# A gas weighing 23.6 g occupies a 10.0 L flask at 27 degrees C and 780 torr of pressure. Calculate...

## Question:

A gas weighing 23.6 g occupies a 10.0 L flask at 27 degrees C and 780 torr of pressure. Calculate the molar mass of the gas.

## Molar Mass:

The molar mass of any gas is the mass of 1mol of gas. That means molar mass is the mass of Avogadro's number of gas molecules. At stp the molar volume of any gas is 22.4 L.

Consider the gas as an ideal gas. Hence it follows the ideal gas equation.

The ideal gas equation is written below.

• {eq}PV = nRT {/eq}

{eq}\ \ \ \ {/eq} or,{eq}n = \frac{PV}{RT} {/eq}

Where, V=Volume=10 L, P=Pressure = 1.026 atm{760 torr = 1 atm}, n=number of moles = ?, R=Gas constant = {eq}0.082 L \ atm \ mol^{-1} \ K^{-1} {/eq}, T = temperature = (27 + 273)K = 300K.

Hence, {eq}n= \frac{1.026 atm \times 10 L }{ 0.082 L \ atm \ mol^{-1} \ K^{-1} \times 300K } = 0.417 mol. {/eq}

Now, molar mass ={eq}\frac{mass}{mole} = \frac{23.6g}{0.417 mol} =56.6 g/mol {/eq}

Therefore the molar mass of the gas is 56.6 g/mol. 