Question

What will be the initial rate of a reaction if its rate constant is ${\text{1}}{{\text{0}}^{{\text{ - 3}}}}{\text{ mi}}{{\text{n}}^{{\text{ - 1}}}}$ and the concentration of reaction is ${\text{0}}{\text{.2 mol d}}{{\text{m}}^{{\text{ - 3}}}}$. How much of the reactant will be converted into a product in ${\text{200 min}}$?

Answer 1

Hint: First we should know the order of the rate of the reaction. The rate of reaction is calculated by multiplication of the rate constant with the concentration of the reaction present before. Then according to time we will calculate the disintegration of the reactant.

Complete step by step answer:
First step should be to predict the order of the reaction and by observing the unit of the rate constant it is confirmed that the reaction is a first order reaction. For a first order reaction the initial rate of the reaction is:
${\text{initial rate = k[A]}}$
Initial rate= ${\text{1}}{{\text{0}}^{{\text{ - 3}}}}{\text{ mi}}{{\text{n}}^{{\text{ - 1}}}}{{ \times 0}}{\text{.2 mol d}}{{\text{m}}^{{\text{ - 3}}}}$
Initial rate =${{2 \times 1}}{{\text{0}}^{{\text{ - 4}}}}{\text{ mol d}}{{\text{m}}^{{\text{ - 3}}}}{\text{ mi}}{{\text{n}}^{{\text{ - 1}}}}$
Since it is a first order reaction the rate for conversion will be following the formula given below:
${\text{k = }}\dfrac{{{\text{2}}{\text{.303}}}}{{\text{t}}}{\text{ log }}\dfrac{{{\text{[A]}}}}{{{\text{[A - x]}}}}$
Here k is the rate of constant
[A] is the original or initial concentration of the reactant
[A-x] is the concentration of the reactant left after t time has passed
Now we will substitute the values of the variable in the rate constant equation:
${\text{1}}{{\text{0}}^{{\text{ - 3}}}}{\text{ = }}\dfrac{{{\text{2}}{\text{.303}}}}{{{\text{200}}}}{\text{ log}}\dfrac{{{\text{0}}{\text{.2}}}}{{{\text{[A - x]}}}}$
${\text{[A - x] = 0}}{\text{.163 d}}{{\text{m}}^{{\text{ - 3}}}}$
Amount of reactant converted into product is ${\text{0}}{\text{.2 - 0}}{\text{.163 = 0}}{\text{.037}}$

So, the Amount of reactant converted into product is ${\text{0}}{\text{.2 - 0}}{\text{.163 = 0}}{\text{.037}}$

Additional information:
There are many different types of reaction which follow different orders of reaction. Some are zero order reaction, some first order, second order, third order etc. All have different rate equations which they follow.

Note: The zero-order reaction does not happen even if we increase the amount of reactant or concentration of the reactant unless we provide the optimum conditions to it. Example photosynthesis is a zero order reaction and it will happen only when sunlight is available otherwise not even if water and oxygen is present.