# Question #13daf

Mar 25, 2015

Start from the ideal gas law equation, $P V = n R T$, where n is the number of moles.

The number of moles can be written as the ratio between the weight of the gas, i.e. its mass, and its molecular mass.

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

This means that you can write

$P V = \left(\frac{m}{M} _ M\right) R T$

Density is defined as mass per unit of volume

$\rho = \textcolor{b l u e}{\frac{m}{V}}$

Therefore, if you rearrange the equation, you obtain

$P V = \frac{m}{M} _ M \cdot R T \implies P \cdot {M}_{M} \cdot V = m R T$

$P \cdot {M}_{M} = \textcolor{b l u e}{\frac{m}{V}} \cdot R T = \rho \cdot R T$

As a result,

${M}_{M} = \frac{\rho \cdot R T}{P} = \left(1.43 \text{g"/cancel("L") * 0.082(cancel("atm") * cancel("L"))/("mol" * cancel("K")) * (273.15 + 23)cancel("K"))/("0.789"cancel("atm}\right)$

${M}_{M} = \text{44 g/mol}$ $\to$ rounded to two sig figs.

The gas could be carbon dioxide, $C {O}_{2}$.