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First Order Reaction - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • First Order Reaction, Half Life of First Order Reaction, Graphs of First Order Kinetics are considered the most difficult concepts.

  • 77 Questions around this concept.

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QuestionEASY

t_{1/4}  can be taken as the time taken for the concentration of a reactant to drop to 3/4 of its initial value. If the rate constant for a first order reaction is k, the  t_{1/4}  can be written as

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The rate equation for the reaction 2A+B\rightarrow C is found to be : rate =k\left [ A \right ]\left [ B \right ]. The correct statement in relation to this reaction is that the

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The half-life period of a first-order reaction is 15 minutes. The amount of substance left after one hour will be :

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

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Select the reaction which is not follows the first order Kinetics:

 

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If we start a reaction from 100 mol, having the rate constant is \mathrm{0.0693 \mathrm{~min}^{-1}}. What will be the rate of the reaction offer 20 min.

 

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Which of the following reactions is first order reaction

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Which of the following correctly represents the first order reaction.

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Which expression is not correctly represent the first order reaction?

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Consider a reaction \mathrm{A \rightarrow B+C} follow the first-order kinetics with a rate constant \mathrm{( k ) \: 0.02 \mathrm{~s}^{-1}}. What percentage of A will be left after after 5 half-lives?

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Concepts Covered - 4

First Order Reaction

The rate of the reaction is proportional to the first power.

                                

The chemical reaction occurs as follows:

R    \rightarrow        P

a                 0

a-x             x

We have,
rate[r]=K[R]^{1}

\frac{-d(a-x)}{dt}=K(a-x)

\frac{-dx}{dt}=K(a-x)  [differentiate rate law]

ln \:[\frac{a}{a-x}]=kt \:(Integrated\: rate\: law)

\mathrm{k\: =\: \frac{1}{t}\, ln\left [ \frac{a}{a-x} \right ]}

Unit of k=sec^{-1}

Other Forms of Rate Law

We know that the first-order equation is given as follows:

\mathrm{log_{10}A\: =\: log_{10}A_{o}\: -\: \frac{kt}{2.303}}

But there are other forms of rate law also available that we use for different purposes. These forms are mentioned below:

  • Use to solve numericals:

    \mathrm{log_{10}A\: =\: log_{10}A_{o}\: -\: \frac{kt}{2.303}}

    \mathrm{\Rightarrow log_{10}\left [ \frac{A_{o}}{A} \right]\: =\: \frac{kt}{2.303}}

    \mathrm{Thus, t\: =\: \frac{2.303}{k}\, log_{10}\left [ \frac{A_{o}}{A} \right]}
     
  • Exponential form:

    \mathrm{log_{e}A\: -\: log_{e}A_{o}\: -kt}
    \\\mathrm{\Rightarrow log\frac{A}{A_{o}}\: =\: -kt}\\\\\mathrm{\Rightarrow \frac{A}{A_{o}}\: =\: e^{-kt}}\\\\\mathrm{Thus,\: A\: =\: A_{o}e^{-kt}}
    This equation is also known as exponential form.
Half Life of First Order 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 t1/2.
For a zero order reaction, rate constant is given as:
k=\frac{[\mathrm{R}]_{0}-[\mathrm{R}]}{t}
\text { At } t=t_{1 / 2}, \quad[\mathrm{R}]=\frac{1}{2}[\mathrm{R}]_{0}
The rate constant at t1/2 becomes:

k=\frac{[\mathrm{R}]_{0}-1 / 2[\mathrm{R}]_{0}}{t_{1 / 2}}

t_{1 / 2}=\frac{[\mathrm{R}]_{0}}{2 \mathrm{k}}
It is clear that t1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant.
For the first order reaction,

k=\frac{2.303}{t} \log \frac{[\mathrm{R}]_{0}}{[\mathrm{R}]}

\text { at } t_{1 / 2} \quad[\mathrm{R}]=\frac{[\mathrm{R}]_{0}}{2}
So, the above equation becomes

k=\frac{2.303}{t_{1 / 2}} \log \frac{[\mathrm{R}]_{0}}{[\mathrm{R}]_{0} / 2}

\text { or } \quad t_{1 / 2}=\frac{2.303}{k} \log 2

t_{1 / 2}=\frac{0.693}{k}

 

Graphs of First Order Kinetics

Study it with Videos

First Order Reaction
Other Forms of Rate Law
Half Life of First Order Reaction

Study other Related Concepts

First Order Reaction Current Topic

Rate of Reaction
Rate Law
Order of Reaction
Zero Order Reaction
First Order Reaction
Second Order Reaction
nth Order Reaction
Methods of Determining Reaction Order
Molecularity of reaction
Pseudo First Order Reaction

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