91Ó°ÊÓ

Reaction involved the effective collision of two reactants to produce the desired products. Reactions can be natural which are occurring in the surrounding environment whereas it can be artificially done in the laboratory to form a desired required product.

The reaction rate can be defined as the speed of reaction to produce the products. The reaction rate can be slow, fast or moderate. The reaction can take less than a millisecond to produce products or it can take years to produce a desired product.

\({\bf{Rate = K }}{\left( {\bf{A}} \right)^{\bf{n}}}\)

A = concentration of reactant.

K = Rate constant.

Three rates are given there regarding the same reaction at given time.

From the table given in the question there are three rates \({\bf{Rat}}{{\bf{e}}_{\bf{1}}}{\bf{, Rat}}{{\bf{e}}_{\bf{2}}}{\bf{, Rat}}{{\bf{e}}_{\bf{3}}}\).

\(\begin{align}\frac{{Rate3}}{{Rate1}}{\bf{ }} &= {\bf{ }}\frac{{k \times {{\left( {A3} \right)}^n}}}{{k \times {{\left( {A1} \right)}^n}}}{\bf{ }}\\\frac{{4.0{\bf{ }} \times {\bf{ }}{{10}^{ - 6}}}}{{2.0{\bf{ }} \times {\bf{ }}{{10}^{ - 6}}}}{\bf{ }} &= {\bf{ }}\frac{{k \times {{\left( {2.0{\bf{ }} \times {\bf{ }}{{10}^{ - 10}}} \right)}^n}}}{{k \times {{\left( {1.0{\bf{ }} \times {\bf{ }}{{10}^{ - 10}}} \right)}^n}}}\\2{\bf{ }} &= {\bf{ }}{\left( 2 \right)^n}\\n &= 1\end{align}\)

The reaction of penicillin follows first-order reaction.

The rate constant of the reaction as follows:

\(\begin{align}Rate{\bf{ }} &= K{\bf{ }}{\left( A \right)^n}\\1.0{\bf{ }} \times {\bf{ }}{10^{ - 10}}{\bf{ }} &= K{\bf{ }}{\left( {2.0{\bf{ }} \times {\bf{ }}{{10}^{ - 6}}} \right)^1}\\K &= \frac{{1.0{\bf{ }} \times {\bf{ }}{{10}^{ - 10}}}}{{2.0{\bf{ }} \times {\bf{ }}{{10}^{ - 6}}}}\\K &= 5.0{\bf{ }} \times {\bf{ }}{10^{ - 5}}\end{align}\)

Hence, the rate constant of the reaction is \({\bf{5}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 5}}}}{\bf{L/mole/min}}\).