Question

Which of the following statements is/are false?
A.A fast reaction has a large rate constant and short half life
B.Half life depends on the concentration of reactants for first order reaction
C.For a first order reaction, the half life is independent of concentration
D.The half life of a reaction is half the time required for the reaction to go to completion

Answer 1

The order of the reaction is nothing but some of the power of concentrations in the rate law equation. The reaction with order one is known as first order reaction and it is linearly dependent on the elementary concentration.

Complete step by step answer:
The first statement in the given problem is that; a fast reaction has a large rate constant and short half life. The proportionality constant that shows the relation between rate of the reaction and the concentration of the species participating in the reaction as reactants is known as the rate constant. The rate of reaction is directly proportional to the rate constant and inversely proportional to half life so, if the reaction is faster then the rate constant will be large and the half life is short. Hence it is a true statement.
The second statement is; half life depends on the concentration of reactants for first order reaction. The sum of the powers of concentrations of reactants in the rate law equation is termed as order of the reaction and when this total sum becomes one, the reaction is considered as first order reaction. The half life of the first order reaction is always independent of the concentrations. The formula to calculate half life for the first order reaction is: ${t_{\dfrac{1}{2}}} = \dfrac{{0.693}}{k}$ . Hence it is a false statement.
The third statement is; for a first order reaction, the half life is independent of concentration. And it is a true statement. As we have discussed in the previous statement that ${t_{\dfrac{1}{2}}} = \dfrac{{0.693}}{k}$, here the concentration term is not used in this formula.
The fourth statement is; half life of a reaction is half the time required for the reaction to go to completion. And it is a false statement. Half life time is basically defined for the concentration, the time taken to degrade half of the concentration is the half life of the reaction.
Hence we can conclude that statements ${\text{B and D}}$ are correct.

Note:
From the integrated rate laws it is derived that the half life time for the first order reaction is independent of the initial concentration of the reactant. The half life for the first order reaction is also inversely proportional to rate constant $k$ .