Question

If 1.00x10^15 atoms of radium (Ra) produce an average of 1.373x10^4 atoms of Rn per second, how many liters of Rn, measured at STP, are produced per day by 5.53g of Ra?

Answer 1

atoms of Ra in 5.53 g = ( 5.53 g / 223.0185 g/mol )* 6.022 x 10^23 atoms/mol

= 1..493 x 10^22 atoms

1..493 x 10^22 atoms will produce = (1..493 x 10^22 / 1.00x10^15 )* 1.373x10^4 atoms of Rn per second

= 2.05 x 10^11 atoms of Rn per second

therefore

atoms of Rn per day = 2.05 x 10^11 atoms / s x 24 x 60 x 60 s /day

= 1.77 x 10^16 atoms/day

moles of Rn = 1.77 x 10^16 atoms / 6.022 x 10^23 atom/mol

   = 2.94 x 10^-8 mol

therefore

volume of Rn =  2.94 x 10^-8 mol x 22.4 L /mol

   = 6.59 x 10^-7 Liter