States of Matter and Gas Laws: Boyle’s, Charles’s, Avogadro’s Law and PV = nRT Explained

Everything around us – the air we breathe, the water we drink, the chair we sit on – is made of matter. Matter is anything that has mass and occupies space (volume). It is made of tiny particles (atoms and molecules) that are always moving and attract each other. How tightly these particles are packed and how fast they move decide whether a substance is a solid, liquid or gas. Gases follow simple mathematical rules called the gas laws, which link pressure, volume, temperature and amount of gas.

States of matter and gas laws are asked regularly in SSC CGL, CHSL, MTS, GD, RRB NTPC, Group D, WBCS, WBPSC, Police and State PSC exams. Typical questions cover the properties of solids, liquids and gases, sublimation, latent heat, the effect of pressure on boiling point, the fourth and fifth states of matter, and Boyle's, Charles's and Avogadro's laws. This guide explains everything simply with diagrams, tables, solved examples, tricks and 20 MCQs with answers.

➤ Matter: Anything with mass and volume · made of particles that move and attract one another
➤ Five states: Solid, liquid, gas, plasma (4th), Bose–Einstein condensate (5th)
➤ Boyle's law: P ∝ 1/V at constant temperature (PV = constant)
➤ Charles's law: V ∝ T (in kelvin) at constant pressure
➤ Ideal gas equation: PV = nRT · R = 8.314 J mol⁻¹ K⁻¹
➤ Molar volume at STP: 22.4 litres (0 °C, 1 atm) · Absolute zero: 0 K = −273.15 °C
➤ Bose–Einstein condensate: Predicted by Satyendra Nath Bose and Albert Einstein (1924–25)

What is Matter? – Characteristics of Particles

The particles of matter have four key characteristics, which are easy to show with simple experiments:

Diffusion is fastest in gases, slower in liquids and slowest in solids. It increases with temperature because particles move faster.

The Three Common States of Matter

Figure 1 shows how particles are arranged in each state.

Figure 1: Arrangement of particles in a solid, a liquid and a gas

Exam points: Gases are highly compressible, so LPG and CNG are compressed into cylinders. A sponge is a solid even though it can be pressed – it has tiny holes filled with air. Rubber bands change shape under force but are solids. Ice floats on water because ice is less dense than water; water is densest at 4 °C.

Change of State

Matter can change from one state to another by changing temperature or pressure (Figure 2).

Figure 2: Interconversion of the three states of matter

Latent Heat – Hidden Heat

During melting or boiling, the temperature stays constant even though heat is being supplied. This heat is used to overcome the forces between particles and is called latent heat (hidden heat).

• Latent heat of fusion of ice: about 334 kJ/kg (≈ 80 cal/g). This is why ice at 0 °C cools a drink better than water at 0 °C.
• Latent heat of vaporisation of water: about 2260 kJ/kg (≈ 540 cal/g). This is why steam at 100 °C causes more severe burns than boiling water at 100 °C.

Evaporation – A Surface Phenomenon

Evaporation is the change of a liquid into vapour at any temperature below its boiling point. It happens only at the surface and causes cooling. It increases with higher temperature, larger surface area, lower humidity and higher wind speed. That is why wet clothes dry faster on a sunny, windy day; water in an earthen pot (matka) stays cool; we sweat in summer; and cotton clothes are preferred in hot weather.

Effect of Pressure on Boiling and Melting Point

Increasing pressure raises the boiling point of water – the principle of the pressure cooker, which cooks food at about 120 °C. At high altitudes such as hill stations, air pressure is low, so water boils below 100 °C and food takes longer to cook. Increasing pressure lowers the melting point of ice, which helps ice skaters glide. Adding salt or sugar (impurities) raises the boiling point and lowers the freezing point of water.

Plasma and Bose–Einstein Condensate

Gas Laws

The behaviour of a gas is described by four quantities: pressure (P), volume (V), temperature (T) and number of moles (n). In all gas law calculations, temperature must be in kelvin (K = °C + 273).

1. Boyle's Law (1662)

Robert Boyle found that at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure: P ∝ 1/V, or P₁V₁ = P₂V₂. If pressure is doubled, the volume becomes half (Figure 3). Examples: a bubble rising from the bottom of a pond grows bigger as pressure decreases; a syringe; breathing (lungs expand → pressure falls → air rushes in).

Figure 3: Boyle's law gives a curve (P × V constant); Charles's law gives a straight line through absolute zero

2. Charles's Law (1787)

Jacques Charles found that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature: V ∝ T, or V₁/T₁ = V₂/T₂. For every 1 °C rise, the volume of a gas increases by 1/273 of its volume at 0 °C. Extending this to the point where volume would become zero gives absolute zero (−273.15 °C or 0 K). Examples: hot air balloons rise; tyres burst in summer; a dented ping-pong ball regains its shape in hot water.

3. Gay-Lussac's Law (Pressure–Temperature Law)

At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature: P ∝ T, or P₁/T₁ = P₂/T₂. This is why aerosol cans can explode if heated and why tyre pressure rises after a long drive.

4. Avogadro's Law (1811)

Amedeo Avogadro stated that equal volumes of all gases at the same temperature and pressure contain an equal number of molecules. So V ∝ n. One mole of any gas at STP (0 °C and 1 atm) occupies 22.4 litres, and contains 6.022 × 10²³ particles – the Avogadro number.

5. Combined Gas Law and Ideal Gas Equation

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

PV = nRT

where R is the universal gas constant = 8.314 J mol⁻¹ K⁻¹ = 0.0821 L atm mol⁻¹ K⁻¹. For a fixed amount of gas, the combined gas law is P₁V₁/T₁ = P₂V₂/T₂. An ideal gas obeys these laws exactly; real gases behave nearly ideally at high temperature and low pressure.

6. Dalton's Law and Graham's Law

Dalton's law of partial pressures (1801): The total pressure of a mixture of non-reacting gases equals the sum of the partial pressures of each gas: P_total = P₁ + P₂ + P₃ + …

Graham's law of diffusion (1848): The rate of diffusion of a gas is inversely proportional to the square root of its density (or molar mass): r ∝ 1/√M. So hydrogen, the lightest gas, diffuses fastest. Hydrogen (M = 2) diffuses 4 times faster than oxygen (M = 32), since √(32/2) = 4.

Gas Laws at a Glance

Solved Examples

Example 1 (Boyle's law): A gas occupies 6 L at 2 atm. What will be its volume at 3 atm, temperature unchanged?
P₁V₁ = P₂V₂ → 2 × 6 = 3 × V₂ → V₂ = 4 L

Example 2 (Charles's law): A gas occupies 300 mL at 27 °C. What will be its volume at 127 °C, pressure unchanged?
T₁ = 300 K, T₂ = 400 K → V₂ = 300 × 400/300 = 400 mL

Example 3 (Avogadro): What volume does 2 moles of CO₂ occupy at STP?
2 × 22.4 = 44.8 L

Temperature Scales

Conversion formulas: K = °C + 273 and °F = (9/5 × °C) + 32. The SI unit of temperature is the kelvin.

West Bengal Connection – Satyendra Nath Bose and the Fifth State of Matter

The fifth state of matter carries the name of a Bengali scientist. Satyendra Nath Bose (1894–1974), born in Kolkata and a student of Presidency College, was teaching at Dhaka University when, in 1924, he sent Albert Einstein a paper deriving Planck's radiation law in a new way. Einstein translated it into German, had it published, and extended the idea to atoms – predicting what we now call the Bose–Einstein condensate. Particles that follow Bose's statistics are named bosons in his honour. Bose was awarded the Padma Vibhushan in 1954 and named a National Professor in 1959. The S.N. Bose National Centre for Basic Sciences in Salt Lake, Kolkata, set up in 1986, continues his legacy.

For related physics and chemistry topics, read Light – Reflection and Refraction, Carbon and Organic Chemistry and Climatology and Atmospheric Pressure. See the Darbhanga Planetarium and ISRO Space Gallery to learn about stars made of plasma.

20 MCQs on Nature of Matter and Gas Laws

Q1. Which state of matter has a definite volume but no definite shape?
(a) Solid
(b) Liquid
(c) Gas
(d) Plasma

Answer: (b) – A liquid takes the shape of its container but keeps its volume.

Q2. The intermolecular force of attraction is the strongest in:
(a) Gases
(b) Liquids
(c) Plasma
(d) Solids

Answer: (d) – That is why solids have fixed shape and volume.

Q3. Which of the following undergoes sublimation?
(a) Camphor
(b) Common salt
(c) Sugar
(d) Wax

Answer: (a) – It changes directly from solid to vapour.

Q4. Steam at 100 °C causes more severe burns than boiling water at 100 °C because steam has:
(a) Higher temperature
(b) Higher density
(c) Extra latent heat of vaporisation
(d) Lower specific heat

Answer: (c) – Steam releases about 540 cal/g extra heat on condensing.

Q5. Food cooks faster in a pressure cooker because:
(a) Boiling point of water increases
(b) Boiling point of water decreases
(c) Heat is lost faster
(d) Steam is cooler

Answer: (a) – Higher pressure raises the boiling point to about 120 °C.

Q6. Evaporation of a liquid causes:
(a) Heating
(b) No change in temperature
(c) Increase in boiling point
(d) Cooling

Answer: (d) – Particles with high energy escape, lowering the average energy of the rest.

Q7. The fourth state of matter is:
(a) Bose–Einstein condensate
(b) Plasma
(c) Colloid
(d) Vapour

Answer: (b) – Plasma is an ionised gas found in the Sun, stars and lightning.

Q8. The Bose–Einstein condensate is named after Albert Einstein and which Indian scientist?
(a) C.V. Raman
(b) Meghnad Saha
(c) Satyendra Nath Bose
(d) Jagadish Chandra Bose

Answer: (c) – S.N. Bose of Kolkata sent his paper to Einstein in 1924.

Q9. Boyle's law states that at constant temperature:
(a) V ∝ T
(b) P ∝ T
(c) V ∝ n
(d) P ∝ 1/V

Answer: (d) – Pressure and volume are inversely proportional.

Q10. According to Charles's law, at constant pressure, the volume of a gas is directly proportional to its:
(a) Absolute temperature
(b) Pressure
(c) Density
(d) Molar mass

Answer: (a) – Temperature must be measured in kelvin.

Q11. Absolute zero is equal to:
(a) 0 °C
(b) −100 °C
(c) −273.15 °C
(d) −459 °C

Answer: (c) – It is 0 K, the lowest possible temperature.

Q12. The volume occupied by one mole of an ideal gas at STP is:
(a) 11.2 L
(b) 22.4 L
(c) 24.8 L
(d) 44.8 L

Answer: (b) – This is the molar volume at 0 °C and 1 atm.

Q13. "Equal volumes of all gases at the same temperature and pressure contain an equal number of molecules." This is:
(a) Boyle's law
(b) Charles's law
(c) Dalton's law
(d) Avogadro's law

Answer: (d) – Proposed by Amedeo Avogadro in 1811.

Q14. In the ideal gas equation PV = nRT, the value of R is:
(a) 8.314 J mol⁻¹ K⁻¹
(b) 6.022 × 10²³
(c) 9.8 m s⁻²
(d) 1.38 J K⁻¹

Answer: (a) – 6.022 × 10²³ is the Avogadro number.

Q15. A gas occupies 6 L at 2 atm. At constant temperature, its volume at 3 atm will be:
(a) 9 L
(b) 3 L
(c) 4 L
(d) 12 L

Answer: (c) – P₁V₁ = P₂V₂ → 2 × 6 = 3 × V₂.

Q16. Which gas diffuses the fastest?
(a) Oxygen
(b) Hydrogen
(c) Carbon dioxide
(d) Nitrogen

Answer: (b) – By Graham's law, the lightest gas diffuses fastest.

Q17. Real gases behave most like ideal gases at:
(a) Low temperature and high pressure
(b) Low temperature and low pressure
(c) High temperature and high pressure
(d) High temperature and low pressure

Answer: (d) – Molecules are far apart, so attractions become negligible.

Q18. At which temperature do the Celsius and Fahrenheit scales show the same reading?
(a) −40°
(b) 0°
(c) 40°
(d) −273°

Answer: (a) – −40 °C = −40 °F.

Q19. Water has maximum density at:
(a) 0 °C
(b) 100 °C
(c) 4 °C
(d) −4 °C

Answer: (c) – This is why ice floats and lakes freeze from the top.

Q20. The total pressure of a mixture of non-reacting gases equals the sum of their partial pressures. This is:
(a) Graham's law
(b) Dalton's law
(c) Gay-Lussac's law
(d) Henry's law

Answer: (b) – John Dalton stated this law of partial pressures in 1801.

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Conclusion

Matter exists as solid, liquid and gas in daily life, with plasma and Bose–Einstein condensate as two more extreme states. The difference between them comes from how closely packed the particles are and how much energy they have. Change of state, latent heat, evaporation and the effect of pressure explain many everyday observations, from the cooling of a matka to the pressure cooker. The gas laws of Boyle, Charles, Gay-Lussac and Avogadro combine into PV = nRT, the single equation behind most numerical questions. Revise the tables and tricks, and practise the MCQs and solved examples.

Reference: NCERT Science Class IX ("Matter in Our Surroundings"); NCERT Chemistry Class XI ("States of Matter").