Question

The half-life period for a first-order reaction is:
A.Independent of concentration
B.Proportional to concentration
C.Inversely proportional to concentration
D.Inversely proportional to the square of the concentration

Answer 1

Hint:The order of the reaction is defined as the sum of the stoichiometric coefficient of the concentration of the reactants raised to their powers. Half-life is the time required for the concentration of reactants to be reduced to half its value.

Complete step by step answer:
The order of the reaction can have a whole number as well as fractional order values. In the first order reaction, the rate is dependent only one the concentration of the reactant raised to the power one, which means that the reaction rate depends on the concentration of only reactant. The mathematical expression of the reaction is:
   $ {\text{k = }}\dfrac{{{\text{2}}{\text{.303}}}}{{\text{t}}}{\text{log}}\left( {\dfrac{{{{\text{A}}_{\text{0}}}}}{{\text{A}}}} \right) $
where ‘k’ is the rate constant of the reaction, ’t’ is the time period of the reaction, $ {{\text{A}}_{\text{0}}} $ is the initial concentration of the reactant while $ {\text{A}} $ is the concentration of the reactant at time ‘t’.
The half-life of any reaction is defined as the time required for the disintegration of half of the concentration of the reactants.
The half-life for a first-order reaction can be given as:
   $ {{\text{t}}_{1/2}}{\text{ = }}\dfrac{{{\text{0}}{\text{.693}}}}{{\text{k}}} $
where, the $ {{\text{t}}_{1/2}} $ is the half-life of the reaction. From this equation it is clear that the half-life of a first-order reaction is dependent only on the rate constant of the reaction.

So, the correct answer is option A.
Note:
The rate of the reaction is determined from the rate-determining step which also decide s the order of the reaction. For the second-order reactions, the rate of the reaction is dependent upon the concentrations of both the reactants, while for the third-order reaction the rate of the reaction depends on three reactant concentrations.