Question

A substance ‘A’ decomposes by a first-order reaction starting initially with [A] = 2.00 m and after 200 min [A] = 0.15 m, for this reaction, what is the value of k.
(A) \[1.29 \times {10^{ - 2}}{\min ^{ - 1}}\]
(B) \[2.29 \times {10^{ - 2}}{\min ^{ - 1}}\]
(C) \[3.29 \times {10^{ - 2}}{\min ^{ - 1}}\]
(D) \[4.40 \times {10^{ - 2}}{\min ^{ - 1}}\]

Answer 1

Hint: In order to find the value of k in the first order reaction, we must first order reaction, we must first have an idea about what a rate of a reaction is. Rate of a reaction is defined as the speed at which a product will be formed from the reactant in a given chemical equation.

Complete step by step answer: Let us first understand about the rate of the reaction. Rate of a reaction is defined as the speed at which a product will be formed from the reactant in a given chemical equation. Now we have to see what a first-order reaction is. First-order reaction is a reaction in which rate of the reaction is proportional to concentration of only one reactant.
- Now let us move onto the problem given.
In the problem, the following things are given they are:
[A] = 2.00 m = a
[A] = 0.15m = a - x
t = 200 min
\[k = \dfrac{{2.303}}{t}\log \dfrac{a}{{a - x}}\]
\[k = \dfrac{{2.303}}{{200}}\log \dfrac{2}{{0.15}}\]
\[k = \dfrac{{2.303}}{{200}}(0.301 + 0.824) = 1.29 \times {10^{ - 2}}{\min ^{ - 1}}\]
The correct option is option “A” .

Note: We have to remember that there are certain factors which can affect the rate of the reaction. They are:
- Nature of the reaction
- Solvent used.
- the Catalyst used.
- Effect of concentration.
- temperature
- Pressure factor
- order of the reaction.
- electromagnetic radiation.
- intensity of the light used.
- Reactant’s surface area