Question

The half-life period of a reaction becomes $ 16 $ times when reactant concentration is halved. The order of reaction is?

Answer 1

Hint: We know that for a nth order reaction the rate is proportional to nth power of the reactant concentration. Half-life is the time in which the concentration of the reactant gets reduced to half. For a nth order reaction the half life

Complete answer:
The half-life chemistry or a half-life of a reaction, $ {{t}_{1/2}}\text{ }, $ is defined as the specific amount of time required for a reactant concentration to decrease by half when compared to its initial concentration. The half-life application is used in chemistry and in medicine to predict the concentration of a substance over time.
First of all let us see what order of a reaction is. The order of a reaction is basically the sum of the powers of the reactant concentration in the rate law expression. The order of a reaction can be $ 0,\text{ }1,\text{ }2,\text{ }3 $ and also a fraction. Also for a zero order reaction the reaction rate is proportional to zero power of the reactant concentration.
For nth order reaction, $ {{t}_{1/2}}\propto {{a}^{\left( 1-n \right)}}. $ When the reactant concentration is halved, the half-life period becomes $ 16 $ times.
 $ \dfrac{{{t}_{1/2}}}{t{{\prime }_{1/2}}}=\dfrac{{{a}^{\left( 1-n \right)}}}{a{{\prime }^{\left( 1-n \right)}}}, $ thus substitute values in the above expression; $ \dfrac{1}{16}={{\left( \dfrac{2}{1} \right)}^{1-n}} $
On further solving we get the value of $ n=5. $

Additional Information:
The half-life definition, chemistry is the time it takes for half an initial amount to disintegrate. The time that is required for half of a reactant to be converted into products. The time it takes for half of a given sample to undergo radioactive decay. The half-life definition is given by the time that it takes for one-half of the atoms of a nuclide or of an unstable element to decay the radioactively into another nuclide or element. For a given half-life reaction, the $ {{t}_{1/2}} $ of a reactant is the time required for its concentration to reach a value, the arithmetic mean of its initial and final or equilibrium) value. For an entirely consumed reactant, it is the time taken for the reactant concentration to fall to one half of its initial value.

Note:
Remember that the concepts of half-life play a vital role in the administration of drugs into the target, especially in the elimination phase, where half-life is used to discover how quickly a drug decrease in the target once it has been absorbed in a period of time (sec, minute, day) or the elimination rate constant $ ke\text{ }\left( minut{{e}^{-1}},\text{ }hou{{r}^{-1}},\text{ }da{{y}^{-1}} \right). $ It is essential to make note that the half-life is varied between different types of reaction.