Question

How do you calculate the density of a gas with temperature change?

Answer 1

Hint: In order to calculate the density of a gas with temperature change, we must first know what an ideal gas is. The gas which can follow all the gas equations that involves temperature and pressure are called the Ideal gas.

Complete step by step answer:
- First let us learn about the ideal gas. Gas is one of the fundamental states of matter and it is of two types: one is the real gas and the other is the ideal gas. Ideal gases are those gases which can follow all gas laws that involve temperature and pressure.
- Let us now understand what the density of a gas is. Density of a gas can be defined as the mass per unit volume under various conditions of the temperature and pressure. In other words, we can also say that the density is the mass divided by the volume. Density is represented by the symbol \[\rho \] and it is given as
\[\rho = \dfrac{m}{V}\]
We can write the ideal gas equation as
\[PV = nRT\]
Where,
P is said to be the pressure of the gas, V is said to be the volume of the gas, n is the number of moles of the gas, R is the gas constant and T is the temperature.
\[n = \dfrac{m}{{{M_o}}}\]
Where m is the mass of the gas and \[{M_o}\] is the molar mass of the gas. Therefore, we can write
\[PV = \dfrac{m}{{{M_o}}}RT\]
\[P{M_o} = \dfrac{m}{V}RT\]
Where the density, \[\rho = \dfrac{m}{V}\]
\[P{M_o} = \rho RT\]
\[\rho = \dfrac{{P{M_o}}}{{RT}}\]
As we know that R and \[{M_o}\] are constants and therefore, we can write as
\[\rho \propto \dfrac{P}{T}\]
From the above equation we can say that the density is directly proportional to the Pressure and inversely proportional to the Temperature.

Note: Real gases are different from the ideal gases. Real gases are those gases which obey gas laws at only low pressure and high temperature. Volume occupied by molecules of a gas are not negligible compared to the total volume of gas. Real gases are said to follow the Vander Waals equation.
 \[\left( {P + \dfrac{{a{n^2}}}{{{V^2}}}} \right)\left( {V - nb} \right) = nRT\]