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Class 11 Chemistry Notes

States of Matter Class 11 Notes

Complete, exam-ready notes on the states of matter: the gas laws, the ideal gas equation and Graham's law, Dalton's law of partial pressures, the kinetic molecular theory, real gases and the van der Waals equation, and the liquid state — written for CBSE, JEE and NEET revision.

Class11SubjectChemistryCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What is the ideal gas equation in one line?

PV = nRT connects pressure, volume, amount and temperature of a gas — the combined result of Boyle's, Charles' and Avogadro's laws.

The Three States

  • Solids: fixed shape and volume; strong forces; particles vibrate about fixed positions.
  • Liquids: fixed volume, no fixed shape; intermediate forces; particles slide past each other.
  • Gases: neither fixed shape nor volume; particles far apart in random motion, weak forces between them.
  • The state depends on temperature and pressure, and on the balance between kinetic energy and intermolecular forces.

The Gas Laws

Boyle's and Charles' laws

PV=constant  (T fixed),VT=constant  (P fixed)PV = \text{constant}\;(T\text{ fixed}),\qquad \frac{V}{T} = \text{constant}\;(P\text{ fixed})

Boyle's law: at constant temperature, volume is inversely proportional to pressure. Charles' law: at constant pressure, volume is proportional to absolute temperature.

P1V1T1=P2V2T2\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}
Combined gas law

Avogadro's law + ideal gas equation

V∝n,PV=nRTV \propto n,\qquad PV = nRT

Avogadro's law: equal volumes of gases at the same T and P contain equal numbers of molecules. Combining with Boyle and Charles gives the ideal gas equation. STP: R = 0.0821 L·atm·mol⁻¹·K⁻¹.

Dalton's Law and Graham's Law

Dalton's law of partial pressures

Ptotal=P1+P2+P3+…P_{\text{total}} = P_1 + P_2 + P_3 + \dots

The total pressure of a mixture of non-reacting gases equals the sum of the pressures each gas would exert alone. Partial pressure of a gas = its mole fraction × total pressure.

Graham's law of diffusion

r1r2=M2M1\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}

Lighter gases diffuse and effuse faster: the rate of diffusion is inversely proportional to the square root of the molar mass. Hydrogen diffuses faster than oxygen.

Pi=xi×PtotalP_i = x_i \times P_{\text{total}}
Partial pressure from mole fraction

Kinetic Molecular Theory

  • Gases consist of tiny particles in constant, random, straight-line motion.
  • The particles occupy negligible volume compared with the gas volume.
  • Collisions are perfectly elastic — no energy is lost.
  • There is no attractive or repulsive force between gas particles.
  • Average kinetic energy depends only on absolute temperature: KE ∝ T, so at the same T all gases have the same average KE.
KE=32kBT,vrms=3RTMKE = \tfrac32 k_BT,\qquad v_{\text{rms}} = \sqrt{\frac{3RT}{M}}
Kinetic energy and root-mean-square speed

Ideal vs Real Gases — van der Waals Equation

Real gases

(P+an2V2)(V−nb)=nRT\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT

Real gases deviate from PV = nRT because molecules occupy finite volume (correction b) and attract each other (correction a). The van der Waals equation applies the two corrections. Deviations are largest at high pressure and low temperature.

  • Compressibility factor Z = PV/nRT: Z = 1 for ideal; Z < 1 when attraction dominates (moderate pressure); Z > 1 when volume dominates (high pressure).
  • Gases approach ideal behaviour at low pressure and high temperature.
  • Boyle temperature is where a real gas behaves most ideally.

The Liquid State

  • Vapour pressure: the pressure of vapour above a liquid at equilibrium; it rises with temperature and is independent of liquid surface area.
  • Boiling occurs when vapour pressure equals external pressure.
  • Surface tension: the force along the liquid surface (per unit length) that minimises surface area — water has strong hydrogen bonding and high surface tension.
  • Viscosity: internal resistance to flow; liquids with stronger intermolecular forces and lower temperature flow more slowly.

Atmospheric pressure

1 atm = 101.325 kPa = 760 mm Hg = 101325 Pa. At higher altitude, atmospheric pressure drops, so water boils at a lower temperature.

Solved Examples

Example: A gas occupies 2 L at 300 K and 1 atm. What volume at 600 K and 0.5 atm?

Solution: Use the combined law: V₂ = V₁ × (T₂/T₁) × (P₁/P₂) = 2 × (600/300) × (1/0.5) = 8 L.

Example: Which effuses faster, hydrogen or oxygen, at the same temperature?

Solution: By Graham's law, rate ∝ 1/√M. H₂ (M = 2) has √(32/2) = 4 times the effusion rate of O₂ (M = 32).

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

Ideal gas equation

PV=nRTPV = nRT

Combined gas law

P1V1T1=P2V2T2\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}

Dalton's law

Ptot=P1+P2+…,  Pi=xiPtotP_{\text{tot}} = P_1 + P_2 + \dots,\; P_i = x_iP_{\text{tot}}

Graham's law

r1r2=M2M1\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}

rms speed

vrms=3RTMv_{\text{rms}} = \sqrt{\frac{3RT}{M}}

van der Waals equation

(P+an2V2)(V−nb)=nRT\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT

Compressibility factor

Z=PVnRTZ = \frac{PV}{nRT}

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • Ideal gas: PV = nRT with R = 0.0821 L·atm·mol⁻¹·K⁻¹.
  • Graham's law: lighter gas diffuses faster, rate ∝ 1/√M.
  • Partial pressure = mole fraction × total pressure (Dalton).
  • van der Waals corrections: a = attraction, b = molecule volume.
  • Real gases behave ideally at LOW pressure and HIGH temperature.
  • Z = 1 ideal; Z < 1 attraction dominates; Z > 1 size dominates.
  • Boiling point = temperature at which vapour pressure equals external pressure.

FAQ

Common questions

What is the ideal gas equation?

PV = nRT, combining Boyle's, Charles' and Avogadro's laws. P is pressure, V volume, n number of moles, T absolute temperature, and R the universal gas constant (0.0821 L·atm·mol⁻¹·K⁻¹).

What is Graham's law of diffusion?

The rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass, so hydrogen (M = 2) diffuses four times faster than oxygen (M = 32).

Why do real gases deviate from ideal behaviour?

Real molecules occupy a finite volume and attract each other, which the ideal model ignores. The van der Waals equation adds corrections (a for attraction, b for volume); deviations peak at high pressure and low temperature.

What is vapour pressure?

The pressure of the vapour in equilibrium with its liquid at a given temperature. It increases with temperature and equals atmospheric pressure at the boiling point.

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