States of Matter (Gases and Liquids)NEET Chemistry · Class 11 · NCERT Chapter 13

Intermolecular Forces and States of Matter

Matter exists in three common states: solid, liquid, and gas. Which state a substance is in depends on a balance between two competing factors:

• Intermolecular forces (IMF): attractive forces between molecules that pull them together (favour condensed states)
• Thermal energy (kT): kinetic energy due to temperature that keeps molecules moving and apart (favours the gaseous state)

At low temperature or high pressure: IMF dominates → solid or liquid. At high temperature or low pressure: thermal energy dominates → gas.

Types of Intermolecular Forces

• Dispersion forces (London forces): present in all molecules; arise from temporary instantaneous dipoles. Increase with molecular mass and surface area. These are the weakest IMF.
• Dipole-dipole interactions: between polar molecules (permanent dipoles). Stronger than dispersion forces for similarly sized molecules.
• Hydrogen bonding: between H bonded to highly electronegative small atoms (F, O, N) and the lone pair on another electronegative atom. This is the strongest type of intermolecular force (not to be confused with covalent bonds, which are stronger intramolecular).
• Ion-dipole interactions: between ions and polar molecules (important in solutions, not in pure gases).

Intermolecular forces are responsible for the physical properties of substances: boiling/melting points, surface tension, viscosity, solubility.

Properties of Gases

Gases have no fixed shape or volume; they expand to fill their container. Gas molecules are far apart and move at high speeds. The study of gases uses four variables: pressure (P), volume (V), temperature (T, in Kelvin), and amount (n, in moles).

SI units: Pressure: pascal (Pa = N/m²). Other common units: atmosphere (atm), bar, mmHg. Conversions: 1 atm = 101325 Pa = 760 mmHg = 1.01325 bar.

Standard conditions: STP (Standard Temperature and Pressure) = 0 °C (273.15 K) and 1 bar pressure. At STP, 1 mole of an ideal gas occupies 22.7 L.

Gas Laws: Boyle, Charles, Gay-Lussac, Avogadro

Select a gas law and drag the slider to see how one variable changes when another is varied. All based on PV = nRT.

Boyle's Law (1662) — Temperature Constant (Isothermal)

At constant temperature, the volume of a given mass of gas is inversely proportional to its pressure.

A graph of P vs V is a rectangular hyperbola. A graph of P vs 1/V is a straight line through the origin. A graph of PV vs P is a horizontal straight line for an ideal gas.

Charles's Law (1787) — Pressure Constant (Isobaric)

At constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature.

Temperature must be in Kelvin (K = °C + 273.15). If you plot V vs T (in Kelvin), you get a straight line that extrapolates to V = 0 at T = 0 K (absolute zero, −273.15 °C). At 0 K, an ideal gas would have zero volume. Real gases liquefy before reaching absolute zero.

Gay-Lussac's Law — Volume Constant (Isochoric)

At constant volume, the pressure of a given mass of gas is directly proportional to its absolute temperature.

Avogadro's Law (1811)

Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.

One mole of any ideal gas at STP (0 °C, 1 bar) occupies 22.7 L. One mole contains $N_A=6.022\times 10^{23}$ molecules (Avogadro's number).

The Ideal Gas Equation and Applications

Combining Boyle's, Charles's, and Avogadro's laws gives the ideal gas equation:

where R is the universal gas constant:

Combined Gas Law

Density of an Ideal Gas

From PV = nRT, since n = m/M (m = mass, M = molar mass):

So for a fixed gas (fixed M): density increases with pressure and decreases with temperature.

Molar Mass from Density

Partial Pressure

When a mixture of non-reacting gases occupies a container, each gas contributes to the total pressure. The partial pressure of a gas is the pressure it would exert if it alone occupied the entire volume:

where $x_i=n_i/n_{\text{total}}$ is the mole fraction of gas i.

Dalton's Law and Graham's Law

Dalton's Law of Partial Pressures

The total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.

Application: When a gas is collected over water (by downward displacement), the gas is saturated with water vapour. Total pressure = gas pressure + aqueous tension (saturated water vapour pressure at that temperature).

Graham's Law of Diffusion and Effusion

Under the same conditions of temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

Diffusion is the spontaneous mixing of gases. Effusion is the escape of gas through a tiny hole. Both follow Graham's law.

Example: H₂ (M = 2) vs O₂ (M = 32):

So hydrogen diffuses 4 times faster than oxygen.

Kinetic Molecular Theory

The kinetic molecular theory (KMT) gives a molecular-level explanation for the behaviour of ideal gases. Its postulates are:

1. Gases consist of a large number of identical molecules in continuous, random motion.
2. The volume of individual gas molecules is negligible compared to the total volume of the gas (molecules are point masses).
3. There are no intermolecular attractions or repulsions between gas molecules (no IMF).
4. Collisions between gas molecules (and between molecules and container walls) are perfectly elastic (no net loss of kinetic energy).
5. At any given temperature, all gas molecules have the same average kinetic energy, regardless of the type of gas.

From KMT, the pressure of a gas arises from the impacts of molecules on the container walls. The average kinetic energy of a molecule is:

where $k_B=R/N_A$ is Boltzmann's constant and $u_{\text{rms}}$ is the root-mean-square speed.

KMT directly explains all the ideal gas laws:

• Boyle's law: at constant T, each molecule has the same average speed, so doubling the volume halves the number of collisions per unit area → halves pressure.
• Charles's law: at constant P, increasing T increases molecular speed → molecules hit the walls harder and more often → container must expand to keep P constant.
• Avogadro's law: at constant T and P, more molecules = more collisions → volume must increase to keep collision rate (pressure) constant.

Molecular Speeds and Maxwell Distribution

The Maxwell speed distribution shows the fraction of gas molecules having each speed. Adjust temperature and select a gas to see the curve shift.

Not all gas molecules move at the same speed. The Maxwell-Boltzmann distribution describes the distribution of molecular speeds at a given temperature. Three important speed quantities:

Most Probable Speed, u_mp

The speed at the peak of the Maxwell distribution (most molecules have this speed):

Average Speed, u_av

Root Mean Square Speed, u_rms

The square root of the average of the squares of all molecular speeds:

Ratio of the Three Speeds

So the ordering is always: $u_{mp}<u_{av}<u_{rms}$

Key relationships:

• All three speeds are proportional to $\sqrt{T}$ (increase with temperature)
• All three speeds are proportional to $1/\sqrt{M}$ (decrease with increasing molar mass)
• The Maxwell distribution broadens at higher temperature (more molecules at higher speeds)

Real Gases and Deviation from Ideal Behaviour

Real gases deviate from the ideal gas equation PV = nRT. A useful way to measure deviation is the compressibility factor Z:

• Z = 1: ideal gas (no deviation)
• Z < 1: gas is more compressible than ideal (attractive forces dominate, usually at moderate pressure)
• Z > 1: gas is less compressible than ideal (repulsive forces / volume of molecules dominates, usually at very high pressure)

At low pressures: Z ≈ 1 for most gases (all gases approach ideal). At moderate pressures: Z < 1 (attractive forces cause negative deviation — especially for gases with strong IMF like CO₂, NH₃). At very high pressures: Z > 1 for all gases (molecular volume effect). H₂ and He show Z > 1 at all pressures because their intermolecular attractions are negligibly small.

Causes of Deviation

1. Intermolecular attractive forces: In an ideal gas, there are no IMF. In real gases, attractive forces pull molecules toward each other, reducing the pressure on the walls below the ideal value. Correction: add a pressure term $a{n}^2/V^2$.
2. Finite molecular volume: In an ideal gas, molecules are point masses. In real gases, each molecule has a finite volume, so the free volume available for movement is less than V. Correction: subtract a volume term nb.

Van der Waals Equation

The compressibility factor Z = PV/nRT measures how much a real gas deviates from ideal behaviour. Z = 1 for an ideal gas.

Van der Waals (1873) modified the ideal gas equation to account for both real gas corrections:

For 1 mole of gas ($n=1$):

where $V_m$ is the molar volume.

Van der Waals Constants

Remember: At very high pressure, the volume correction (b) dominates and Z > 1. At moderate pressure (intermediate), the pressure correction (a) dominates and Z < 1. At the Boyle temperature (T_B = a/Rb), these two effects cancel and Z = 1 over a wide range of pressures.

Comparison of Real Gas Behaviour

Gases with larger a values (e.g., SO₂, NH₃, CO₂) have stronger attractive forces and show larger negative deviations at moderate pressures. H₂ and He have very small a values; they always show Z > 1 (volume effect always dominates).

Liquefaction of Gases and Critical Constants

Gases can be liquefied by cooling them below a certain temperature and then compressing them. Three critical constants describe this:

Critical Temperature, T_c

The temperature above which a gas cannot be liquefied, no matter how high the pressure. Above T_c, the kinetic energy is too high for intermolecular attractions to hold molecules together in a liquid.

Higher a (stronger attractions) = higher T_c (easier to liquefy). For example: CO₂ (T_c = 31.1 °C), NH₃ (T_c = 132.4 °C), H₂O (T_c = 374 °C). So these gases can be liquefied at or near room temperature with modest pressure.

Critical Pressure, P_c

The minimum pressure needed to liquefy a gas at its critical temperature:

Critical Volume, V_c

At the critical point (T = T_c, P = P_c), the gas and liquid phases have the same density and are indistinguishable. This is the critical state.

Liquefaction Methods

• Linde's method (Joule-Thomson effect): A compressed gas, when allowed to expand suddenly through a tiny orifice (throttle) into a region of lower pressure, shows a change in temperature. For most gases at room temperature, this is a cooling effect (below the inversion temperature). Repeated expansion cools the gas until it liquefies. Used to liquefy air, N₂, O₂.
• Claude's process: Gas is compressed, then made to do work against a piston (adiabatic expansion). This cools the gas (work is done at the expense of internal energy). More efficient than Linde's method for gases with a low inversion temperature.

Properties of Liquids

Liquids have a fixed volume but no fixed shape; they conform to their container. The particles in a liquid are close together but can move past each other (unlike solids). Key properties of liquids for NEET:

Vapour Pressure

Vapour pressure is the pressure exerted by the vapour of a liquid in equilibrium with the liquid at a given temperature. At equilibrium, the rate of evaporation equals the rate of condensation.

• Increases with temperature: higher T gives more molecules enough energy to escape the liquid surface.
• Normal boiling point: the temperature at which vapour pressure = 1 atm. Water boils at 100 °C at 1 atm. At higher altitude (lower P), water boils below 100 °C.
• Stronger IMF = lower vapour pressure (more difficult for molecules to escape). E.g., water has lower vapour pressure than ethanol at the same temperature.

Surface Tension, γ

Surface tension is the force per unit length acting along the surface of a liquid:

It arises because surface molecules experience a net inward pull (unlike interior molecules which are attracted equally from all sides). The surface therefore contracts to a minimum area. Consequences:

• Spherical droplets (sphere has minimum surface area for a given volume)
• Capillary action (water rises in a thin glass tube)
• Water striders walking on water
• Beading of water on a waxed surface

Surface tension decreases as temperature increases (increased thermal energy weakens intermolecular attractions at the surface). Surfactants (detergents, soaps) also reduce surface tension.

Viscosity, η

Viscosity is the resistance of a liquid to flow. It is a measure of friction between adjacent layers of liquid moving at different velocities (internal friction).

SI unit of viscosity: pascal-second (Pa·s) or poise (P); 1 poise = 0.1 Pa·s.

• Viscosity decreases as temperature increases (thermal energy helps molecules overcome intermolecular friction).
• Stronger IMF = higher viscosity (e.g., glycerol > water > ethanol — glycerol has multiple -OH groups forming extensive H-bonds).
• Longer chain molecules = higher viscosity (more surface area for van der Waals contact between chains, e.g., engine oil vs petrol).

Key distinction for NEET: For liquids, viscosity decreases with temperature. For gases, viscosity increases with temperature (because gas viscosity arises from momentum transfer between colliding molecules, which increases at higher T).

Worked NEET Problems

Summary Cheat Sheet

Gas Laws Quick Reference

Molecular Speeds

Real Gas / Van der Waals Quick Facts

• Z = PV/nRT: ideal = 1; Z < 1 = IMF dominant; Z > 1 = volume dominant
• Van der Waals: $(P+a{n}^2/V^2)(V-nb)=nRT$
• a = pressure correction (IMF); b = volume correction (molecular size)
• Critical constants: $T_c=8a/(27Rb)$, $P_c=a/(27b^2)$, $V_c=3b$
• Above T_c: gas cannot be liquefied by pressure alone

Liquid Properties Summary