PROBLEM 104P

A gaseous compound containing hydrogen and carbon is decomposed and found to contain 85.63% C and 14.37% H by mass. The mass of 258 mL of the gas, measured at STP, is 0.646 g. What is the molecular formula of the compound?

Solution 104P

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 |
85.63 |
85.63/12 = 7.14 |
7.14/7.14 = 1 |
1 |

H |
14.37 |
14.37/1 = 14.37 |
14.37/7.14 = 2.01 |
2 |

Hence, empirical formula of the compound is CH2.

Empirical formula mass = (1 x 12) + (2 x 1) = 12 + 2 = 14

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 = 1 atm (STP)

V = 258 mL = 258 / 1000 L = 0.258 L

T = 273 K (STP)

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

n = pV / RT

n = (1 atm x 0.258 L) / (273 K x 0.0821 L atm K-1 mol-1)

= (0.258 L atm) / (22.4133 L atm mol-1)

n = 0.0115 mol.