Chemistry Chapter States of Matter & laws
States of Matter & Gas Laws
TOPIC 1: States of Matter — Comparison
Three States of Matter
Matter exists in three main physical states: SOLID, LIQUID, and GAS. The state depends on the balance between the kinetic energy of particles and the strength of intermolecular forces.
| Property | SOLID | LIQUID | GAS |
| Shape | Definite shape ⭐ | No fixed shape — takes shape of container | No fixed shape — fills entire container |
| Volume | Definite volume ⭐ | Definite volume ⭐ | No fixed volume — expands to fill container |
| Compressibility | Virtually incompressible | Virtually incompressible | HIGHLY compressible ⭐ |
| Density | High (closely packed) | High (similar to solid) | Very LOW ⭐ (particles far apart) |
| Particle arrangement | Regular, ordered lattice | Random, close but mobile | Random, far apart |
| Particle motion | Vibrate in fixed positions | Move/slide past each other | Move rapidly in all directions |
| Intermolecular forces | STRONGEST ⭐ | Moderate | Very weak (negligible) ⭐ |
| Diffusion rate | Negligible | Slow | FASTEST ⭐ |
Changes of State
Changes of state occur when sufficient energy is added or removed to overcome/establish intermolecular forces. The temperature stays CONSTANT during a change of state (latent heat).
| Change | Name | Energy Change | Example |
| Solid → Liquid | Melting (fusion) | Energy ABSORBED (endothermic) | Ice melts at 0°C |
| Liquid → Solid | Freezing (solidification) | Energy RELEASED (exothermic) | Water freezes at 0°C |
| Liquid → Gas | Vaporisation (boiling/evaporation) | Energy ABSORBED (endothermic) | Water boils at 100°C |
| Gas → Liquid | Condensation | Energy RELEASED (exothermic) | Steam condenses on cool surface |
| Solid → Gas | Sublimation | Energy ABSORBED (endothermic) | Dry ice (CO₂), iodine, naphthalene |
| Gas → Solid | Deposition | Energy RELEASED (exothermic) | Frost forming on cold surfaces |
| KEY FACT | Latent heat — heat energy during state change (temperature stays constant): • Latent heat of fusion (melting/freezing): energy to break/form intermolecular forces between solid and liquid • Latent heat of vaporisation (boiling/condensing): energy to break/form intermolecular forces between liquid and gas • Latent heat of vaporisation > latent heat of fusion (more forces to break going from liquid to gas) • Water: latent heat of fusion = 334 J/g | latent heat of vaporisation = 2260 J/g ⭐ |
TOPIC 2: Kinetic Molecular Theory of Gases
Postulates of Kinetic Molecular Theory (KMT)
The kinetic molecular theory explains the behaviour of IDEAL GASES. An ideal gas is a hypothetical gas that perfectly obeys all gas laws. Real gases approximate ideal behaviour at LOW pressure and HIGH temperature.
- Postulate 1: Gases consist of a large number of tiny particles (atoms or molecules) that are in CONSTANT, RANDOM motion.
- Postulate 2: The volume of individual gas particles is NEGLIGIBLE compared to the total volume of the gas. (Gas particles are mostly empty space.)
- Postulate 3: Gas particles NEITHER ATTRACT NOR REPEL each other (no intermolecular forces between ideal gas particles).
- Postulate 4: Gas particles undergo PERFECTLY ELASTIC collisions (no energy loss in collisions — kinetic energy is conserved).
- Postulate 5: The AVERAGE KINETIC ENERGY of gas particles is directly proportional to the ABSOLUTE TEMPERATURE (in Kelvin): KE ∝ T(K) ⭐
| KEY FACT | Temperature and Kinetic Energy: Average KE = (3/2)kT, where k = Boltzmann constant, T = absolute temperature (Kelvin) Higher temperature → higher average KE → particles move faster Converting between Celsius and Kelvin: T(K) = T(°C) + 273 ⭐ 0°C = 273 K | 100°C = 373 K | 25°C = 298 K | −273°C = 0 K (absolute zero) Absolute zero (0 K = −273°C): theoretical temperature at which all molecular motion stops |
Real vs Ideal Gases
| Feature | Ideal Gas | Real Gas |
| Intermolecular forces | None (assumed) | Present — cause deviations |
| Particle volume | Negligible (assumed zero) | Finite, non-zero |
| Obeys gas laws | Perfectly, under all conditions | Approximately — deviates at high P and low T |
| Compression | Exactly PV = nRT | PV ≠ nRT at high pressure or low temperature |
| Behaviour | Hypothetical model | All real gases (N₂, O₂, CO₂, H₂O etc.) |
| When closest to ideal | — | At LOW pressure + HIGH temperature ⭐ |
TOPIC 3: Gas Laws — The Most Tested Chemistry Topic in AFNS
Boyle’s Law — Pressure and Volume (constant T, n)
At constant temperature, the volume of a fixed mass of gas is INVERSELY PROPORTIONAL to its pressure:
P ∝ 1/V OR PV = constant OR P₁V₁ = P₂V₂ ⭐
Stated by Robert Boyle (1662). At higher pressure → gas compresses → smaller volume. At lower pressure → gas expands → larger volume.
| 📌 WORKED EXAMPLE
Q: A gas has volume 4 L at pressure 2 atm. What volume at 8 atm (constant T)? A: P₁V₁ = P₂V₂ 2 × 4 = 8 × V₂ V₂ = 8/8 = 1 L As pressure quadrupled (2→8 atm), volume quartered (4→1 L). Inverse relationship confirmed. |
Charles’ Law — Volume and Temperature (constant P, n)
At constant pressure, the volume of a fixed mass of gas is DIRECTLY PROPORTIONAL to its absolute temperature (in Kelvin):
V ∝ T OR V/T = constant OR V₁/T₁ = V₂/T₂ ⭐
Stated by Jacques Charles (1787). Must use KELVIN temperature (not Celsius). At higher temperature → gas expands → larger volume. At lower temperature → gas contracts → smaller volume.
| 📌 WORKED EXAMPLE
Q: A gas occupies 3 L at 27°C. What volume at 127°C (constant P)? A: Convert to Kelvin: T₁ = 27+273 = 300 K | T₂ = 127+273 = 400 K V₁/T₁ = V₂/T₂ 3/300 = V₂/400 V₂ = (3 × 400)/300 = 4 L ⭐ |
Gay-Lussac’s Law — Pressure and Temperature (constant V, n)
At constant volume, the pressure of a fixed mass of gas is DIRECTLY PROPORTIONAL to its absolute temperature (in Kelvin):
P ∝ T OR P/T = constant OR P₁/T₁ = P₂/T₂ ⭐
Named after Joseph Gay-Lussac. Used in pressure cooker calculations: higher temperature → higher pressure.
| 📌 WORKED EXAMPLE
Q: A gas has pressure 1.5 atm at 300 K. What is the pressure at 600 K (constant V)? A: P₁/T₁ = P₂/T₂ 1.5/300 = P₂/600 P₂ = (1.5 × 600)/300 = 3.0 atm |
Avogadro’s Law — Volume and Moles (constant T, P)
At constant temperature and pressure, EQUAL VOLUMES of all gases contain EQUAL NUMBERS of molecules (Avogadro’s hypothesis, 1811):
V ∝ n OR V/n = constant OR V₁/n₁ = V₂/n₂ ⭐
This means the molar volume of ANY gas at STP = 22.4 L/mol (regardless of the gas identity).
TOPIC 4: The Ideal Gas Equation — Most Important Gas Law
Combining All Gas Laws: PV = nRT
All four gas laws (Boyle’s, Charles’, Gay-Lussac’s, Avogadro’s) combine into the IDEAL GAS EQUATION:
PV = nRT ⭐⭐⭐
| KEY FACT | PV = nRT — Variables: P = pressure (atm, Pa, kPa, mmHg — must be consistent) V = volume (litres if P in atm, m³ if P in Pa) n = number of moles of gas R = universal gas constant ⭐ R = 0.0821 L·atm/mol·K (if P in atm, V in litres) R = 8.314 J/mol·K (if P in Pa, V in m³) T = absolute temperature in KELVIN (T(K) = T(°C) + 273) ⭐ STP conditions: T = 0°C = 273 K, P = 1 atm → 1 mol gas = 22.4 L RTP conditions: T = 25°C = 298 K, P = 1 atm → 1 mol gas = 24.5 L |
| 📌 WORKED EXAMPLE
Q: Calculate the volume of 2 mol of an ideal gas at 27°C and 2 atm pressure. A: T = 27+273 = 300 K | n = 2 mol | P = 2 atm | R = 0.0821 L·atm/mol·K PV = nRT 2 × V = 2 × 0.0821 × 300 V = (2 × 0.0821 × 300)/2 = 24.63 L ≈ 24.6 L |
| 📌 WORKED EXAMPLE
Q: A 5 L container holds a gas at 3 atm and 27°C. How many moles of gas? A: P=3 atm | V=5 L | T=300 K | R=0.0821 n = PV/RT = (3×5)/(0.0821×300) = 15/24.63 = 0.609 mol |
Combined Gas Law
When both temperature AND pressure change (constant n):
P₁V₁/T₁ = P₂V₂/T₂ ⭐
| 📌 WORKED EXAMPLE
Q: A gas occupies 10 L at 2 atm and 300 K. Find volume at 4 atm and 600 K. A: P₁V₁/T₁ = P₂V₂/T₂ (2×10)/300 = (4×V₂)/600 V₂ = (2×10×600)/(300×4) = 12000/1200 = 10 L |
TOPIC 5: Dalton’s Law and Graham’s Law
Dalton’s Law of Partial Pressures
In a mixture of gases, the TOTAL PRESSURE equals the SUM of the PARTIAL PRESSURES of each individual gas:
P_total = P₁ + P₂ + P₃ + … ⭐
Partial pressure of a gas = mole fraction of that gas × total pressure
P_A = χ_A × P_total
| 📌 WORKED EXAMPLE
Q: A mixture contains 2 mol N₂ (partial P = 1 atm) and 3 mol O₂ (partial P = 1.5 atm). Total pressure? A: P_total = P_N₂ + P_O₂ = 1 + 1.5 = 2.5 atm Mole fractions: χ_N₂ = 2/5 = 0.4 | χ_O₂ = 3/5 = 0.6 Check: P_N₂ = 0.4×2.5 = 1.0 ✓ | P_O₂ = 0.6×2.5 = 1.5 ✓ |
Graham’s Law of Effusion/Diffusion
Effusion = escape of gas through a tiny hole | Diffusion = spreading of gas through space
Graham’s Law: the rate of effusion (or diffusion) of a gas is INVERSELY PROPORTIONAL to the square root of its molar mass:
Rate₁/Rate₂ = √(M₂/M₁) ⭐
Lighter gases move FASTER and effuse/diffuse more quickly. This is why H₂ leaks faster than O₂ from a container.
| 📌 WORKED EXAMPLE
Q: Compare the rates of effusion of H₂ (M=2) and O₂ (M=32). A: Rate_H₂/Rate_O₂ = √(M_O₂/M_H₂) = √(32/2) = √16 = 4 H₂ effuses 4 times faster than O₂ ⭐ |
. At absolute zero (0 K), gas particles:
- A) Move very fast
- B) Have maximum kinetic energy
- C) Stop moving completely (theoretically)
- D) Become liquid
✔ Answer: C) Stop moving completely (theoretically)
- Absolute zero in Celsius is:
- A) 0°C
- B) −100°C
- C) −273.15°C
- D) −373°C
✔ Answer: C) −273.15°C
- Boyle’s Law states that at constant temperature, pressure and volume are:
- A) Directly proportional
- B) Inversely proportional
- C) Equal
- D) Unrelated
✔ Answer: B) Inversely proportional
- Charles’s Law states that at constant pressure, volume and temperature are:
- A) Inversely proportional
- B) Directly proportional
- C) Unrelated
- D) Constant
✔ Answer: B) Directly proportional
- The Ideal Gas equation is:
- A) PV = nRT
- B) PV = RT
- C) P = nRT/V²
- D) PV² = nRT
✔ Answer: A) PV = nRT
- In the ideal gas equation PV = nRT, R is:
- A) Avogadro’s number
- B) Universal gas constant (8.314 J mol⁻¹ K⁻¹)
- C) Boltzmann constant
- D) Planck’s constant
✔ Answer: B) Universal gas constant (8.314 J mol⁻¹ K⁻¹)
- Gay-Lussac’s Law states that at constant volume, pressure is _____ proportional to temperature:
- A) Inversely
- B) Not
- C) Directly
- D) Exponentially
✔ Answer: C) Directly
- Avogadro’s Law states that equal volumes of gases at same T and P contain:
- A) Same mass
- B) Same number of molecules
- C) Same density
- D) Same kinetic energy
✔ Answer: B) Same number of molecules
- Avogadro’s number is:
- A) 6.022 × 10²³
- B) 6.022 × 10²²
- C) 3.0 × 10⁸
- D) 1.6 × 10⁻¹⁹
✔ Answer: A) 6.022 × 10²³
- Diffusion is the movement of particles from a region of:
- A) Low to high concentration
- B) High to low concentration
- C) High to high pressure
- D) Equal concentration
✔ Answer: B) High to low concentration
- Graham’s Law of diffusion states that the rate of diffusion is inversely proportional to:
- A) Pressure
- B) Temperature
- C) Square root of molar mass
- D) Volume
✔ Answer: C) Square root of molar mass
- Real gases deviate from ideal behaviour at:
- A) Low pressure and high temperature
- B) High pressure and low temperature
- C) Standard conditions
- D) Low density
✔ Answer: B) High pressure and low temperature
- The kinetic molecular theory assumes gas molecules have:
- A) Strong intermolecular forces
- B) Negligible volume and negligible intermolecular forces
- C) Fixed positions
- D) Equal masses
✔ Answer: B) Negligible volume and negligible intermolecular forces
- Condensation is the change from:
- A) Solid to liquid
- B) Gas to liquid
- C) Liquid to gas
- D) Solid to gas
✔ Answer: B) Gas to liquid
- Sublimation is the change from:
- A) Liquid to gas
- B) Solid to gas directly
- C) Gas to solid
- D) Liquid to solid
✔ Answer: B) Solid to gas directly
- The boiling point is the temperature at which:
- A) Surface evaporation begins
- B) Vapour pressure equals atmospheric pressure
- C) All intermolecular forces break
- D) Density becomes zero
✔ Answer: B) Vapour pressure equals atmospheric pressure
- Surface tension is caused by:
- A) Gravity alone
- B) Unbalanced intermolecular forces at the liquid surface
- C) Temperature change
- D) Dissolved gases
✔ Answer: B) Unbalanced intermolecular forces at the liquid surface
- Viscosity is a measure of a liquid’s:
- A) Surface tension
- B) Resistance to flow
- C) Boiling point
- D) Vapour pressure
✔ Answer: B) Resistance to flow
- In a mixture, the total pressure equals the sum of partial pressures. This is:
- A) Boyle’s Law
- B) Dalton’s Law of Partial Pressures
- C) Graham’s Law
- D) Henry’s Law
✔ Answer: B) Dalton’s Law of Partial Pressures
- Henry’s Law states that solubility of a gas in liquid is _____ proportional to the gas pressure above it:
- A) Inversely
- B) Not
- C) Directly
- D) Exponentially
✔ Answer: C) Directly
- Which state of matter has a definite shape and volume?
- A) Gas
- B) Liquid
- C) Solid
- D) Plasma
✔ Answer: C) Solid
- Which state of matter has a definite volume but no definite shape?
- A) Solid
- B) Liquid
- C) Gas
- D) Plasma
✔ Answer: B) Liquid
- STP stands for:
- A) 25°C and 1 atm
- B) 0°C (273 K) and 1 atm
- C) 100°C and 2 atm
- D) 37°C and 1 atm
✔ Answer: B) 0°C (273 K) and 1 atm
- Molar volume of an ideal gas at STP is:
- A) 11.2 L
- B) 22.4 L
- C) 44.8 L
- D) 1 L
✔ Answer: B) 22.4 L
- Van der Waals forces increase with increasing:
- A) Temperature
- B) Molecular size and molar mass
- C) Pressure only
- D) Atomic number alone
✔ Answer: B) Molecular size and molar mass
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