Unit 7
General and Physical Chemistry
Class 11 Chemistry
States of Matter
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NEB/CDC syllabus scope: Unit 7 – States of Matter is an 8-teaching-hour General and Physical Chemistry unit. It covers the gaseous state through kinetic theory, major gas laws, partial pressure, diffusion, ideal-gas behavior and real-gas deviation; the liquid state through evaporation, vapour pressure, boiling point, surface tension, viscosity and liquid crystals; and the solid state through crystalline/amorphous solids, efflorescent/deliquescent/hygroscopic substances, crystallization, water of crystallization, crystal lattice and unit cell.
1. Three States of Matter
Matter commonly appears as solid, liquid and gas. The differences arise from particle spacing, intermolecular attraction and freedom of motion.
| Property | Solid | Liquid | Gas |
|---|---|---|---|
| Shape | Definite | Takes container shape | Fills container |
| Volume | Definite | Nearly definite | No fixed volume |
| Particle spacing | Very close | Close | Far apart |
| Particle motion | Vibration around fixed positions | Particles can move past one another | Rapid random translational motion |
| Compressibility | Very low | Low | High |
| Intermolecular attraction | Generally strongest | Intermediate | Weakest in idealized model |
Diagram 1: Particle arrangement in solid, liquid and gas
2. Gaseous State: Kinetic Theory of Gases
Kinetic molecular theory
A model explaining gas behavior in terms of the continuous random motion of a very large number of tiny particles.
A model explaining gas behavior in terms of the continuous random motion of a very large number of tiny particles.
Main Postulates
- A gas consists of a very large number of tiny particles.
- The particles are far apart compared with their own size; their individual volume is negligible in the ideal-gas model.
- Gas particles move continuously and randomly in straight lines between collisions.
- Collisions between particles and with container walls are perfectly elastic in the ideal model.
- Intermolecular forces are neglected except during collisions.
- Gas pressure results from collisions of particles with container walls.
- The average kinetic energy of particles depends on absolute temperature.
- At the same absolute temperature, all ideal gases have the same average translational kinetic energy per molecule.
Temperature must be absolute
Gas-law equations that involve temperature require kelvin (K), not °C.
Gas-law equations that involve temperature require kelvin (K), not °C.
Diagram 2: Gas particles in random motion
3. Boyle’s Law
Boyle’s law
For a fixed amount of gas at constant temperature, pressure is inversely proportional to volume.
For a fixed amount of gas at constant temperature, pressure is inversely proportional to volume.
P ∝ 1/V
PV = constant
P₁V₁ = P₂V₂
If pressure doubles at constant temperature, volume becomes half.
Diagram 3: Boyle’s law is an inverse relation
4. Charles’ Law
Charles’ law
For a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.
For a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.
V ∝ T
V/T = constant
V₁/T₁ = V₂/T₂
Use kelvin
T(K) = temperature in °C + 273.15.
T(K) = temperature in °C + 273.15.
Diagram 4: Charles’ law
5. Avogadro’s Law
Avogadro’s law
At constant temperature and pressure, the volume of a gas is directly proportional to the amount of gas in moles.
At constant temperature and pressure, the volume of a gas is directly proportional to the amount of gas in moles.
V ∝ n
V/n = constant
V₁/n₁ = V₂/n₂
Equal volumes of ideal gases at the same temperature and pressure contain equal numbers of molecules.
6. Combined Gas Equation
Combining Boyle’s and Charles’ laws for a fixed amount of gas:
PV/T = constant
P₁V₁/T₁ = P₂V₂/T₂
When to use it
Use the combined equation when pressure, volume and temperature all change but the amount of gas is fixed.
Use the combined equation when pressure, volume and temperature all change but the amount of gas is fixed.
7. Dalton’s Law of Partial Pressure
Partial pressure
The pressure a gas in a mixture would exert if it alone occupied the same volume at the same temperature.
The pressure a gas in a mixture would exert if it alone occupied the same volume at the same temperature.
Dalton’s law
For a mixture of non-reacting gases, total pressure equals the sum of the component partial pressures.
For a mixture of non-reacting gases, total pressure equals the sum of the component partial pressures.
Ptotal = P₁ + P₂ + P₃ + …
For an ideal-gas mixture:
Pᵢ = xᵢPtotal
where xᵢ is the mole fraction of component i.
Diagram 5: Total pressure as the sum of partial pressures
8. Graham’s Law of Diffusion
Diffusion
The spontaneous mixing of gas particles due to their random molecular motion.
The spontaneous mixing of gas particles due to their random molecular motion.
Graham’s law
At the same temperature and pressure, the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass.
At the same temperature and pressure, the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass.
r ∝ 1/√M
r₁/r₂ = √(M₂/M₁)
Using gas density d under the same conditions:
r₁/r₂ = √(d₂/d₁)
Interpretation
A lighter gas diffuses faster than a heavier gas under comparable conditions.
A lighter gas diffuses faster than a heavier gas under comparable conditions.
9. Ideal Gas and Ideal Gas Equation
Ideal gas
A hypothetical gas that follows the ideal-gas equation exactly under all conditions and obeys the assumptions of the kinetic molecular model.
A hypothetical gas that follows the ideal-gas equation exactly under all conditions and obeys the assumptions of the kinetic molecular model.
Combining the basic gas laws gives:
PV = nRT
where P = pressure, V = volume, n = moles, R = universal gas constant and T = absolute temperature.
Useful Rearrangements
V = nRT/P
n = PV/RT
P = nRT/V
Molar Mass from Gas Data
Since n = m/M:
PV = (m/M)RT
M = mRT/(PV)
Density Relation
Since density d = m/V:
d = PM/(RT)
M = dRT/P
Diagram 6: The ideal gas equation
10. Universal Gas Constant and Its Significance
R has the same physical meaning in the ideal-gas equation regardless of the gas identity, provided compatible units are used.
| Pressure-volume units | Useful R value |
|---|---|
| Pa and m³ | 8.314 J mol⁻¹ K⁻¹ |
| kPa and L | 8.314 L·kPa mol⁻¹ K⁻¹ |
| atm and L | ≈ 0.082057 L·atm mol⁻¹ K⁻¹ |
Unit consistency
Never insert a pressure in atm with R = 8.314 J mol⁻¹ K⁻¹ unless you first convert the pressure/volume units consistently.
Never insert a pressure in atm with R = 8.314 J mol⁻¹ K⁻¹ unless you first convert the pressure/volume units consistently.
11. Deviation of Real Gases from Ideality
Real gases do not perfectly satisfy ideal-gas assumptions because:
- gas molecules have finite volume;
- intermolecular attractive and repulsive forces exist.
Real gases behave most ideally at:
- low pressure, where particles are far apart;
- high temperature, where kinetic energy reduces the relative importance of attractions.
Compressibility factor, Z
A convenient measure of deviation from ideality:
A convenient measure of deviation from ideality:
Z = PV/(nRT)
- Z = 1: ideal behavior.
- Z ≠ 1: non-ideal behavior.
Syllabus level
The current Unit 7 requires the concept of real-gas deviation; an advanced derivation of the van der Waals equation is not necessary unless your teacher specifically includes it as enrichment.
The current Unit 7 requires the concept of real-gas deviation; an advanced derivation of the van der Waals equation is not necessary unless your teacher specifically includes it as enrichment.
Diagram 7: Why real gases deviate from the ideal model
12. Liquid State
Liquid particles are close enough for significant intermolecular attraction, but they have enough freedom to flow and change positions.
12.1 Evaporation
Evaporation
The escape of molecules from the surface of a liquid into the vapour phase at temperatures below the boiling point.
The escape of molecules from the surface of a liquid into the vapour phase at temperatures below the boiling point.
Evaporation is faster when:
- temperature is higher;
- surface area is larger;
- air movement removes vapour above the surface;
- intermolecular forces are weaker.
12.2 Condensation
Condensation
The conversion of vapour or gas into the liquid state.
The conversion of vapour or gas into the liquid state.
In a closed container, evaporation and condensation may eventually reach dynamic equilibrium.
Diagram 8: Opposing phase processes in a closed system
13. Vapour Pressure and Boiling Point
Vapour pressure
The pressure exerted by the vapour in equilibrium with its liquid at a given temperature in a closed system.
The pressure exerted by the vapour in equilibrium with its liquid at a given temperature in a closed system.
Vapour pressure increases with temperature because a larger fraction of molecules can escape the liquid surface.
Boiling point
The temperature at which the vapour pressure of a liquid becomes equal to the external pressure.
The temperature at which the vapour pressure of a liquid becomes equal to the external pressure.
Pressure effect
Lower external pressure lowers the boiling point; higher external pressure raises it.
Lower external pressure lowers the boiling point; higher external pressure raises it.
| Concept | Evaporation | Boiling |
|---|---|---|
| Where it occurs | Surface | Throughout liquid |
| Temperature | Can occur below boiling point | At boiling point for given pressure |
| Bubbles | No bulk vapour bubbles required | Vapour bubbles form in liquid |
14. Surface Tension
Surface tension
A property of a liquid surface arising from cohesive intermolecular forces; it tends to minimize the surface area.
A property of a liquid surface arising from cohesive intermolecular forces; it tends to minimize the surface area.
Molecules inside a liquid are attracted in all directions. Surface molecules lack neighboring liquid molecules above them, producing a net inward effect and a surface that behaves as though under tension.
Examples
- Small liquid drops tend toward spherical shapes.
- A carefully placed light object may be supported by a water surface.
- Detergents reduce water’s surface tension and improve wetting.
Diagram 9: Qualitative origin of surface tension
15. Viscosity
Viscosity
The resistance of a fluid to flow arising from internal friction between neighboring layers.
The resistance of a fluid to flow arising from internal friction between neighboring layers.
A more viscous liquid flows more slowly under otherwise similar conditions.
Temperature Effect
For ordinary liquids, viscosity generally decreases as temperature rises because molecules can overcome intermolecular attractions more readily.
Syllabus level
Surface tension and viscosity are required as qualitative ideas in Unit 7; detailed mathematical fluid mechanics is not necessary here.
Surface tension and viscosity are required as qualitative ideas in Unit 7; detailed mathematical fluid mechanics is not necessary here.
16. Liquid Crystals and Their Applications
Liquid crystal
A state of matter with fluidity like a liquid but some degree of molecular order resembling a crystal.
A state of matter with fluidity like a liquid but some degree of molecular order resembling a crystal.
Liquid crystals are anisotropic: some properties depend on direction because molecules have partial orientational order.
Applications
- Liquid-crystal displays (LCDs).
- Digital watches and calculators.
- Computer, television and instrument displays.
- Temperature-sensitive indicators in some applications.
- Optical and sensing technologies.
17. Solid State
Solids have closely packed particles with restricted motion. Their structural order determines whether they are crystalline or amorphous.
18. Crystalline and Amorphous Solids
| Property | Crystalline Solid | Amorphous Solid |
|---|---|---|
| Particle arrangement | Long-range regular order | No long-range periodic order |
| Melting behavior | Usually sharp melting point | Softens over a range |
| Geometry | Regular crystal form possible | Irregular form |
| Anisotropy | May show direction-dependent properties | Usually approximately isotropic |
| Examples | NaCl, quartz, sugar crystals | Glass, many plastics |
Diagram 10: Ordered and disordered solid structures
19. Efflorescent, Deliquescent and Hygroscopic Solids
| Type | Behavior in air | Typical example |
|---|---|---|
| Efflorescent | Loses some or all water of crystallization to air; crystal surface may become powdery | Na₂CO₃·10H₂O |
| Deliquescent | Absorbs enough water vapour from air to dissolve in the absorbed water | CaCl₂, NaOH |
| Hygroscopic | Absorbs moisture from air without necessarily dissolving into a solution | Concentrated H₂SO₄, silica gel |
Key distinction
All deliquescent materials are strongly moisture-absorbing, but “deliquescent” specifically means absorption continues until the substance forms a solution.
All deliquescent materials are strongly moisture-absorbing, but “deliquescent” specifically means absorption continues until the substance forms a solution.
20. Crystallization and Crystal Growth
Crystallization
The formation of an ordered crystalline solid from a solution, melt or vapour.
The formation of an ordered crystalline solid from a solution, melt or vapour.
Crystallization from Solution
- Prepare a hot concentrated or saturated solution.
- Remove insoluble impurities if necessary.
- Allow the solution to cool or allow some solvent to evaporate.
- Supersaturation develops.
- Nuclei form and crystals grow as particles arrange in an ordered lattice.
- Separate and dry the crystals.
Crystal quality
Slow, controlled crystal growth generally favors larger, better-formed crystals; rapid precipitation often gives smaller crystals.
Slow, controlled crystal growth generally favors larger, better-formed crystals; rapid precipitation often gives smaller crystals.
Diagram 11: Stages of crystallization
21. Water of Crystallization
Water of crystallization
A definite number of water molecules incorporated into the crystal structure of a hydrated salt.
A definite number of water molecules incorporated into the crystal structure of a hydrated salt.
Examples:
- CuSO₄·5H₂O — copper(II) sulfate pentahydrate.
- Na₂CO₃·10H₂O — sodium carbonate decahydrate.
- MgSO₄·7H₂O — magnesium sulfate heptahydrate.
Not ordinary surface moisture
Water of crystallization is part of the defined crystal composition and is represented explicitly in the chemical formula.
Water of crystallization is part of the defined crystal composition and is represented explicitly in the chemical formula.
22. Crystal Lattice and Unit Cell
Crystal lattice
An idealized three-dimensional periodic array of points representing the repeating arrangement in a crystal.
An idealized three-dimensional periodic array of points representing the repeating arrangement in a crystal.
Unit cell
The smallest repeating geometrical portion of a crystal lattice that reproduces the crystal by translation in three dimensions.
The smallest repeating geometrical portion of a crystal lattice that reproduces the crystal by translation in three dimensions.
A unit cell is described by edge lengths and angles. At this introductory level, the key idea is that repeating the unit cell builds the complete lattice.
Diagram 12: Unit cell and crystal lattice
23. Worked Numericals
Example 1: Boyle’s Law
A gas occupies 500 mL at 1.0 atm. Find its volume at 2.0 atm at constant temperature.
P₁V₁ = P₂V₂ V₂ = (1.0 × 500)/2.0 = 250 mL
Example 2: Charles’ Law
300 mL of gas at 27°C is heated to 127°C at constant pressure.
T₁ = 300 K; T₂ = 400 K.
V₂ = V₁T₂/T₁ V₂ = 300 × 400/300 = 400 mL
Example 3: Combined Gas Equation
1.5 L gas at 1.0 atm and 300 K changes to 2.0 atm and 400 K. Find V₂.
P₁V₁/T₁ = P₂V₂/T₂ V₂ = (1.0 × 1.5 × 400)/(300 × 2.0) = 1.0 L
Example 4: Dalton’s Law
A mixture contains gases with partial pressures 200, 150 and 100 kPa.
Ptotal = 200 + 150 + 100 = 450 kPa
Example 5: Graham’s Law
Compare diffusion rates of H₂ (M = 2) and O₂ (M = 32).
r(H₂)/r(O₂) = √(32/2) = √16 = 4Hydrogen diffuses four times as fast under the same conditions.
Example 6: Ideal Gas Law
Find the volume of 2.0 mol ideal gas at 300 K and 1.00 atm. Use R = 0.082057 L·atm mol⁻¹ K⁻¹.
V = nRT/P V = 2.0 × 0.082057 × 300 / 1.00 ≈ 49.2 L
Example 7: Molar Mass from Gas Data
0.50 g gas occupies 250 mL at 1 atm and 300 K. Find molar mass.
V = 0.250 L.
M = mRT/(PV) M = 0.50 × 0.082057 × 300 /(1 × 0.250) ≈ 49.2 g mol⁻¹
Example 8: Partial Pressure by Mole Fraction
A mixture contains 2 mol N₂ and 1 mol O₂ at total pressure 300 kPa.
x(N₂) = 2/3.
P(N₂) = xPtotal = (2/3)(300) = 200 kPa24. Formula Sheet
| Topic | Formula |
|---|---|
| Boyle’s law | P₁V₁ = P₂V₂ |
| Charles’ law | V₁/T₁ = V₂/T₂ |
| Avogadro’s law | V₁/n₁ = V₂/n₂ |
| Combined gas equation | P₁V₁/T₁ = P₂V₂/T₂ |
| Dalton’s law | Ptotal = ΣPᵢ |
| Partial pressure | Pᵢ = xᵢPtotal |
| Graham’s law | r₁/r₂ = √(M₂/M₁) |
| Ideal gas | PV = nRT |
| Molar mass from gas | M = mRT/(PV) |
| Gas density | d = PM/(RT) |
| Compressibility factor | Z = PV/(nRT) |
25. Common Exam Mistakes
- Using Celsius directly in Charles’ law, combined gas equation or PV = nRT.
- Forgetting to keep amount of gas fixed when applying Boyle’s or Charles’ law.
- Writing Boyle’s law as P ∝ V rather than P ∝ 1/V.
- Writing Charles’ law as V ∝ 1/T.
- Using Graham’s law with molar masses in the wrong order under the square root.
- Calling diffusion and effusion identical: diffusion is mixing; effusion is escape through a tiny opening.
- Forgetting that Dalton’s law applies to component partial pressures in a gas mixture.
- Mixing atm, Pa, kPa, L and m³ without matching the chosen value of R.
- Using °C instead of K in PV = nRT.
- Calling a real gas ideal at high pressure and low temperature; those conditions usually increase non-ideality.
- Forgetting molecular volume and intermolecular forces when explaining real-gas deviation.
- Saying evaporation occurs only at the boiling point.
- Confusing vapour pressure with atmospheric pressure.
- Defining boiling point without mentioning equality of vapour pressure and external pressure.
- Saying surface tension is caused by gravity; it mainly arises from intermolecular cohesion.
- Saying liquid viscosity increases with temperature as a general rule; ordinary liquid viscosity usually decreases with temperature.
- Confusing liquid crystals with ordinary crystalline solids; liquid crystals can flow while retaining partial order.
- Calling glass a crystalline solid; glass is generally amorphous.
- Confusing efflorescence with deliquescence.
- Calling all hygroscopic substances deliquescent.
- Confusing water of crystallization with accidental surface moisture.
- Calling the crystal lattice the same as a single unit cell; the unit cell repeats to generate the lattice.
26. Important Exam Questions
Short Questions
- State the postulates of kinetic molecular theory of gases.
- Define Boyle’s law and draw its P–V graph.
- Define Charles’ law and state why kelvin scale is used.
- State Avogadro’s law.
- Write the combined gas equation.
- State Dalton’s law of partial pressures.
- Define partial pressure and mole fraction.
- State Graham’s law of diffusion.
- Define ideal gas and write PV = nRT.
- State the significance and common units of R.
- Why do real gases deviate from ideal behavior?
- Under what conditions do real gases approach ideal behavior?
- Define evaporation and condensation.
- Define vapour pressure.
- Define boiling point.
- Differentiate evaporation and boiling.
- Define surface tension.
- Define viscosity.
- What are liquid crystals? Give applications.
- Differentiate crystalline and amorphous solids.
- Define efflorescent, deliquescent and hygroscopic substances.
- Define crystallization.
- What is water of crystallization?
- Define crystal lattice and unit cell.
Long Questions
- Explain the kinetic theory of gases and relate it to pressure and temperature.
- State and explain Boyle’s, Charles’ and Avogadro’s laws.
- Derive or explain the combined gas equation from the gas-law relationships.
- Explain Dalton’s law and solve partial-pressure problems.
- Explain Graham’s law and compare diffusion rates of gases.
- Explain the ideal-gas equation and the significance of R.
- Discuss why real gases deviate from ideality.
- Explain evaporation, condensation, vapour pressure and boiling point.
- Explain surface tension and viscosity qualitatively.
- Explain liquid crystals and their applications.
- Compare crystalline and amorphous solids.
- Explain crystallization, crystal growth and water of crystallization.
- Explain the concepts of crystal lattice and unit cell.
Numerical Practice
- Problems based on P₁V₁ = P₂V₂.
- Problems based on V₁/T₁ = V₂/T₂.
- Combined P–V–T problems.
- Dalton partial-pressure calculations.
- Graham diffusion-rate calculations.
- PV = nRT calculations.
- Molar-mass and density calculations using gas data.
Exam Strategy
Prioritize the gaseous-state formula block first: Boyle → Charles → Avogadro → combined equation → Dalton → Graham → PV=nRT. Then revise the liquid-state definitions and the solid-state comparison/terminology tables.
Prioritize the gaseous-state formula block first: Boyle → Charles → Avogadro → combined equation → Dalton → Graham → PV=nRT. Then revise the liquid-state definitions and the solid-state comparison/terminology tables.
27. One-Minute Revision
- Unit 7: States of Matter — 8 teaching hours.
- Gas particles move rapidly and randomly.
- Gas pressure comes from wall collisions.
- Average molecular kinetic energy rises with absolute temperature.
- Boyle: P₁V₁ = P₂V₂ at constant T.
- Charles: V₁/T₁ = V₂/T₂ at constant P.
- Avogadro: V ∝ n at constant T and P.
- Combined gas equation: P₁V₁/T₁ = P₂V₂/T₂.
- Dalton: Ptotal = sum of partial pressures.
- Graham: diffusion rate ∝ 1/√molar mass.
- Ideal gas equation: PV = nRT.
- R = 8.314 J mol⁻¹ K⁻¹ in SI.
- Real gases deviate because molecules have volume and intermolecular forces.
- Low pressure and high temperature favor ideal behavior.
- Evaporation occurs at a liquid surface below boiling point.
- Condensation converts vapour to liquid.
- Vapour pressure increases with temperature.
- Boiling occurs when vapour pressure equals external pressure.
- Surface tension arises from cohesive intermolecular forces.
- Liquid viscosity generally decreases as temperature rises.
- Liquid crystals flow but retain partial molecular order.
- Crystalline solids have long-range periodic order.
- Amorphous solids lack long-range periodic order.
- Efflorescent solids lose water of crystallization.
- Deliquescent solids absorb enough moisture to form a solution.
- Hygroscopic solids absorb moisture without necessarily dissolving.
- Water of crystallization is part of a hydrate’s crystal composition.
- A unit cell is the repeating building unit of a crystal lattice.
28. Diagram Practice
- Particle model of solid, liquid and gas.
- Kinetic molecular picture of a gas.
- Boyle’s law P–V curve.
- Charles’ law V–T graph.
- Dalton partial-pressure concept.
- Ideal gas equation concept map.
- Ideal vs real gas comparison.
- Evaporation and condensation.
- Surface tension molecular picture.
- Crystalline vs amorphous structure.
- Crystallization process.
- Unit cell and crystal lattice.
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