PROBLEM 103P

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 mm Hg and 25 °C, is 0.275 g. What is the molecular formula of the compound?

Solution 103P

Here, we are going to find the molecular formula of the given compound.

Step 1:

Molecular formula gives the total number of atoms in a molecule.

Step 2:

In order to determine the whole number ratio of C and H in the formula, the following table is drawn:

Element |
% |
Relative number of atoms(% / atomic mass) |
Simple ratio |
Whole number ratio |

C |
82.66 |
82.66/12 = 6.89 |
6.89/6.89 = 1 |
x 2 = 2 |

H |
17.34 |
17.34/1 = 17.34 |
17.34/6.89 = 2.5 |
x 2 = 5 |

Hence, empirical formula of the compound is C2H5.

Empirical formula mass = (2 x 12) + (5 x 1) = 24 + 5 = 29

Step 3:

Again, from ideal gas equation, we have,

pV = nRT ----(1)

Where, p = pressure

V = volume of the gas

n = number of moles of the gas

R = universal gas constant and its value is 0.0821 L atm K-1 mol-1

T = temperature

Here, p = 556 mm Hg = 556 / 760 atm = 0.73 atm

V = 158 mL = 158 / 1000 L = 0.158 L

T = 25oC = 25 + 273 K = 298 K

Substituting the values in equation (1), we get,

n = pV / RT

n = (0.73 atm x 0.158 L) / (298 K x 0.0821 L atm K-1 mol-1)

= (0.11534 L atm) / (24.4658 L atm mol-1)

n = 0.0047 mol.