Question

Answer in one word or sentence.
What happens to the half life period of a first order reaction if the initial concentration of the reactants is increased?

Answer 1

Hint: If time is ${t_{1/2}}$ then the concentration of the reactant becomes half of its initial concentration. So, put these values in the formula: $k = \frac{{2.303}}{t}\log \frac{{{R_ \circ }}}{R}$ and find out the value of ${t_{1/2}}$.

Complete step by step answer:
- First of all let us see what a first order reaction is.
Any reaction which has a rate depending linearly only on one reactant concentration only is known as a first order reaction.
- For any first order reaction the differential equation can be written as:
 $Rate = - \frac{{d[A]}}{{dt}} = k{[A]^1} = k[A]$
For this reaction: $k = \frac{{2.303}}{t}\log \frac{{{R_ \circ }}}{R}$ , where ${R_ \circ }$ is the initial concentration of the reactant and R is the concentration of reactant at time ‘t’.
- Example of a first order reaction: Hydrogenation of ethene.
 ${C_2}{H_5}(g) + {H_2}(g) \to {C_2}{H_6}(g)$
 For this reaction the differential equation will be: $Rate = k[{C_2}{H_4}]$
- Now let us talk about half life.
The time in which the concentration of the reactant is reduced to half of its initial concentration is known as half life of the reaction. It is represented as ${t_{1/2}}$.
At t = ${t_{1/2}}$, R = $\frac{{{R_ \circ }}}{2}$.
So, for first order reaction k will be written as:
$k = \frac{{2.303}}{{{t_{1/2}}}}\log \frac{{{R_ \circ }}}{{{R_ \circ }/2}}$
${t_{1/2}} = \frac{{2.303}}{k}\log 2$
${t_{1/2}} = \frac{{2.303}}{k}(0.301)$

This will give: ${t_{1/2}} = \frac{{0.693}}{k}$
- From the above obtained equation we can see that the half life for a first order reaction is independent of the concentration of the reactant. Thus if we increase the concentration of the reactant there will be no change in the half life.
So, in one line we can write that: The half life of a first order reaction remains unchanged with increase in concentration of reactant.

Note: Any substance decays at its own rate and therefore its half life is constant and does not depend on external factors or physical conditions like temperature, pressure, etc that occur in its surroundings.