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Consider the reaction, \mathrm{2A+B\rightarrow 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 rate constant for this reaction is:

 

Option: 1

\mathrm{s^{-1} }


Option: 2

\mathrm{mol}^{-1} \mathrm{~L}^1 \mathrm{~s}^{-1}


Option: 3

No unit


Option: 4

\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}


Answers (1)

best_answer

Consider the reaction,
\mathrm{2A+B\rightarrow 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.
We know that for a first order reaction:

\mathrm{ t_{1 / 2}=\frac{0.693}{K} }
Half-life does not depend on the concentration of reactants. Hence the order of ' B ' will be one.
By initial rate method,

\mathrm{ \frac{r_1}{r_2}=\left(\frac{\left[A_o\right]_1}{\left[A_o\right]_2}\right)^p }

For reactant ' \mathrm{ A } '

\mathrm{ \frac{R}{2 R}=\left(\frac{A}{2 A}\right)^a \\ }

\mathrm{ \frac{1}{2}=\left(\frac{1}{2}\right)^a }
Thus, an order of reaction with respect to A is also one.
Hence, Total order \mathrm{ =1+1=2 }
The unit rate of constant for reaction is mol \mathrm{ ^{1-n} L^{n-1} time ^{-1} }
where \mathrm{ n} is order of the reaction
When \mathrm{ n=2}
The unit rate of constant for reaction is \mathrm{ \mathrm{mol}^{-1} L^1 \mathrm{~s}^{-1}}.

 

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Pankaj

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