An organic compound A decomposes the following two parallel first-order reactions $\mathrm{A} \xrightarrow{K_1} \mathrm{B}$ and $\mathrm{A} \xrightarrow{K_2} \text{C}.$ If $K_1$ is $1.25 \times 10^{-5} \mathrm{~s}^{-1}$ and $\frac{K_1}{K_2}=\frac{1}{9},$ then the value of $\frac{[\mathrm{C}]}{[\mathrm{A}]}$ after one hour of start of reaction by taking only $\mathrm{A},$ is $(\ln 1.568=0.45)$

JEE CHEMISTRY MCQ: CHEMICAL KINETICS

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An organic compound A decomposes the following two parallel first-order reactions

\mathrm{A} \xrightarrow{K_1} \mathrm{B}

and

\mathrm{A} \xrightarrow{K_2} \text{C}.

K_1

1.25 \times 10^{-5} \mathrm{~s}^{-1}

and

\frac{K_1}{K_2}=\frac{1}{9},

then the value of

\frac{[\mathrm{C}]}{[\mathrm{A}]}

after one hour of start of reaction by taking only

\mathrm{A},

(\ln 1.568=0.45)

View answer and explanation

Correct option: B

0.5112

Option B (0.5112) is correct because it is calculated using the integrated rate laws for parallel first-order reactions, considering the ratio of rate constants and the reaction time.

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The reaction

\mathrm{A}_2+\mathrm{B}_2 \rightarrow 2 \mathrm{AB}

follows the mechanism

\begin{aligned} & {{\text{A}}_2}\mathop \rightleftharpoons \limits_{{{\text{k}}_{ - 1}}}^{{{\text{k}}_1}} {\text{A}} + {\text{A (fast) }} \\ & \mathrm{A}+\mathrm{B}_2 \xrightarrow{\mathrm{k}_2} \mathrm{AB}+\mathrm{B} \text { (slow) } \\ & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{AB} \text { (fast) } \end{aligned}

The overall order of the reaction is: For the first order reaction with the rate constant

k

, which expression gives the rate half-life period?

(Initial\mathrm{ }conc.\mathrm{ } = a)

Which of the following is a zero order reaction? For a certain reaction involving a single reactant, it is found that

C_0 \sqrt{T}

is constant, where

C_0

is the initial concentration of the reactant and

T

is the half-life. What is the order of the reaction? Arrhenius equation is The energy of activation for an uncatalysed reaction is

100 \mathrm{~kJ/mol}.

Presence of a catalyst lowers the energy of activation by

75 \%

. The

\log _{10} \frac{K_2}{K_1}

of the ratio of rate constant of catalysed and uncatalysed reactions at

27^{\circ} \mathrm{C}

is?

Assume the frequency factor is same for both reactions. (Given

2.303 \times 8.314=19.147

)