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  • For reaction, aA+bB → Product. Rate of reaction = <img alt="\mathrm{K[A]^a[B]^b}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BK%5BA%5D%5Ea%5BB%5D%5Eb%7D"

For reaction, aA+bB → Product.
Rate of reaction = \mathrm{K[A]^a[B]^b}.
If concentration of 'A' is doubled, rate is increased to four times.  If concentration of B is made four times, rate is doubled. What is relation between rate of disappearance of A and that of B?

Option: 1

\mathrm{-\left\{\frac{d[A]}{d t}\right\}=-\left\{\frac{d[B]}{d t}\right\}}


Option: 2

\mathrm{-\left\{\frac{d[A]}{d t}\right\}=-\left\{\frac{4 d[B]}{d t}\right\}}


Option: 3

\mathrm{-\left\{\frac{4 d[A]}{d t}\right\}=-\left\{\frac{d[B]}{d t}\right\}}


Option: 4

None of these.


Answers (1)

best_answer

Initial rate method:
\mathrm{R=K[A]^p[B]^q[C]^r}
p, q, and r are order of reaction with respect to A, B and C respectively.


When two different intial concentration of A,
\mathrm{\left[A_o\right]_1 and \left[A_o\right]_2} are taken

 \mathrm{r_1=K^{\prime}\left[A_o\right]_1^p }

\mathrm{r_2=K^{\prime}\left[A_o\right]_2^p }

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

From this relation 'p' can be calculated.

For given reaction

aA + bB \mathrm{\rightarrow} Product

Rate \mathrm{=K[A]^a[B]^b}


Let us consider, rate of reaction is ' R '

On doubling concentration of A,

Concentration of A is 2A

Rate of reaction is 4R

By initial rate method,
\mathrm{ \frac{R}{4 R}=\left(\frac{A}{2 A}\right)^a \\ }

\mathrm{ \frac{1}{4}=\left(\frac{1}{2}\right)^a }
Thus, a = 2

Similarly when 'B' is made to four times, the rate of reaction is doubled.
\mathrm{ \frac{R}{2 R}=\left(\frac{B}{4 B}\right)^b \\ }
 \mathrm{ \frac{1}{2}=\left(\frac{1}{4}\right)^b }
Thus, \mathrm{ b=\frac{1}{2} }

Hence, the rate of reaction (ROR) is
\mathrm{ \text { Rate }=K[A]^2[B]^{\frac{1}{2}} \\ }

\mathrm{2 A+\frac{1}{2} B \rightarrow \text { Product } }

\mathrm{\because R O R=\frac{-1 d[A]}{a d t}=-\frac{1 d[B]}{b d t} }

\mathrm{ \therefore \\ R O R=\frac{-1 d[A]}{2 d t}=-\frac{1 d[B]}{\frac{1}{2} d t} }

\mathrm{ \frac{-d[A]}{d t}=-4 \frac{d[B]}{d t} }

Posted by

avinash.dongre

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