 1.$$</p> <p>Hence, the overall order of the reaction is 1.</p>