Respuesta :
Deuterium is isotope of hydrogen with percent natural abundance 0.015%. Thus, if 100 gram of naturally occurring hydrogen gas is taken it will have 0.015 g of deuterium.
Or,
[tex]0.015g ^{2}H\rightarrow 100 g ^{1}H[/tex]
or,
[tex]1 g^{2}H\rightarrow 6666.67 g ^{1}H[/tex]
The number of deuterium atoms are given [tex]2.50\times 10^{21}[/tex].
Since, 1 mol is equal to [tex]6.023\times 10^{23}[/tex] atoms thus,
[tex]1 atom\rightarrow \frac{1}{6.023\times 10^{23}}mol=1.66\times 10^{-24}mol[/tex]
Thus, [tex]2.50\times 10^{21}[/tex] will be equal to [tex]2.50\times 10^{21}\times 1.66\times 10^{-24}=0.00415 mol[/tex]
Molar mass of deuterium is 2.0140 u or 2.0140 g/mol thus, mass can be calculated as:
[tex]m=n\times M=0.00415 mol\times 2.0140 g/mol=0.00836 g[/tex]
thus, mass of [tex]^{2}H[/tex] is 0.00836 g
Since, [tex]1 g^{2}H\rightarrow 6666.67 g ^{1}H[/tex]
Thus, [tex]0.00836 g ^{2}H\rightarrow 0.00836\times 6666.67=55.73 g ^{1}H[/tex]
Therefore, mass of naturally occurring hydrogen gas that has to be processed is 55.73 g.
