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.
37 Questions around this concept.

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Units of the rate constant of first and zero-order reactions in terms of molarity M unit are respectively.

$sec^{-1},Msec^{-1},$

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$sec^{-1},M$

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$Msec^{-1},sec^{-1},$

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$M,sec^{-1},$

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The unit of rate constant for a zero order reaction is :

L² mol^-2 s^-1

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s^-1

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mol L^-1 s^-1

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L mol^-1 s^-1

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for a zero-order reactor, the plot of concentration versus time is:

A straight line with positive slope

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A straight line with a negative slope

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A curved line

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If horizontal line

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Select the corret option regarding zero-ordes Reaction

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Select the correct half-life for a 3 order reaction.

$\frac{1}{2} \frac{k}{a^2}$

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$a^2 / 2 k$

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$2 \mathrm{k} / \mathrm{a}$

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$a / 2 k$

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select the correct option from the following about the unit of rate constant for zero order reaction?

$mol L-1 S^{-1}$

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$mol L S^{-1}$

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$Lmol ^{-1} S^{-1}$

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$S^{-1}$

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Which of the following represent the zero order reaction?

$\mathrm{\left[A_0\right]-\left[A_t]=k t\right.}$

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$\mathrm{[A]_0+(A)_t=k t}$

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$\mathrm{k t=2.303 \log \left(A_0 / A_t\right)}$

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$\mathrm{\frac{1}{(A)_0}-\frac{1}{(A)_t}=k t}$

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Consider the reaction follows zero order reaction. What is the t completion or t 100% of the reaction if $\mathrm{\text { (A) }_{\circ}}$ is initial concentration of reaction k is rate constant

$\mathrm{(A)_0-(A)}$

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$\mathrm{(A)_{0} / K}$

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Can't predicted

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$\mathrm{\frac{1}{k}}$

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The correct of plot for first order reaction is :

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Calculate the half life and completion time, respectively of a zero order reaction:

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

If concentration of A initially and after 15 min is 0.5 M and 0.015 M, respectively

10,20

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25,50

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$2 \times 10^{-3}, 4 \times 10^{-3}$

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7.73,15.47

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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.