# How do you find the moles of a substance or the molecular formula with gas laws? Specifically, how do you explain n = m/M?

Jan 30, 2014

The Ideal Gas Law allows us to calculate the number of moles, which we can then use to calculate the molar mass. If we know the empirical formula, we can then calculate the molar mass and the molecular formula.

The molar mass M is the mass of a given substance divided by its number of moles.

M = $\frac{m}{n}$

We can solve this equation to get n = $\frac{m}{M}$.

EXAMPLE:

Cyclopropane has the empirical formula CH₂. At 50.0 °C and
0.984 atm pressure, 1.56 g of cyclopropane has a volume of 1.00 L. What is the molecular formula of cyclopropane?

Solution

Use the Ideal Gas Law to calculate the number of moles.

PV = nRT

n = $\frac{P V}{R T}$ = ((0.984 atm)×(1.00 L))/((0.082 06 L•atm•K⁻¹mol⁻¹)× (323.2 K)) =
0.0371 mol

M = $\frac{m}{n} = \frac{1.56 g}{0.0371 m o l}$ = 42.0 g/mol

The empirical formula mass of CH₂ is (12.01 + 2.016) g/mol =
14.03 g/mol

Now divide the molar mass by the empirical formula mass. This tells you how many times the empirical formula is repeated to make the molecular formula.

$\frac{42.0}{14.03}$ = 3.00 ≈ 3

The molecular formula of cyclopropane is (CH₂)₃ or C₃H₆.