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For an acid catalyzed reaction\mathrm{ R \stackrel{H^{+}}{\longrightarrow} P}. half life is independent of concentration of A at given PH. At definite concentration of A, half life time is 100min at PH=2 and half life lime is 1000 min at PH=3. If the rate law expression of reaction is \mathrm{r=k[R]^a\left[\mathrm{H}^{+}\right]^b} then calculate the value of (a+b)=?

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

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\mathrm{r=k[R]^a\left[H^{+}\right]^b .}

\mathrm{\because}  Half -life is independent of conc of A so order of reaction w.r.t. R=1

a=1

\mathrm{\begin{aligned} \therefore \quad & \gamma=k^{\prime}\left[H^{+}\right]^b \quad\left\{k^{\prime}=k[R]^{1}\right\} \\ & \frac{a / 2}{180}=k^{\prime}\left[10^{-2}\right]^b \text {-(i) } \\ & \frac{a / 2}{1000}=k^{\prime}\left[10^{-3}\right]^b \text {-(ii) } \end{aligned}}

\mathrm{\text { By (i) } \div \text { (ii), } \quad 10=(10)^b \Rightarrow b=1}

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Ritika Kankaria

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