# At 18.0 Celsius and 765 torr, 2.29 dm^3 of a gas weigh 3.71 g. How to calculate the approximate molar mass, in g/mol, of the gas?

Feb 28, 2015

The approximate molar mass of the gas is $\text{40.2 g/mol}$.

In order to determine molar mass, which expresses the weight of 1 mole of gas, you need two things - the gas' mass, which you know to be 3.71 g, and the number of moles of gas in that sample, which you must calculate.

Now, when dealing with gases always think ideal gas law equation, $P V = n R T$. In this case, you can use this euation to determine the number of moles of gas

$P V = n R T \implies n = \frac{P V}{R T} = \left(\left(\frac{765}{760}\right) \text{atm" * "2.29 L")/(0.082("L" * "atm")/("mol" * "K") * (273.15 + 18.0)"K}\right)$

n_("gas") = "0.0923 moles"

Notice that I've convertyed the pressure to atm, the volume to liters, and the temperature to K - all necessary if you want to use the 0.082 L atm/mol K value for R.

Now that you know how many moles the sample contains, solve for the molar mass by

$\text{molar mass" = m/n = "3.71 g"/"0.0923 moles" = "40.2 g/mol}$