Tag: chemical kinetics

Questions Related to chemical kinetics

For the reaction $A + B \rightarrow C$, determine the order of the reaction with respect to $B$ from the information given below.

$\displaystyle { \left[ A \right]  } _{ \circ  }$ $\displaystyle { \left[ B \right]  } _{ \circ  }$ Initial rate (M/s)
1.00 1.00 2.0
1.00 2.00 8.1
2.00 2.00 15.9
chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. Zero order

  2. First order

  3. Second order

  4. Third order

  5. Fourth order

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Correct Option: C
Explanation:

Analyzing first and second raw,when concentration of $B$ is doubled then initial rate increased by four times,so it is increasing by square of concentration.Hence it is a second order reaction.


$Rate$$=$$k[A]^x [B]^2$  Using this rate expression and keeping $[A]$ constant,if we double $[B]$ then rate increases four times. 

Statement 1: In a second-order reaction with respect to $A$, when you double [$A$], the rate is quadrupled.
Statement 2: The rate equation is $r = k[A]^2$ for such a reaction.

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.

  2. Both the Statement 1 and Statement 2 are correct, but Statement 2 is not the correct explanation of Statement 1.

  3. Statement 1 is correct, but Statement 2 is not correct.

  4. Statement 1 is not correct, but Statement 2 is correct.

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Correct Option: A
Explanation:

$\bullet \quad $If rate = ${ K\left[ A \right]  }^{ 2 }$ for a reaction.

       then it is a second order reaction with respect to A.
$\bullet \quad $Let ${ \gamma  } _{ 1 }={ K\left[ A \right]  } _{ t }^{ 2 }$
       if ${ \left[ A \right]  } _{ t }$ is doubled.
             ${ \gamma  } _{ 2 }={ K\left( { 2\left[ A \right]  } _{ t } \right)  }^{ 2 }$
   $\Rightarrow \quad { \gamma  } _{ 2 }={ 4\gamma  } _{ 1 }$.
Hence, statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1.

The unit for the rate constant is calculated from the rate law.
For the given rate law, determine the units of the rate constant for rate $= k[A]^{2} [B]$.

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. $s^{-1}M^{-3}$

  2. $s^{-1}M^{-2}$

  3. $s^{-1}M^{-1}$

  4. $s^{-1}$

Show answer
Correct Option: B
Explanation:

Since rate constant is given by $k[A]^2[B]$.
Where 1+2=3, so it is probably third order reaction.
So rate constant should have units of $L^2 mol^{-2} s^{-1} \implies M^{-2}s^{-1}$

A graph of concentration versus time data for a second-order reaction gives a straight line in which of the following plots of the data?

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. $[A] _{t} = -kt + [A] _{0}$

  2. $ln [A] _{t} = -kt + ln [A] _{0}$

  3. $\dfrac {1}{[A _{t}]} = kt + \dfrac {1}{[A _{0}]}$

  4. All of the above

  5. None of the above

Show answer
Correct Option: A
Explanation:

Let the concentration at $t=0$ be $[{ A } _{ o }]$ & at $t=t$ be $ [{ A } _{ t }]$

 By graph,
$ [{ A } _{ t }]=Kt+[{ A } _{ o }]$
 For negative slop,
$ [{ A } _{ t }]=-Kt+[{ A } _{ o }]$

The rate of the reaction, $C{ Cl } _{ 3 }CHO+NO\longrightarrow CH{ Cl } _{ 3 }+NO+CO$, is given by the equation, rate $=k\left[ C{ Cl } _{ 3 }CHO \right] \left[ NO \right] $. If concentration is expressed in ${mol}/{litre}$, the unit of $k$ is:

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. ${ mol }^{ -2 }{ L }^{ 2 }{ s }^{ -1 }$

  2. $mol$ ${ L }^{ -1 }{ s }^{ -1 }$

  3. $L$ ${ mol }^{ -1 }{ s }^{ -1 }$

  4. ${ s }^{ -1 }$

Show answer
Correct Option: C
Explanation:

Since it is second order reaction as clear by rate equation so unit of $k$ is given by $M^{-1} s^{-1}$ or $L\space mol^{−1}s^{−1}$

Units of rate constants for first and zero order reactions in terms of molarity $M$ unit are respectively:

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. ${ sec }^{ -1 },M\ { sec }^{ -1 }$

  2. ${ sec }^{ -1 },M$

  3. $M\ { sec }^{ -1 },{ sec }^{ -1 }$

  4. $M,{ sec }^{ -1 }$

Show answer
Correct Option: A
Explanation:

$K=\frac{dx}{dt[A]} $ for Ist order = $sec^{−1}$
$ K = \frac{dx}{dt}$ for zero order = $mol \space litre^{−1}sec^{−1}$

Hence A is the correct answer.

Consider the reaction, $2A+B\longrightarrow $ Products. When the concentration of $B$ alone was doubled, the half-life did not change. When the concentration of $A$ alone was doubled, the rate increased by two times. The unit of the rate constant for this reaction is:

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. ${ s }^{ -1 }$

  2. $L$ ${ mol }^{ -1 }{ s }^{ -1 }$

  3. Unitless

  4. $mol$ ${ L }^{ -1 }{ s }^{ -1 }$

Show answer
Correct Option: B
Explanation:

Concentration change in '$B$' does not change half life, it means the reaction is first order with respect to $B$. When concentration of only '$A$' is doubled, the rate of reaction becomes double, thus order with respect to $A$ will also be one.
Overall order of reaction $=2$
Unit of rate constant $=L$ ${ mol }^{ -1 }{ s }^{ -1 }$

Consider following two reactions:
$A\longrightarrow $ Product,         $-\dfrac { d\left[ A \right]  }{ dt } ={ k } _{ 1 }{ \left[ A \right]  }^{ 0 }$
$B\longrightarrow $ Product,         $-\dfrac { d\left[ B \right]  }{ dt } ={ k } _{ 2 }{ \left[ B \right]  }^{ 1 }$
${ k } _{ 1 }$ and ${ k } _{ 2 }$ are expressed in terms of molarity $\left( mol\ { L }^{ -1 } \right) $ and time $\left( { s }\right) $ as:

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. ${ s }^{ -1 },M{ s }^{ -1 }{ L }^{ -1 }$

  2. $M{ s }^{ -1 },M{ s }^{ -1 }$

  3. ${ s }^{ -1 },{ M }^{ -1 }{ s }^{ -1 }$

  4. $M{ s }^{ -1 },{ s }^{ -1 }$

Show answer
Correct Option: D
Explanation:

The units of rate of reaction is $Ms^{-1}$.

For zero order reaction, unit of K, will be $Ms^{-1}$
For 1st order reaction, unit of $K _2$ will be $s^{-1}$

Rate law expression of a reaction is:
            Rate $=k{ \left[ A \right]  }^{ { 2 }/{ 3 } }\left[ B \right] $
Which of the following are correct about the corresponding reaction?

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. Order of reaction $=\dfrac { 2 }{ 3 } +1=\dfrac { 5 }{ 3 } $

  2. Unit of rate constant $={ L }^{ { 2 }/{ 3 } }{ mol }^{ { -2 }/{ 3 } }{ sec }^{ -1 }$

  3. Unit of rate constant $={ atm }^{ { -2 }/{ 3 } }{ sec }^{ -1 }$

  4. Unit of rate constant $=mol$ ${ L }^{ -1 }{ sec }^{ -1 }$

Show answer
Correct Option: A,B,C
Explanation:

Overall order=$\frac{2}{3}+1=\frac{5}{3}$

Unit of rate constant=$mol^{1-n}L^{n-1}sec^{-1}$
where n=order of reaction
For given reaction, unit of rate constant=$mol^{1-5/3}L^{5/3-1}sec^{-1}$
=$L^{2/3}mol^{-2/3}sec^{-1}$
For gaseous reaction, concentration term= pressure in atm
unit of rate constant=$atm^{-2/3}sec^{-1}$

Mechanism of a hypothetical reaction $X _2+Y _2\rightarrow 2XY$ is given below;
(i) $ X _2\rightarrow X+X$ (fast)
(ii) $X+Y _2\rightleftharpoons XY+Y$ (slow)
(iii) $ X+Y \rightarrow XY$ (fast)
The overall order of the reaction will be: 

chemistry chemical kinetics dependence of reaction rate on concentration of reactants order of reactions factors influencing rate of a reaction

  1. $2$

  2. $0$

  3. $3$

  4. $1$

Show answer
Correct Option: A
Explanation:

Order of Reaction is given by the slowest step of Reaction. In slowest step we 

have 2 reactants so, $2^{nd}$ order reaction.