238 U 96 changes to P 96 206 by successive radioactive decay. A sample of uranium was analyzed and found to contain 1 . 0 g of U 238 and 0 . 1 g of Pb 206 had accumulated due to decay of 238 U , find out the age of ore. (Half-life of U 238 = 4 . 5 × 10 9 years).

All radioactive reactions are first order reactions. Half life of first order reactions can be given as : t 1 2 = 0 . 693 k . So, k = 0 . 693 4 . 5 × 10 9 = 1 . 54 × 10 - 10 years -1 . Integrated rate equation for first order reactions can be given as : k = 2 . 303 t log R ∘ R , where k is rate constant. Age of the ore, t = 2 . 303 1 . 54 × 10 - 10 log 1 g 0 . 1 g = 2 . 303 × 10 10 1 . 54 = 1 . 49 × 10 10 years.

For the hydrolysis of methyl acetate in the aqueous solution, following results were obtained : t / s 0 30 60 CH 3 OCH 3 / mol L - 1 0 . 60 0 . 30 0 . 15 Show that it follows pseudo first order reaction, as the concentration of water remains constant.

Pseudo first order reactions are bimolecular but first order reactions. Hydrolysis of methyl acetate is a pseudo first order reaction as the concentration of water has no effect on the rate of reaction. Methyl acetate hydrolysis is a bimolecular reaction. In first order reactions, the value of rate constant remains same at different time intervals and reactant concentrations. Rate constant of first order reaction can be expressed as : k = 2 . 303 t log R ∘ R , where R ∘ is the initial molar concentration of reactants. At t = 30 s , k = 2 . 303 30 log 0 . 6 0 . 3 . k = 2 . 303 30 log 2 . At t = 60 s , k = 2 . 303 60 log 0 . 6 0 . 15 k = 2 . 303 60 log 2 2 = 2 . 303 × 2 60 log 2 = 2 . 303 30 log 2 . Hence, methyl acetate hydrolysis is a pseudo first order reaction.

For the hydrolysis of methyl acetate in the aqueous solution, following results were obtained : t / s 0 30 60 CH 3 OCH 3 / mol L - 1 0 . 60 0 . 30 0 . 15 Calculate the average rate of reaction between the time interval 30 s to 60 s .

The rate of reaction over a certain period of time during the course of reaction is called average rate of reaction. Average rate of reaction = R 1 - R 2 t 2 - t 1 = 0 . 30 - 0 . 15 60 - 30 = 0 . 15 30 = 0 . 005 . Hence, the average rate of reaction for the given reaction is 5 × 10 - 3 mol L - 1 s - 1 .

Under what condition a bimolecular reaction behaves kinetically first order reaction?

In a bimolecular reaction, when the amount of one of the reactants is present in excess, the reaction is kinetically first order because the concentration of reactant present in excess does not affect the order of reaction. Hence, it does not affect the rate of reaction and such reactions are called pseudo first order reactions. Example : Hydrolysis of sucrose yielding glucose and fructose.

E M B I B E

All In One ISC Chemistry Class 12>Chapter 4 - Chemical Kinetics>Chapter Practice>Q 44

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12th ICSE

IMPORTANT

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Consider the reaction, $A \to B$ . The change in concentration with time $t$ is shown in the graph. Predict the order of the reaction.

Important Questions on Chemical Kinetics

HARD

12th ICSE

IMPORTANT

All In One ISC Chemistry Class 12>Chapter 4 - Chemical Kinetics>Chapter Practice>Q 44

Consider the reaction, $A \to B$ . The change in concentration with time $t$ is shown in the graph. Derive the expression for the time which is
required to complete the reaction.

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HARD

12th ICSE

IMPORTANT

All In One ISC Chemistry Class 12>Chapter 4 - Chemical Kinetics>Chapter Practice>Q 44

Consider the reaction, $A \to B$ . The change in concentration with time $t$ is shown in the graph. Predict the order of the reaction.

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HARD

12th ICSE

IMPORTANT

All In One ISC Chemistry Class 12>Chapter 4 - Chemical Kinetics>Chapter Practice>Q 45

$^{238} U_{96}$ changes to ${}^{206}P_{96}$ by successive radioactive decay. A sample of uranium was analyzed and found to contain $1.0 g$ of ${}^{^{238}}U$ and $0.1 g$ of ${}_{206}{Pb}$ had accumulated due to decay of $^{238} U$ , find out the age of ore. (Half-life of ${}^{^{238}}U = 4.5 \times 10^{9}$ years).