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Help me solve this The correct difference between first-second-order reactions is that

The correct difference between first-second-order reactions is that

  • Option 1)

    a first-order reaction can be catalyzed; a second-order reaction cannot be catalyzed

  • Option 2)

    the half-life of a first-order reaction does not depend on [A]o; the half-life of a second-order reaction does depend on [A]o

  • Option 3)

    the rate of a first-order reaction does not depend on reactant concentrations; the rate of a second-order reaction does depend on reactant concentrations

  • Option 4)

     the rate of a first-order reaction does depend on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations

 
Answers (1)
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As we learnt that

nth order reaction -

The rates of the reaction is proportional to nth power of reactant

- wherein

Differential rate law

=\frac{dx}{dt}=k(a-x)^{n}

Integrated rate laws,

=\frac{1}{x-1}=[(a-x)^{1-n} -a^{(1-n)}]=kt

a= initial, concentration of reactant at t=0 sec

x= concentration of product formed at t= tsec

t_\frac{1}{2}=\frac{1}{(a^{n-1})(k^{n-1})}[2^{n-1}-1]

 

 

 

First Order Reaction -

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

- wherein

Formula:

R    \rightarrow        P

a                 0

a-x             x

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)

Unit of k=sec^{-1}

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

 

 

 \left ( t_{\frac{1}{2}} \right ) 2^{nd} order \alpha \frac{1}{Initial \;Concentration}

 

 

\left ( t_{\frac{1}{2}} \right ) 1^{st} order = Independent \; of \; concentration     

\left ( t_{\frac{1}{2}} \right ) 2^{nd} order \alpha \frac{1}{Initial \;Concentration}


Option 1)

a first-order reaction can be catalyzed; a second-order reaction cannot be catalyzed

This is incorrect.

Option 2)

the half-life of a first-order reaction does not depend on [A]o; the half-life of a second-order reaction does depend on [A]o

This is correct.

Option 3)

the rate of a first-order reaction does not depend on reactant concentrations; the rate of a second-order reaction does depend on reactant concentrations

This is incorrect.

Option 4)

 the rate of a first-order reaction does depend on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations

This is incorrect.

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