Tag: dependence of reaction rate on concentration of reactants

Questions Related to dependence of reaction rate on concentration of reactants

The rate of certain hypothetical reaction $A+B+C\rightarrow $ products is given by, $\displaystyle r=-\frac{\mathrm{d} [A]}{\mathrm{d} t}=K[A]^{1/2}:K[B]^{1/3}:K[C]^{1/4}$. The order of the reaction:

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

  1. 1

  2. $\displaystyle \frac{1}{2}$

  3. 2

  4. $\displaystyle \frac{13}{12}$

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Correct Option: D
Explanation:

$r=-\dfrac { d[A] }{ dt } =K[A{ ] }^{ \cfrac { 1 }{ 2 }  }K[B{ ] }^{ \cfrac { 1 }{ 3 }  }K[C{ ] }^{ \cfrac { 1 }{ 4 }  }\ $


$rate=\dfrac { 1 }{ 2 } +\dfrac { 1 }{ 3 } +\dfrac { 1 }{ 4 } \ $

$rate=\dfrac { 13 }{ 12 }$

Hence, the answer is D.

The rate constant of third order reaction is:

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

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

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

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

  4. mol$^{-2}$ lit$^{-1}$ s$^{-1}$

Show answer
Correct Option: B
Explanation:

Units of rate constant for $n$th order = $[(mol\  lit^{-1})]^{1-n} t^{-1}$
For third order reaction $n = 3$
$\therefore $ Units are $(mol  lit^{-1})^{1- 3} t^{-1} = mol\ l^{-2} lit^{-2} t^{-1}$

The rate constant of a reaction depends on:

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

  1. Temperature

  2. Initial concentration ofthe reaction

  3. Time ofreaction

  4. Extent of reaction

Show answer
Correct Option: A
Explanation:

The rate constant of a reaction depends only on two factors
(i) Temperature and (ii) Catalyst.

The rate constant of a first-order reaction is $3 \times 10^{-6}$ per second and initial concentration is 0.10 M. Then the initial rate of reaction is:

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

  1. $3 \times 10^{-6} Ms^{-1}$

  2. $3 \times 10^{-8} Ms^{-1}$

  3. $3 \times 10^{-7} Ms^{-1}$

  4. $3 \times 10^{-9} Ms^{-1}$

Show answer
Correct Option: C
Explanation:

Rate = k [concentration] for first order reaction.
Given $k = 3 \times 10^{-6}/sec,$ [concentration] = 0.1 M
$\therefore rate = 3 \times 10^{-6} \times 0.1  = 3 \times 10^{-7} ms^{-1}$

What is the unit for the rate constant of a second order reaction?

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

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

  2. mol $\displaystyle { L }^{ -1 }$

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

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

  5. $\displaystyle { mol }^{ 2 }{ L }^{ -2 }{ s }^{ -2 }$

Show answer
Correct Option: D
Explanation:

The unit for the rate constant of a second order reaction is $\displaystyle \displaystyle L { mol }^{ -1 }{ s }^{ -1 } $. 
For a second order reaction, $\displaystyle rate = k [A]^2 $
$\displaystyle mol { L }^{ -1 }{ s }^{ -1 }  = k (mol { L }^{ -1 })^2$
$\displaystyle k = L { mol }^{ -1 }{ s }^{ -1 }  $

Statement I : In a second order reaction doubling [A] quadruples the rate
Because
Statement II : The rate equation is $\displaystyle r={ k\left[ A \right]  }^{ 2 }$ 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 and 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.

  5. Both the Statement 1 and Statement 2 are not correct.

Show answer
Correct Option: A
Explanation:

Secon order rate expression is given as $r$$=$$k[A]^2$ so if we double the concentration of a then rate increases by 4 times, hence both statements are correct and statement 2 is correct explanation of statement 1.

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

Show answer
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.

Show answer
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 }]$