Question

How do you find density in ideal gas law?

Answer 1

Ideal gas law:

1. It states that the product of one gram molecule's pressure and volume is equal to the product of the gas's absolute temperature and the universal gas constant.
2. This is given by the equation $\mathrm{PV}=\mathrm{nRT}$ where P is the pressure of ideal gas, V is the volume of gas, n is the moles of an ideal gas, T is temperature and R is the universal gas constant.
3. For calculating density we must know the volume and mass of gas.
4. From the above formula, we get volume V $=\frac{\mathrm{nRT}}{\mathrm{P}}$
5. From the formula of moles i.e.$\mathrm{n}=\frac{\mathrm{Given}\mathrm{mass}\left(\mathrm{m}\right)}{\mathrm{molar}\mathrm{mass}\left(\mathrm{M}\right)}$, we get moles in terms of masses.
6. Replacing the formula of moles in ideal gas law we get $\mathrm{PV}=\frac{\mathrm{mRT}}{\mathrm{M}}$, volume $\mathrm{V}=\frac{\mathrm{mRT}}{\mathrm{MP}}$
7. Density is defined as mass per volume, diving both the sides by $\mathrm{m}$ we get $\frac{\mathrm{m}}{\mathrm{V}}=\frac{\mathrm{MP}}{\mathrm{RT}}$
8. Therefore, Density $\mathrm{\rho }=\frac{\mathrm{MP}}{\mathrm{RT}}$