Read the following passage and answer the ...

CBSE Class 12 Chemistry 2022 Term 2 Delhi Set 3

Question : 12 of 12

Marks: +1, -0

Read the following passage and answer the question that follow:

The rate of reaction is concerned with decrease in concentration of reactants or increase in the concentration of products per unit time. It can be expressed as instantaneous rate at a particular instant of time and average rate over a large interval of time. A number of factors such as temperature,

concentration of reactants, catalyst affect the rate of reaction. Mathematical representation of rate of a reaction is given by rate law:

\;\text{Rate}\;=k[A]^x[B]^y

x

and

y

indicate how sensitive the rate is to change in concentration of A and B. Sum of

x+y

gives the overall order of a reaction.

When a sequence of elementary reaction gives us the products, the reaction is called complex reaction. Molecularity and order of an elementary reaction are same. Zero order reaction are relatively uncommon but they occur under special condition. All natural and artificial radioactive decay of unstable nuclei take place by first order kinetics.

(a) What is the effect of temperature on the rate constant of a reasons.

(b) For a reaction

A+B \rightarrow

Product, the rate given by, rate

k[A]^2[B]^{\frac{1}{2}}

. What is the order of the reaction?

(d) A first order reaction has a rate constant

2 \times 10^{-3}\,\mathrm{s}^{-1}

. How long will

6\,\mathrm{g}

of this reactant take to reduce to

2\,\mathrm{g}

The half life for radioactive decay of

{}^{14}\mathrm{C}

is 6930 years. An archaeological artifact containing wood had only

75\%

of the

{}^{14}\mathrm{C}

found in a living tree. Find the age of the sample.

[\log 4=0.6021,\ \log 3=0.4771,

\log 2=0.3010,\ \log 10=1]

Solution:

(a) The rate constant (

k

) for a reaction increases with increase in temperature and becomes almost double with every

10^{\circ}

rises in temperature. This effect is expressed by Arrhenius equation

k=\;\frac{A e^{-E_a}}{RT}

(b) According to the equation,

r=k[A]^2[B]^{\frac{1}{2}}

Order of the reaction

=2+\;\frac{1}{2}=\;\frac{5}{2}

(c) Order of reaction is defined as the sum of the powers of the molar concentration of the reaction species in the rate equation of the reaction. It is applicable for both elementary and complex reactions.

Molecularity of a reaction is defined as the total number of reacting species participating in an elementary reaction. It has no significance for complex reactions as applicable for only elementary reactions.

(d)

k\;=2 \times 10^{-3}\,\mathrm{s}^{-1}

t\;=\;\frac{2.303}{k} \log\;\frac{[R]_0}{[R]}

t\;=\;\frac{2.303}{2 \times 10^{-3}} \log\;\frac{6}{2}

t\;=1151.5 \times 0.4771=549.3\,\mathrm{s}

According to first order reaction,

\;\text{Half-life}\;(t_{1/2})\;=\;\frac{0.693}{k}

t_{1/2}\;=6980\;\text{years}\;

k\;=\frac{0.693}{6980}

However, the time taken can be calculated using first order rate of reaction when wood contain only

75\%

\mathrm{C}^{14}

Initial concentration of

C_{14},[R]_0=100

Amount at time

t\,\mathrm{s},[R]=75

\;t=\;\frac{2.303}{k} \log\;\frac{[R]_0}{[R]}

\;t=\;\frac{2.303}{\frac{0.693}{6980}} \log\;\frac{100}{75}

\;t=2898\;\text{years}\;

Thus, the age of the sample is approximately 2898 years.

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