Question

The rate constant for the first-order decomposition of n2o is 3.40 s-1. what is the half-life of the decomposition?

Answer 1

Answer : The half-life of the decomposition is, 0.203 seconds.

Solution :

Half-life period of a first order reaction is defined as the the time taken for any fraction of the reaction to complete is independent of the initial concentration.

Formula of the half-life period of a first order reaction will be,

$t_{1/2}=\frac{0.693}{k}$

where,

$t_{1/2}$ = half-life of the reaction

k = rate constant = $3.40s^{-1}$

Now put all the values in this formula, we get the half-life of the reaction.

$t_{1/2}=\frac{0.693}{3.40s^{-1}}=0.203s$

Therefore, the half-life of the decomposition is, 0.203 seconds.

Answer 2

 We are given with the rate constant of a first-order decomposition of n2o which is equal to 3.40 s-1. Half life of the radioactive material can be determined through the formula: t= ln2 /k where t is the half life of the material. t then upon substitution is equal to 0.2048 s.