Question

How do you find the density in the ideal gas law?

Answer 1

Hint In reality ideal gas does not exist it is just a hypothetical gas which is proposed to simplify the equations. It is made up of a set of randomly moving point particles which interact only through elastic collisions and there is no loss of kinetic energy during collision.

Complete answer:
If we take one mole sample of any gas and put them in a container and maintain a constant temperature and pressure and lower the density then at really lower densities all the real gases tend to obey the universal law which is known as ideal gas law. This law describes an equation which is known as ideal gas equation and this equation is given by the equation:
$PV=nRT$
Where P = Pressure, V = Volume, n = number of moles, R = Gas constant and T = Absolute temperature.
Now we know that density is given $\dfrac{mass}{volume}$so we need to know the mass of the gas and volume.
$V=\dfrac{nRT}{P}$
Number of moles of gas can be calculated by given mass of the gas divided by its molar mass whose equation can be given by:
$n=\dfrac{m}{M}$
Put the value of n in equation of volume
$V=\dfrac{mRT}{MP}$
Density is given by$\dfrac{mass}{volume}$. Divide the above equation by m on both sides
$\dfrac{V}{m}=\dfrac{mRT}{mMP}$ i.e $Density=\dfrac{m}{V}=\dfrac{MP}{RT}$
Density is denoted by the symbol$\sigma $. Hence we can say that in this we can calculate the density of ideal gas law.

Note: Ideal gas law also suffers from a serious limitation that equations hold only in that condition when the density is low. The shape of the pressure-temperature curve and volume-temperature curve for the ideal gas is always a straight line.