# Given the following data, calculate the molar mass. Barometric pressure: 639.4 mm Hg Mass of...

## Question:

Given the following data, calculate the molar mass.

Barometric pressure: 639.4 mm Hg

Mass of the flask and foil: 79.5 g

Mass of the flask, foil, and condensed liquid: 81.4 g

Temperature of water bath: 99.9 degree C

## Ideal Gas Law

The ideal gas law can be used to model gas behaviors by relating its pressure, volume, amount in moles and temperature. Though it is not perfect, it does give pretty good approximation under common conditions. The ideal gas law is expressed as PV = nRT, where R is the universal gas constant.

{eq}molar\;mass=550.\;g/mole {/eq}

This is the Dumas method for molar mass of gas determination where a volatile liquid is heated to vaporize and allowed to fill a container. Then left to cool so the amount of gas in the container can be determined by weighing. Then using ideal gas law, the moles of gas can be calculated. Along with the calculated moles and measured mass, molar mass can be calculated.

Pressure

$$639.4\;mmHg \times \frac {1\;atm}{760\;mmHg} = 0.841\;atm$$

Volume

$$125.8\;mL \times \frac {1\;L}{1000\;mL} = 0.1258\;L$$

Temperature

$$99.9\;^oC +273.15 = 373.05\;K$$

Mass of gas$$81.4\;g - 79.5\;g = 1.9\;g$$

Moles of gas (n) is calculated using the idea gas law

$$PV = nRT$$

$$n = \frac {PV}{RT}$$

$$n = \frac {(0.841\;atm)(0.1258\;L)}{(0.0821 \frac {atm \cdot L}{mole \cdot K})(373.05\;K)} =0.003456\;mole$$

The molar mass is then

$$\frac {1.9\;g}{0.003456\;mole} = 550.\;g/mole$$ 