Question

What is the density of an ideal gas?

Answer 1

1. Ideal gas is just a hypothetical gas that in general has no existence.
2. Ideal gas is a gas in which particles are moving randomly in all directions and the gases interacted through elastic collision without any energy loss.
3. According to the Ideal gas law if we put one mole of a sample of gas in any container maintained under constant temperature and pressure, also lowering the densities then gases will behave ideally.
4. The ideal gas equation is given as follows:$\mathrm{PV}=\mathrm{nRT}$; where P is the pressure, V is the volume, n is the number of moles, R is the gas constant and T is the temperature.
5. Density is mass per unit volume.
6. The number of moles of gasesdefined as the given mass over molecular mass.

Step 1: Writing the number of moles in terms of mass

• $\mathrm{Number}\mathrm{of}\mathrm{moles}\left(\mathrm{n}\right)=\frac{\mathrm{Given}\mathrm{mass}\left(\mathrm{m}\right)}{\mathrm{Molecular}\mathrm{mass}\left(\mathrm{M}\right)}$

Step 2: Calculating the density

• Putting the value of (n) in Ideal gas.
• $\mathrm{PV}=\frac{\mathrm{m}}{\mathrm{M}}\mathrm{RT}$; It can also be written as follows:
• $\mathrm{V}=\frac{\mathrm{mRT}}{\mathrm{MP}}$
• Dividing both sides with “m” we get;
• $\frac{\mathrm{V}}{\mathrm{m}}=\frac{\mathrm{mRT}}{\mathrm{mMP}}$; or reciprocal of both the sides$\frac{\mathrm{m}}{\mathrm{V}}=\frac{\mathrm{MP}}{\mathrm{RT}}$
• Thus, we get density which is represented as follows: $\mathrm{Density}\left(\frac{\mathrm{m}}{\mathrm{V}}\right)=\frac{\mathrm{MP}}{\mathrm{RT}}$