Zero Order Reaction MCQ - Practice Questions & Answers

Quick Facts

Zero Order Kinetics - Zero Order Reaction, Integrated Rate Law - Zero Order Reaction, Half Life and Life Time of Reaction, Graphs for Zero-Order Reaction is considered one of the most asked concept.
38 Questions around this concept.

Concepts Covered - 5

Zero Order Kinetics - Zero Order Reaction

In such reactions rate of reaction is independent of concentration of the reactants.
   $\frac{-\mathrm{dx}}{\mathrm{dt}} \propto[\text { concentration }]^{0}$
   $\text { that is, } \mathrm{dx} / \mathrm{dt}=\mathrm{K}$
On integration we get:
   $\mathrm{x=K t+C}$
if c = 0, t = 0 then
$\begin{array}{l}{\mathrm{x}=\mathrm{Kt}} \\ {\mathrm{K}=\mathrm{x} / \mathrm{t}}\end{array}$
$\text { Unit of } \mathrm{K} \text { is } \mathrm{mol} \: \mathrm{L}^{-1} \text { time }^{-1}$
Example: Photo Chemical reaction.
$\bullet \: \: t_{\frac{1}{2}}=\text { time required for half completion of reaction }=\frac{a}{2 k}$

Integrated Rate Law - Zero Order Reaction

Zero order reaction means that the rate of the reaction is proportional to zero power of the concentration of reactants. Consider the reaction,

$\mathrm{A\rightarrow P}$

$\text { Rate }=-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\mathrm{k[A]^{0}}$

$\text { Rate }=-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\mathrm{k\: x\: 1}$

$\mathrm{d[A]\: =\: -kdt}$

At t = 0, A = A_o
At t = t, A = A
Thus, on integrating both sides, we get:

$[\mathrm{A}]=\mathrm{-kt}+[\mathrm{A]_{o}}$

Comparing the above equation with the equation of a straight line, y = mx + c, if we plot [R] against t, we get a straight line as shown in the above figure with slope = –k and intercept equal to [R]_o.

Further simplifying the above equation, we get the rate constant, k as:

$\mathrm{k=\frac{[\mathrm{A}]_{0}-[\mathrm{A}]}{t}}$

Half Life and Life Time of Reaction

Half-life of reaction: The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration. It is represented as t_1/2.
For a zero order reaction, rate constant is given as follows:

$\mathrm{k=\frac{[\mathrm{A}]_{o}-[\mathrm{A}]}{t}}$
At t = t_1/2, [A] = [A]_o/2
Thus, the rate constant at t_1/2 becomes:

$\mathrm{k=\frac{[\mathrm{A}]_{0}-1 / 2[\mathrm{A}]_{0}}{t_{1 / 2}}}$
$\mathrm{t_{1 / 2}=\frac{[\mathrm{R}]_{0}}{2 \mathrm{k}}}$
Thus, it is clear that t_1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant.
Life time of Reaction: It is time in which 100% of the reaction completes. It is represented as t_lf.
Thus, at t = t_lf, A = 0
Now, from zero order equation, we know:

$\mathrm{A\: =\: A_{o}\: -\: kt}$

$\mathrm{0\: =\: A_{o}\: -\: kt_{lf}}$

$\mathrm{Thus, t_{lf}\: =\:\frac{A_{o}}{k}}$

Graphs for Zero-Order Reaction

Special Zero Order Reaction

This concept can be understood by the following example:

Example:
The reaction occurs as follows:
$\mathrm{3A\: \rightarrow \: P}$
Initial concentration of A is given as and rate of the reaction(r) is given as k[A]^o. Find the concentration of A after time 't' and also determine the half life of A.