States of Matter

1. Introduction

Matter exists in three common physical states - gas, liquid and solid - which differ in how closely and how regularly their particles are packed and in the strength of the forces between them. In gases the particles are far apart and move freely; in liquids they are close but mobile; in solids they are fixed in a regular pattern. This chapter examines each state and the laws that describe gas behaviour.

---

2. The Gaseous State

2.1 Kinetic Theory of Gases and its Postulates

The kinetic molecular theory explains gas behaviour in terms of moving molecules. Its main postulates:

1. A gas consists of a very large number of tiny particles (molecules) in constant, random, straight-line motion.
2. The actual volume of the molecules is negligible compared with the total volume of the gas (molecules are treated as points).
3. There are no forces of attraction or repulsion between the molecules.
4. Collisions between molecules, and with the walls, are perfectly elastic (no kinetic energy is lost).
5. The pressure of the gas arises from the collisions of molecules with the walls of the container.
6. The average kinetic energy of the molecules is directly proportional to the absolute (Kelvin) temperature: $\bar{KE} \propto T$.

2.2 Gas Laws

Boyle's Law (constant $T$, fixed mass): the volume of a gas is inversely proportional to its pressure.

$$ \begin{aligned} & V \propto \frac{1}{P} \ \ & \Rightarrow\ \ & PV = \text{constant} \ \ & \Rightarrow\ \ & P_1V_1 = P_2V_2 \end{aligned} $$

Charles's Law (constant $P$, fixed mass): the volume is directly proportional to the absolute temperature.

$$ \begin{aligned} & V \propto T \ \ & \Rightarrow\ \ & \frac{V}{T} = \text{constant} \ \ & \Rightarrow\ \ & \frac{V_1}{T_1} = \frac{V_2}{T_2} \end{aligned} $$

Gay-Lussac's (Pressure) Law (constant $V$): the pressure is directly proportional to the absolute temperature: $\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$.

Avogadro's Law (constant $T$, $P$): equal volumes of all gases contain equal numbers of molecules; $V \propto n$.

Combined Gas Law:

$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$

2.3 Ideal Gas and the Ideal Gas Equation

An ideal (perfect) gas is a hypothetical gas that obeys the gas laws exactly at all temperatures and pressures, and in which the molecules have negligible volume and no intermolecular forces. Combining the gas laws gives the ideal gas equation:

$$\boxed{PV = nRT}$$

where $n$ is the number of moles and $R$ the universal gas constant. Since $n = \dfrac{m}{M}$, the equation also gives molar mass: $M = \dfrac{mRT}{PV}$.