What is Gas Density ? How to find the Gas Density By Ideal Gas Equation ? Made Easy

To find the density of a gas from ideal gas equation, we come to know that what is density.
What is Density ?
Mass per unit volume is called density.
Density is denoted by a symbol ρ. SI unit of density is killogram per meter cubic.In symbolic form ρ = kgm^-3.

It is easy to find the density of matter if we have mass and occupied volume values. By knowing two from the density, mass and volume we can find the third one.

Ideal Gas Equation.
                                       PV=nRT
where;
P = Pressure of gas
V = Volume of gas
n  = number of moles of gas
R = Gas constant   (In SI Units, the value of gas constant is 8.314 J / mol. K)
T= Temprature of gas

As we have to find the density of gas which is equal to mass per unit volume.
                                     
                                        ρ  = Mass/Volume

In order to find the density of a gas we have to find the volume and mass of the gas with the help of ideal gas equation.
                                       PV=nRT
                                       
                                       V = nRT/P  -----------eq1

Now, we have to find the mass of the gas.As we know that number of moles is equal to mass by Molar Mass

So from n,

                                       n=mass/Molar Mass

                                       n=m/MM

Putting the value of n in eq1

we get

                                     V = mRT/MM·P

By Dividing both sides by mass (m) we get.

                                     V/m = RT/MM·P

By arranging the equation in a way that we get the density, by inverting the whole equation.

                                     m/V = MM·P/RT

                                     ρ = MM·P/RT

Here we have derived the equation, by which we can find the density.But we need the Molar Mass of gas, Pressure of gas and Temprature of the gas.

Examples.

Find the density of ammonia gas at 100॰C when confined by a pressure of 1600mm of Hg.

Solution.

d =?

T=100+273 = 373K

P=1600mm of Hg = 1600/760 mm = 2.105 atm

MM of ammonia = 17g/mole

R = 0.0821 dm^3 atm/mol·K

According to equation we have derived,

                                  ρ = MM·P/RT

                                  ρ = 17x2.105/0.082·273

                                  ρ =  1.598 g dm^-3