Radon Rn is the heaviest and the only radioactive member of

Radon (Rn) is the heaviest and the only radioactive member of Group 8A(18), the noble gases. It is a product of the disintegration of heavier radioactive nuclei found in minute concentrations in many common rocks used for building and construction. In recent years, health concerns about the cancers caused from inhaled residential radon have grown. If 1.00 × 1015 atoms of radium (Ra) produce an average of 1.373 × 104 atoms of Rn per second, how many liters of Rn, measured at STP, are produced per day by 3.39 g of Ra?

Solution

moles of Ra = mass/molecular weight

= 3.39/226 = 0.015 mol

Atoms of Ra = moles x Avogadro number

= 0.015 mol x 6.02 x 10^23

= 9.0345 x 10^21

Atoms of Rn per sec =

= 1.373 x 10^4 x 9.0345 x10^21 / 1 x 10^15

= 1.2404 x 10^11 atoms/s

1 day = 86400 s

Atoms of Rn per day

= 1.2404 x 10^11 atoms/s x 86400 s/day

= 1.0717 x 10^16 atoms /day

Moles of Rn

= 1.0717 x 10^16 / 6.02 x 10^23

= 1.779x 10^-8 mole /day

From the ideal gas equation

V = nRT/P

At STP

Temperature T = 273 K

Pressure P = 1 atm

Gas constant R = 0.0821 L-atm/mol-K

V = 1.779x 10^-8 x 0.0821 x 273 / 1

= 3.988 x 10^-7 L/day