Question

A gaseous compound containing hydrogen and carbon is decomposed and found to contain 82.66 % carbon and 17.34 % hydrogen by mass. The mass of 158 mL of the gas, measured at 556 mmHg and 25 ∘C, is found to be 0.275 g. What is the molecular formula of the compound? Express your answer as a chemical formula.

Answer 1

Basis: 100 g of the compound

Mass of carbon = 82.66 g
Molar mass of carbon atom = 12 g/mol
Moles of carbon atom = 82.66/12 = 6.89

Mass of hydrogen = 17.34 g
Molar mass of hydrogen atom = 1.0 g/mol
Moles of hydrogen = 17.34/1 = 17.34

Smallest no of moles = 6.89 for carbon
Finding mole ratio with respect to smallest mole number carbon

Mole ratio carbon, = 6.89/6.89 = 1.0
Mole ratio hydrogen = 17.34/6.89 = 2.5

Making the mole ratio whole number by multiplying 2

No of carbon = 1*2 = 2
No of hydrogen = 2.5*2 = 5

Empirical formula = C2H5
Empirical formula mass = 2*12+5*1=29 g/mol

The mass of 158 mL of the gas, measured at 556 mmHg and 25 °C, is found to be 0.275 g.
V = 158/1000 = 0.158 L
P = 556 mm Hg * 1/760 atm/mmHg = 0.73 atm
T = 25+273 = 298 K
Gas constant, R = 0.0821 L atm/mol K
no of moles, n = P*V/(R*T) = 0.73*0.158/(0.0821*298) = 0.0047 moles
Mass, w = 0.275 g
Molecular mass, MW = w/n = 0.275/0.0047 = 58 g/mol

multiplying factor, n = molecular mass/empirical formula mass = 58/29 = 2
chemical formula =(empirical formula)2 = (C2H5)2 = C4H10