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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

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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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