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  • Which one of the following is the correct expression for the rate constant of zero order reaction?Option: 1 <img alt="\mathrm k=\frac{1}{t}\left\{[\m

Which one of the following is the correct expression for the rate constant of zero order reaction?

Option: 1

\mathrm k=\frac{1}{t}\left\{[\mathrm{A}]_{0}-[\mathrm{A}]\right\}


Option: 2

\mathrm k=t\left\{[\mathrm{A}]_{0}-[\mathrm{A}]\right\}


Option: 3

\mathrm k=\left\{\mathrm t[\mathrm{A}]_{0}-[\mathrm{A}]\right\}


Option: 4

None of above


Answers (1)

best_answer

As we have learnt,

 

Integrated Rate Law - Zero Order Reaction -

Zero order reaction means that the rate of the reaction is proportional to zero power of the concentration of reactants. Consider the reaction,

\mathrm{A\rightarrow P}

\text { Rate }=-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\mathrm{k[A]^{0}}

\text { Rate }=-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\mathrm{k\: x\: 1}

\mathrm{d[A]\: =\: -kdt}

At t = 0, A = Ao
At t = t, A = A
Thus, on integrating both sides, we get:

[\mathrm{A}]=\mathrm{-kt}+[\mathrm{A]_{o}}


Comparing the above equation with the equation of a straight line, y = mx + c, if we plot [R] against t, we get a straight line as shown in the above figure with slope = –k and intercept equal to [R]o.

Further simplifying the above equation, we get the rate constant, k as:

\mathrm{k=\frac{[\mathrm{A}]_{0}-[\mathrm{A}]}{t}}

 

-


\mathrm k t=[\mathrm{A}]_{0}-[\mathrm{A}]
k=\frac{1}{t}\left\{[\mathrm{A}]_{0}-[\mathrm{A}]\right\}
This is the expression for the rate constant for reactions of zero order.

Therefore, option(1) is correct

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