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Modern Physics Chapters for NEET 2025 - Modern Physics Topics

First Order Reaction MCQ - Practice Questions with Answers

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.

  • 90 Questions around this concept.

Solve by difficulty

Which of the following is the unit of rate constant for first order reaction?

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

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

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

A bacterial infection in an internal wound grows as N(t)=Noexp(t), where the time t is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound.

Once it reaches there, the bacterial population goes down as dNdt=5N2.
What will be the plot of NoN vs. t after 1 hour?

The decomposition of phosphine (PH3) on tungsten at low pressure is a first-order reaction. It is because the

Select the reaction which does not follow the first order Kinetics:

 

If we start a reaction from 100 mol, the rate constant is 0.0693 min1. What will be the rate of the reaction offer 20 min?

 

Which of the following reactions is first order reaction?

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Which of the following correctly represents the first-order reaction?

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

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