Question

A $_{84}^{210}Po$ decays with alpha particles to $_{82}^{206}Pb$ with a half life of 138.4 days. If 1.0g of $_{84}^{201}Po$ is placed in a sealed tube how much helium will accumulate in 69.2 days? Express the answer in cc at STP?

Answer 1

Hint: Chemical kinetics is the branch of chemistry which helps to determine the rate of chemical reaction and the factors that affect the rate of chemical reaction. The radioactive and unstable nuclei undergo decay reaction and emit particles.

Complete step by step answer:
As we know that it is important to know the extent, feasibility and application of a chemical reaction to determine the rate of the reaction and factors affecting it. But it is equally important to know the composition of the chemical reaction which can be determined by the concentration and decomposition of its elements. Thus, chemical kinetics is an important branch of chemistry to determine the rate of a reaction.

All the natural and radioactive decay reactions of all the unstable nuclei take place by first order kinetics. Alpha decay is a type of a radioactive decay reaction in which the nucleus emits alpha particles and decays into a nucleus with a reduced mass number by four and a reduced atomic number by two.
The half life of a reaction is a reaction in which the concentration of a reactant of a reaction is reduced to half of its original or initial concentration. It is given by
${t_{\dfrac{1}{2}}} = \dfrac{{[{R_O}]}}{{2k}}$ where $[{R_O}]$ is the initial concentration of the reactant and $k$ is the rate of reaction.

For the above question we consider the equation,
$_{84}^{210}Po \to _2^4He + _{82}^{2036}Pb$
$ \Rightarrow 1 g Po = \dfrac{1}{{210}}molPo$
It is given that $Po$ left in $69.2days = C$
$ \Rightarrow C = Co{\left( {\dfrac{1}{2}} \right)^y}$
Where $y = \dfrac{{totaltime}}{{{t_{50}}}}$
$ \Rightarrow \dfrac{{69.2}}{{138.4}} = \dfrac{1}{2}$
$ \Rightarrow C = {\left( {\dfrac{1}{2}} \right)^{\dfrac{1}{2}}} = 0.7071g$
We know that
$Po$ changes to helium = $1 - 0.7071g$
$ \Rightarrow 0.2929g$
$
 \Rightarrow 1.3947 \times {10^{ - 3}}mol \\
  \\
 $

Therefore, Helium formed = $31.24cc$ at STP.

 Note:
Helium is a colourless, non-toxic and inert chemical element with symbol $He$ and has atomic number 2. It is one of the noble gases as it is unreactive. Helium gas is used to inflate balloons and for applying pressure to fuel tanks and issued in various medical treatments.