Question

Write any three assumptions of Kinetic Theory of gases.

Answer 1

Hint
The Kinetic Theory of Matter rests upon two basic hypotheses-
1. Molecular constitution of matter
2. Association of heat with molecular motion
$\Rightarrow p = \dfrac{1}{3}\rho {C^2}$ Where $p$ is the pressure exerted by the ideal gas molecules, $\rho $ is the density of the gas and $C$ is the root mean square velocity of the molecules.
$\Rightarrow pV = $ Constant at constant temperature $T$ where $V$ is the volume of the gas.
$\Rightarrow pV \propto T$ $ \Rightarrow \dfrac{V}{T} = $ Constant at constant pressure.
$\Rightarrow p = nKT$ Where $n$ is the number of moles of the gas and $K$ is called the Boltzmann constant.
$\Rightarrow p = \sum\limits_i {{p_i}} $
$\Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = {\left( {\dfrac{{{\rho _2}}}{{{\rho _1}}}} \right)^{\dfrac{1}{2}}}$ Where ${n_1}$ and ${\rho _1}$ are the number of moles and density of gas 1 and, ${n_2}$ and ${\rho _2}$ are the number of moles and density of gas 2.

Complete step by step answer
The Kinetic Theory of Matter essentially deals with the behavior of ideal monatomic gases.
The three main assumptions of the Kinetic Theory are:
1. A small sample of gas consists of a large number of molecules which are like minute hard elastic spheres in perpetual random motion.
2. No forces of attraction or repulsion exist between the molecules and the walls of the container. Thus, their total energy is kinetic in nature.
3. The molecules are assumed to be geometrical mass points such that the volume occupied by them is negligible compared to the volume of the whole gas (the container).
Now, using these assumptions we can establish a number of laws to describe an ideal gas. Some of them are as follows:
- Deduction of pressure expression $p = \dfrac{1}{3}\rho {C^2}$ where $p$ is the pressure exerted by the ideal gas molecules, $\rho $ is the density of the gas and $C$ is the root mean square velocity of the molecules.
- Boyle’s Law- $pV = $ constant at constant temperature $T$ where $V$ is the volume of the gas.
- Charles’ Law- $pV \propto T$ $ \Rightarrow \dfrac{V}{T} = $ constant at constant pressure.
- Clapeyron’s equation- $p = nKT$ where $n$ is the number of moles of the gas and $K$ is called the Boltzmann constant.
- Dalton’s law of partial pressures- $p = \sum\limits_i {{p_i}} $ which states that the pressure of a mixture of a number of gases is equal to the sum of the partial pressures of its components.
- Avogadro’s hypothesis- ${n_1} = {n_2}$ which means that equal volumes of all gases, under like conditions of temperature and pressure, contain equal numbers of molecules.
Graham’s law of diffusion- $\dfrac{{{n_1}}}{{{n_2}}} = {\left( {\dfrac{{{\rho _2}}}{{{\rho _1}}}} \right)^{\dfrac{1}{2}}}$ where ${n_1}$ and ${\rho _1}$ are the number of moles and density of gas 1 and, ${n_2}$ and ${\rho _2}$ are the number of moles and density of gas 2.

Note
The Kinetic Theory of Matter is only applicable for ideal gases. We cannot explain the behavior of real gases from this theory. In order to understand the behavior of real gases we need to modify some of the assumptions of the kinetic theory. We need to account for the definite volume of the gas molecules which were assumed to be negligible for an ideal gas, and account for intermolecular forces between the molecules.