Question

Ima Chemist found the density of Freon-11 (CFCl3) to be 5.58 g/L under her experimental conditions. Her measurements showed that the density of an unknown gas was 4.38 g/L under the same conditions. What is the molar mass of the unknown?

Answer 1

If we assume this two gases behave like ideal gas, then we use the ideal gas law $PV=nRT$, where P is the pressure, V is the volume, n number of moles, R gas constant and T the temperature in kelvins. As well as the density formula $D=\frac{m}{V}$. First we calculate the molarity for Freon

$CFCl_3 = (12+ 18.998 + 3 \times 35.453) =137.36\ g/mol$.

The number of moles for freon are

$D=\frac{m}{V} =\frac{ nM}{L} \implies n= \frac{DL}{M} = \frac{5.58 g \times L}{L \times 137.36g/mol}= 0.0406 mol$

We know $n=\frac{m}{M}$, so we insert this concept to our ideal gas equation

$PV=n \times RT=\frac{m}{M} \times RT= \frac{mRT}{M}$. Since $D=\frac{m}{V}$, we insert this concept to the formula

$PV=\frac{mRT}{M} \\P=\frac{mRT}{VM} = \frac{DRT}{M} \\\\\implies M= \frac{DRT}{P}$. The measurements take place in same conditions so,

$M=\frac{DRT}{P} = \frac{4.38g}{L}\times \frac{1L}{0.0406mol} = 107.9\ g/mol$