Question

Be sure to answer all parts. 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 8.68 g of Ra?

Answer 1

Molar mass of Radium = 226 g/mol

Mass of radium used =  8.68 g

Mols of radium =  8.68 g / 226. g/mol = 0.0389 Moles

No of radium atoms =  0.0389 Moles x 6.023 x 1023 atoms / mol = 2.345 x 1022 atoms

No of radon is produced by 1.00 × 1015 atoms of radium =  1.373 × 104

No of radon is produced by 2.345 x 1022 atoms of radium = (1.373 × 104) x (2.345 x 1022) / (1.00 × 1015 )

= 3.2196 x 1011 atoms / second

Let us calculate the no of atoms produced per day

One day = 24 x 60 x 60 = 84600 seconds

no of atoms produced per day =    3.2196 x 1011 x 86400 = 2.78178 x 1016 atoms /day  

let us convet into moles =   2.78178 x 1016 atoms / 6.023 x 1023 atoms / mol = 4.618 x 10-8 Moles /day

using idea gas equation let us solve to find the volume

PV= nRT

P = Pressure in atm                       V= Volume in Liter

n = no of moles               R = 0.08206 L atm K-1 Mol-1

T = Temperature in Kelvin

At STP   T = 273.15K, P = 1 atm   

v = ?

substitute the values and calculate the volume

V= nRT / P

V = 4.618 x 10-8 Mol x 0.08206 L atm K-1 Mol-1 x 273.15K / 1 atm = 1.035 x 10-6 Liter

Hence 8.68 g of Radium will produce 1.035 x 10-6 Liter of radon under STP condition.