States of Matter

Welcome to HSLC Guru! This page provides complete English-medium notes, summaries, and question answers for ASSEB Class 11 Chemistry Chapter 5 — States of Matter. Whether you are revising for unit tests or the final examination, this resource is structured to help you master intermolecular forces, gas laws, the kinetic molecular theory, real gas behaviour, and the properties of liquids.

---

Chapter Summary

Matter exists in three principal physical states — solid, liquid, and gas — and the state in which a substance occurs depends on the balance between intermolecular forces of attraction and the thermal energy of its particles. The dominant intermolecular forces are dispersion (London) forces present in all molecules, dipole-dipole interactions in polar molecules, dipole-induced dipole forces between polar and non-polar species, and hydrogen bonding which arises when hydrogen is bonded to highly electronegative atoms such as F, O, or N. Hydrogen bonding is responsible for the unusually high boiling point of water, the structure of ice, and the stability of biomolecules like DNA and proteins.

The gaseous state is described quantitatively by the gas laws. Boyle’s law states that at constant temperature the pressure of a fixed mass of gas is inversely proportional to its volume. Charles’s law states that at constant pressure the volume of a gas is directly proportional to its absolute temperature. Gay-Lussac’s law relates pressure and temperature at constant volume, and Avogadro’s law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Combining these gives the ideal gas equation. Dalton’s law of partial pressures states that the total pressure exerted by a mixture of non-reacting gases equals the sum of the partial pressures of individual gases.

The kinetic molecular theory of gases assumes that gas molecules are point masses in continuous random motion, undergoing perfectly elastic collisions with no intermolecular attractions. The average kinetic energy of a gas molecule depends only on the absolute temperature. The Maxwell-Boltzmann distribution describes the spread of molecular speeds at a given temperature; from it we derive the most probable speed, the average speed, and the root-mean-square speed. As temperature rises, the curve flattens and shifts toward higher speeds.

Real gases deviate from ideal behaviour at high pressure and low temperature. Van der Waals corrected the ideal gas equation to account for molecular volume and intermolecular attractions. The compressibility factor Z indicates the extent of deviation: Z = 1 for an ideal gas, Z > 1 for repulsive dominance, and Z < 1 for attractive dominance. Every real gas has a critical temperature above which it cannot be liquefied no matter how high the pressure. The liquid state shows characteristic properties of vapour pressure, surface tension (force per unit length on a liquid surface), and viscosity (resistance to flow). Vapour pressure increases with temperature; surface tension and viscosity decrease with temperature.

---

Key Formulas (KaTeX)

$PV = nRT$

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

$\left(P + \frac{a}{V^2}\right)(V – b) = RT$

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

$KE = \frac{3}{2}RT$

$u_{rms} = \sqrt{\frac{3RT}{M}}$

$u_{avg} = \sqrt{\frac{8RT}{\pi M}}$

$u_{mp} = \sqrt{\frac{2RT}{M}}$

One-Mark Questions

Q1. State Boyle’s law.

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

Q2. What is the SI unit of pressure?

Answer: The SI unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m².

Q3. Define absolute zero.

Answer: Absolute zero is the lowest theoretical temperature, equal to 0 K or –273.15 °C, at which the volume of an ideal gas would become zero.

Q4. What is the value of the universal gas constant R in SI units?

Answer: R = 8.314 J K⁻¹ mol⁻¹.

Q5. Name the strongest type of intermolecular force.

Answer: Hydrogen bonding is the strongest intermolecular (van der Waals type) force.

Q6. Define vapour pressure.

Answer: Vapour pressure is the pressure exerted by the vapour of a liquid in equilibrium with the liquid at a given temperature.

Q7. What is the value of the compressibility factor Z for an ideal gas?

Answer: Z = 1 for an ideal gas at all temperatures and pressures.

Q8. Which property of a liquid causes a small drop to assume a spherical shape?

Answer: Surface tension causes liquid drops to assume a spherical shape, as a sphere has the minimum surface area for a given volume.

Q9. Name the law that relates the volume of a gas to its number of moles.

Answer: Avogadro’s law: at the same temperature and pressure, equal volumes of gases contain equal numbers of molecules (V ∝ n).

Q10. What happens to the viscosity of a liquid when temperature is increased?

Answer: Viscosity decreases as temperature is increased because molecules acquire enough kinetic energy to overcome intermolecular attractions.

Two and Three-Mark Questions

Q1. Differentiate between dipole-dipole and dipole-induced dipole interactions.

Answer: Dipole-dipole interactions occur between two polar molecules that have permanent dipoles, e.g., HCl-HCl. Dipole-induced dipole interactions occur between a polar molecule and a non-polar molecule, where the polar molecule induces a temporary dipole in the non-polar molecule, e.g., water and oxygen. Dipole-dipole forces are generally stronger than dipole-induced dipole interactions.

Q2. State and explain Charles’s law.

Answer: Charles’s law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature, i.e., V ∝ T or V/T = constant. As temperature increases, gas molecules move faster and exert more pressure on container walls, so to keep pressure constant, the volume must increase. Hot air balloons and the expansion of air on heating are practical illustrations.

Q3. Why is hydrogen bonding stronger than ordinary dipole-dipole interaction?

Answer: Hydrogen bonding occurs when hydrogen is bonded to highly electronegative atoms (F, O, N) which strongly polarize the H–X bond. The hydrogen atom acquires a substantial partial positive charge while the small size of H allows close approach to the lone pair of another electronegative atom. This combination of high polarity and small H size makes the H-bond stronger than ordinary dipole-dipole forces.

Q4. Define critical temperature and critical pressure.

Answer: The critical temperature (Tc) is the temperature above which a gas cannot be liquefied no matter how much pressure is applied. The critical pressure (Pc) is the minimum pressure required to liquefy a gas at its critical temperature. The volume occupied at this state is called the critical volume (Vc). For CO₂, Tc = 31.1 °C and Pc = 73.9 atm.

Q5. State and explain Dalton’s law of partial pressures.

Answer: Dalton’s law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases: P(total) = P₁ + P₂ + P₃ + … . The partial pressure of a gas equals its mole fraction multiplied by the total pressure. The law applies to ideal gas mixtures where there is no interaction between the component gases.

Q6. Explain why surface tension decreases with increase in temperature.

Answer: Surface tension arises due to inward attractive forces on the molecules at the surface of a liquid. When temperature increases, the average kinetic energy of molecules increases and the intermolecular attractions weaken. As a result, the inward pull on surface molecules decreases, and so does the surface tension of the liquid.

Five to Seven-Mark Questions

Q1. Derive the ideal gas equation PV = nRT from Boyle’s law, Charles’s law, and Avogadro’s law.

Answer: From Boyle’s law: V ∝ 1/P (at constant T, n). From Charles’s law: V ∝ T (at constant P, n). From Avogadro’s law: V ∝ n (at constant P, T). Combining the three: V ∝ nT/P. Introducing R as proportionality constant: V = nRT/P, which gives PV = nRT, the ideal gas equation. Here R is the universal gas constant with value 8.314 J K⁻¹ mol⁻¹ in SI units, 0.0821 L atm K⁻¹ mol⁻¹ in older units. The equation describes the state of an ideal gas in which molecular volume and intermolecular forces are neglected.

Q2. Calculate the volume occupied by 2 moles of an ideal gas at 27 °C and 2 atm pressure. (R = 0.0821 L atm K⁻¹ mol⁻¹)

Answer: Given n = 2 mol, T = 27 + 273 = 300 K, P = 2 atm. Using PV = nRT: V = nRT/P = (2 × 0.0821 × 300)/2 = 49.26/2 = 24.63 L. Hence the gas occupies 24.63 L.

Q3. A sample of gas occupies 4 L at 300 K and 1 atm. What will be its volume at 600 K and 2 atm?

Answer: Apply the combined gas equation P₁V₁/T₁ = P₂V₂/T₂. Given P₁ = 1 atm, V₁ = 4 L, T₁ = 300 K, P₂ = 2 atm, T₂ = 600 K. (1 × 4)/300 = (2 × V₂)/600. So 4/300 = 2V₂/600, hence 2V₂ = (4 × 600)/300 = 8, giving V₂ = 4 L. The new volume is 4 L.

Q4. Discuss the deviation of real gases from ideal behaviour and write the van der Waals equation explaining its terms.

Answer: Real gases deviate from ideal behaviour because two assumptions of the kinetic theory are not strictly true: (i) molecules have a finite volume, and (ii) intermolecular attractions exist. Deviations are large at high pressure and low temperature. Van der Waals corrected the ideal gas equation by adding two terms: (a) a pressure correction a/V² to account for attractive forces between molecules, and (b) a volume correction b for the actual volume occupied by the molecules themselves. The van der Waals equation is (P + a/V²)(V – b) = RT for one mole of gas. Here ‘a’ measures the strength of attractive forces and ‘b’ is the excluded volume per mole.

Q5. Calculate the pressure exerted by 0.5 mole of an ideal gas occupying 5 L at 273 K. (R = 0.0821 L atm K⁻¹ mol⁻¹)

Answer: Given n = 0.5 mol, V = 5 L, T = 273 K. From PV = nRT, P = nRT/V = (0.5 × 0.0821 × 273)/5 = 11.207/5 = 2.241 atm. Therefore, the pressure exerted by the gas is approximately 2.24 atm.

Multiple Choice Questions

Q1. The SI unit of pressure is —

(a) atm (b) bar (c) pascal (d) torr

Answer: (c) pascal.

Q2. Which gas law relates volume and temperature at constant pressure?

(a) Boyle’s (b) Charles’s (c) Avogadro’s (d) Dalton’s

Answer: (b) Charles’s law.

Q3. Compressibility factor Z = PV/nRT. For an ideal gas Z is —

(a) 0 (b) 1 (c) less than 1 (d) greater than 1

Answer: (b) 1.

Q4. Hydrogen bonding occurs in —

(a) HCl (b) CH₄ (c) H₂O (d) CO₂

Answer: (c) H₂O.

Q5. Average kinetic energy of an ideal gas molecule depends on —

(a) pressure only (b) volume only (c) absolute temperature only (d) molar mass

Answer: (c) absolute temperature only.

Q6. The van der Waals constant ‘a’ represents —

(a) molecular volume (b) attractive forces (c) repulsive forces (d) kinetic energy

Answer: (b) attractive forces.

Q7. Above the critical temperature, a gas —

(a) liquefies easily (b) cannot be liquefied (c) becomes solid (d) condenses to dew

Answer: (b) cannot be liquefied.

Q8. Which speed corresponds to the peak of the Maxwell-Boltzmann distribution curve?

(a) most probable (b) average (c) rms (d) mean square

Answer: (a) most probable speed.

Q9. Surface tension of a liquid generally —

(a) increases with T (b) decreases with T (c) is independent of T (d) becomes zero at room T

Answer: (b) decreases with T.

Q10. The value of R in J K⁻¹ mol⁻¹ is —

(a) 0.0821 (b) 8.314 (c) 1.987 (d) 22.4

Answer: (b) 8.314.

Fill in the Blanks

Q1. The pressure exerted by a column of mercury 76 cm high at 0 °C is called __________.

Answer: one atmosphere.

Q2. At STP, one mole of any ideal gas occupies __________ litres.

Answer: 22.4 (at 273.15 K and 1 atm).

Q3. The intermolecular force present in all molecules, polar or non-polar, is __________ force.

Answer: dispersion (London).

Q4. The temperature above which liquefaction is not possible is the __________ temperature.

Answer: critical.

Q5. The compressibility factor Z is __________ for an ideal gas.

Answer: equal to one.

True or False

Q1. Boyle’s law applies at constant temperature.

Answer: True.

Q2. The viscosity of a liquid increases with temperature.

Answer: False — viscosity decreases with rise in temperature.

Q3. All real gases behave ideally at very high pressures.

Answer: False — they deviate most at high pressure and low temperature.

Q4. Hydrogen bonding is responsible for the high boiling point of water.

Answer: True.

Q5. The average kinetic energy of a gas molecule is independent of temperature.

Answer: False — it is directly proportional to absolute temperature.

Glossary

Term	Meaning
Intermolecular forces	Forces of attraction or repulsion acting between neighbouring molecules.
Dispersion (London) force	Weak attractive force arising from temporary dipoles induced in molecules.
Hydrogen bond	Strong dipole-dipole interaction involving hydrogen bonded to F, O, or N.
Boyle’s law	P ∝ 1/V at constant T and n.
Charles’s law	V ∝ T at constant P and n.
Avogadro’s law	Equal volumes of gases at same T and P contain equal moles.
Compressibility factor (Z)	Ratio PV/nRT; measures deviation from ideal behaviour.
Critical temperature	Temperature above which a gas cannot be liquefied.
Vapour pressure	Pressure exerted by vapour in equilibrium with its liquid.
Surface tension	Force per unit length acting on the surface of a liquid.
Viscosity	Internal resistance offered by a liquid to flow.
Maxwell-Boltzmann distribution	Statistical distribution of molecular speeds in a gas.

Formula Table

Quantity / Law	Formula
Ideal gas equation	PV = nRT
Combined gas law	P₁V₁/T₁ = P₂V₂/T₂
Boyle’s law	P₁V₁ = P₂V₂ (at constant T)
Charles’s law	V₁/T₁ = V₂/T₂ (at constant P)
Gay-Lussac’s law	P₁/T₁ = P₂/T₂ (at constant V)
Dalton’s law	P(total) = P₁ + P₂ + P₃ + …
Van der Waals equation	(P + a/V²)(V – b) = RT
Compressibility factor	Z = PV/nRT
Average kinetic energy	KE = (3/2) RT per mole
Root-mean-square speed	u(rms) = √(3RT/M)
Average speed	u(avg) = √(8RT/πM)
Most probable speed	u(mp) = √(2RT/M)
Density of ideal gas	d = PM/RT
Mole fraction	xᵢ = nᵢ / n(total)

Quick Revision Tips

While revising, always convert temperature into Kelvin before substituting into gas law equations. Watch the units of pressure carefully — atm, mm Hg, bar, and pascal are all common, and the value of R you use must match. For ideal gas calculations use R = 0.0821 L atm K⁻¹ mol⁻¹ when P is in atm and V in litres; use R = 8.314 J K⁻¹ mol⁻¹ in pure SI. Remember Standard Temperature and Pressure: 0 °C and 1 atm in older convention, or 25 °C and 1 bar in current IUPAC convention.

For Maxwell-Boltzmann speeds, recall the order: u(mp) < u(avg) < u(rms). The ratios are approximately 1 : 1.128 : 1.224. The most probable speed corresponds to the peak of the curve, the average speed is the arithmetic mean, and the root-mean-square speed is what appears in the kinetic-energy expression.

Practise these gas law problems and definitions thoroughly. Mastery of PV = nRT and the van der Waals equation is essential for both Class 11 and Class 12 chemistry, as well as for competitive entrance examinations such as JEE and NEET. For more chapter-wise notes and solved question banks visit HSLC Guru.