States of Matter is among the foundational topics in NEET Physical Chemistry, contributing 1–2 questions each year, primarily numerical calculations and conceptual interpretation of gas behavior. It spans the kinetic-molecular description of gases, the laws governing ideal gas behavior, the deviations observed in real gases, the van der Waals model, and the macroscopic properties of the liquid state.

Intermolecular Forces and States

The three states of matter — solid, liquid, and gas — arise from the competition between kinetic energy (which disperses) and intermolecular forces (which attract). Intermolecular forces increase in the order: dispersion (London) forces < dipole-dipole interactions < hydrogen bonding. Stronger intermolecular forces lead to higher boiling points, lower vapor pressures, higher surface tension, and higher viscosity.

The Gas Laws

Four empirical laws describe ideal gas behavior. Boyle's law states that at constant temperature and amount, pressure and volume are inversely proportional: $PV = \text{const}$, or $P_1V_1 = P_2V_2$. Charles's law states that at constant pressure, volume is directly proportional to absolute temperature: $V/T = \text{const}$, or $V_1/T_1 = V_2/T_2$. Gay-Lussac's law states that at constant volume, pressure is directly proportional to absolute temperature: $P/T = \text{const}$. Avogadro's law states that at constant temperature and pressure, equal volumes of all gases contain equal numbers of molecules: $V \propto n$.

Combining these four laws yields the ideal gas equation: $PV = nRT$, where $R = 0.0821\ \text{L·atm/(mol·K)} = 8.314\ \text{J/(mol·K)}$. The value of R used must match the pressure units: use 0.0821 for atm, 8.314 for Pa/J-based problems. Temperature must always be in Kelvin.

Dalton's Law of Partial Pressures

In a gas mixture, each gas exerts its own pressure independently: $P_\text{total} = p_1 + p_2 + \ldots$. The partial pressure of each component is $p_i = x_i \times P_\text{total}$, where $x_i$ is the mole fraction. This applies when gases do not react with each other.

Graham's Law of Diffusion

$\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}$

Lighter gases diffuse faster. The ratio of rates equals the inverse ratio of the square roots of molar masses. This is also the basis for isotope separation: $^{235}\text{UF}_6$ diffuses slightly faster than $^{238}\text{UF}_6$.

Kinetic Molecular Theory

The kinetic molecular theory (KMT) postulates: (1) gas molecules are point masses with negligible volume; (2) they are in constant random motion; (3) collisions between molecules and with the container walls are perfectly elastic; (4) there are no intermolecular forces between gas molecules; (5) the average kinetic energy of molecules is directly proportional to absolute temperature.

From these postulates, three measures of molecular speed are derived:

• Most probable speed: $v_{mp} = \sqrt{2RT/M}$
• Average speed: $v_{avg} = \sqrt{8RT/\pi M}$
• Root mean square speed: $v_{rms} = \sqrt{3RT/M}$

Their order is always $v_{rms} > v_{avg} > v_{mp}$, with ratio approximately $1.224 : 1.128 : 1$.

Real Gases and van der Waals Equation

Ideal gas assumptions break down at high pressure and low temperature — when molecules are close together and intermolecular forces become significant. The van der Waals equation corrects for this:

$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$

Here $a$ is the correction for intermolecular attractions (reduces effective pressure: gas molecules are pulled back before hitting the wall) and $b$ is the correction for finite molecular volume (reduces effective volume available). Higher $a$ means the gas is more easily liquefied; higher $b$ means larger molecules.

Compressibility Factor Z

$Z = PV/(nRT)$. For an ideal gas, $Z = 1$ at all conditions. For a real gas:

• $Z < 1$ at moderate pressures: attractive forces dominate; gas is more compressible than ideal
• $Z > 1$ at high pressures: repulsive forces (finite volume) dominate; gas is less compressible than ideal
• $H_{2}$ and He: $Z > 1$ at all pressures because their intermolecular attraction (constant $a$) is negligibly small

The Boyle temperature $T_B = a/(Rb)$ is the temperature at which a real gas most closely mimics ideal behavior over a wide pressure range.

Critical Constants and Liquefaction

$T_c = \frac{8a}{27Rb}, \quad P_c = \frac{a}{27b^2}, \quad V_c = 3b, \quad \frac{P_cV_c}{T_c} = \frac{3R}{8}$

Gas liquefaction requires pressure above $P_c$ and temperature below $T_c$. The Joule-Thomson effect (cooling by adiabatic expansion below the inversion temperature) is the practical basis for most industrial liquefaction. Andrews' isotherms for $CO_{2}$ ($T_c = 31.1°C$) illustrate the transition from gas to liquid and the supercritical region.

Liquid State

Vapor pressure increases with temperature (Clausius-Clapeyron relationship). Surface tension decreases with temperature (reduced cohesive forces). Viscosity of liquids decreases with temperature (increased kinetic energy helps molecules flow past each other). Boiling point is the temperature at which vapor pressure equals external pressure — this is why water boils at ~70°C on Mount Everest.