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 7.25 g of Ra?
Answers
Answer:
1.1347 * 10 ^ - 8 liter / day
Explanation:
1) convert 9.64 g of Ra to number of moles, using the atomic mass of Ra
number of moles = mass in grams / atomic mass
atomic mass of Ra = 226 g/mol
number of moles Ra = 9.64 g / 226 g/mol = 0.042654867 moles
2) number of atoms in 0.042654867 moles
number of atoms = number of moles * Avogadro's number
number of atoms of Ra = 0.042654867 * 6.022 * 10^ 23 = 2.568676 * 10^ 22 atoms of Ra
3) atoms of Rn produced
Proportion
1.00 × 10^15 atoms of Ra 2.568676 × 10^22 atoms of Ra
------------------------------------- = --------------------------------------------
1.373 × 10^4 atoms of Rn/s x
x = 3.52679 × 10^ 10 atoms of Rn/s
4) liters per day
PV = nRT => V = nRT /P
STP => T = 273.15K, P = 1 atm
n = 3.52679 × 10^ 10 atoms of Rn/s / (6.022 * 10^ 23 atoms / mol) =5.85651 * 10 ^ -14 mol/s
=> V = 5.85651 * 10^ -14 mol/s * 0.0821 atm*liter / mol*K * 273.15 / 1 atm =
V = 1.3133 * 10 ^ -13 liter / s
Per day => 1.313 * 10 ^ -13 liter / s * 24 h/day * 3600 s/h = 1.1347 * 10 ^ - 8 liter / day
And that is the answer: