A gas consists of 85.7 percent carbon and 14.3 percent hydrogen, by weight. A sample of this gas weighing 0.673 g occupies 729 mL at a pressure of 720.0 mmHg and a temperature of 77°C. Calculate its empirical and molecular formulas.

Question

Quizplus · Accepted Answer

1. Calculate the moles of carbon and hydrogen in the sample:
m(C) = 0.673 g x 0.857 = 0.577 g
mol(C) = 0.577 g / 12.01 g/mol = 0.048 mol
m(H) = 0.673 g x 0.143 = 0.096 g
mol(H) = 0.096 g / 1.008 g/mol = 0.095 mol

2. Calculate the empirical formula:
The lowest whole number ratio of moles of carbon to moles of hydrogen is:
0.048 mol / 0.048 mol = 1 C
0.095 mol / 0.048 mol = 2 H
Empirical formula: CH2

3. Calculate the molecular formula:
To determine the molecular formula, we need to know the molar mass of the compound. We can calculate it from the ideal gas law:
PV = nRT
n = (PV) / (RT) = (720.0 mmHg x 0.729 L) / (62.36 L mmHg K^-1 x 350.15 K) = 0.0223 mol
Molar mass = 0.673 g / 0.0223 mol = 30.2 g/mol

The empirical formula mass of CH2 is 14.03 g/mol, so the molecular formula must be a multiple of CH2 that gives a molar mass of 30.2 g/mol:
30.2 g/mol / 14.03 g/mol = 2.15, which is close enough to 2 to conclude that the molecular formula is:
Molecular formula: C2H4

A Gas Consists of 85