Determining the Molar Volume of a Gas

Measurable Properties of Gases:

A gas is said to be a state of matter which can be differentiated from solid and liquid due to its relatively low density, viscosity, and its ability to contract and expand or diffuse with respect to change in the temperature and pressure. The characteristics of the gases can be described using four important properties, which are collectively termed as called as the measurable properties of gases.

The measurable properties of gases are
1.Volume of the gas
2. Pressure of the gas
3. Temperature of the gas
4. Amount of the gas (mass)

Volume

Volume which is one of the measurable property of the gas is denoted by the letter 'V'. It is expressed in litres(L) , milliliters(mL), cubic centimeters(cm³),  cubic metres(dm³)  and cubic decimetres(dm³).
1litre = 1000 millilitres  , 1 millilitre = 1cubic centimetre and 1 cubic metre = 1000 cubic centimetre
1L  = 1dm³ = 10^–3 m³   = 1000 mL = 1000000 cm³
The volume of the gas depends on the pressure, temperature and the amount of gas present.The measurement of volume of gas requires the measurement of volume of the container in which the gas is present.

Pressure

Pressure is the next important measurable property of the gas which is denoted by the letter 'P'. Pressure of the gas is the force exerted by the gas per unit area.It depends on the kinetic energy of the molecules. As the kinetic energy inturn depends on temperature, the pressure is directly proportional to the temperature of the gas.
Pressure (P) = Force/Area = (Mass) (Acceleration)/Area
Pressure is commonly expressed in atmospheres, mm of Hg, torr, bar, and K.Pa.
1atm = 760mm of Hg = 760 torr = 1.01325 bar = 101.325 kPa = 101.326 x 10³ N m^-2  
Pressure of the gas can be measured by Barometer.    

Temperature

The temperature of the gas is denoted by  the letter 'T'.The temperature of a gas depends on the kinetic energy of the gas.The gases  expand on increasing the temperature.The temperature of the gas is generally expressed in Fahrenheit (F^o), Centigrade degree (^oC)  or celsius degree and Kelvin (K).
   K = ^oC + 273  and ^oC/5 = F^o–32/9
The temperature is measured by the help of a Thermometer.

Amount of gas

Amount of gas or the mass is a measurable property of the gas.The mass of the gas is related to the number of moles of the gas. The mass of the gas is generally expressed in kilograms(Kg) or grams(g).
number of moles (n) = mass of the gas/ molar mass of the gas
                                    n = m/M
The mass of the gas can be found through weighing. The mass of the gas can be obtained by subtracting the mass of the container in which the gas is present from the total mass.

Determining The Molar Volume of a Gas:

The Ideal gas law states that,
PV=nRT
Where P is pressure,V is volume, n is number of moles,R is gas constant and T is temperature.
At STP,which means standard temperature and pressure,the values of  temperature and pressure are 273 K [0 C] and 1 atm respectively.
If these values are substituted,we get,
1xV=nRx273
also substitute n= one mole and substitute value of  R= 0.082 Liter-Atmospheres per Mole-Degree Kelvin,
we get,
V=22.4 L
So one mole of a gas at STP would occupy 22.4L of volume.This is called as molar volume of a gas.
So irrespective of a gas,its one mole would occupy 22.4L of volume.

Illustration on Determining the Molar Volume of a Gas :

Find the volume of 88g of CO₂ at STP.
First find moles of CO_2. in 88g of CO_2.
Moles=Mass in g/Molar mass
=88/44
=2 moles
Volume of 2 moles= 2 x 22.4
=44.8 L
The volume of oxygen gas at STP is 128 L.Find the number of moles.
Now the molar mass of oxygen is 32.
So 32g would ocuupy 22.4 L
128 g would occupy 128 x 22.4 /32
=4 x 22.4
=89.6 L

Determining Molar Volume and the Number of Molecules of Gas

Avogadro further determined that a mole of a gas at STP contains 6.022 x 10²³ molecules.
The determination of the molar volume of 22.4 L and the number of molecules i.e. 6.022 x 10²³  and the number of molecules i.e. 6.022 x 10²³ at STP,brought out a revolution in the study of gases as well as other phases.
Let us consider an example.
Find out the number of molecules in   128g of oxygen gas at pressure 1 atm and temperature 273⁰K.
Let us find the number of moles.
Moles=Mass in g/molar mass
=128/32
=4
Now one mole of a gas contains 6.022 x 10²³
So 4 moles would contain,
4 x 6.022 x 10²³
=24.088 x 10²³ molecules.