States of Matter: Gases, Liquids, Solids & Phase Changes

TAKEAWAYS:

• States of matter are defined by particle arrangement, movement, and forces: solids (fixed shape, strong forces), liquids (fixed volume, weak forces), gases (no fixed shape/volume, negligible forces).
• Intermolecular forces (IMFs) determine physical properties: hydrogen bonding (strongest in H₂O), dipole-dipole, London dispersion (weakest).
• Kinetic theory explains gas behavior: particles move randomly, collide elastically, and have average kinetic energy proportional to temperature.
• Phase changes (melting, boiling, freezing, etc.) involve energy transfer (endothermic/exothermic) and are represented on heating/cooling curves.
• Gases follow gas laws: Boyle’s (P ∝ 1/V), Charles’s (V ∝ T), Gay-Lussac’s (P ∝ T), and the Combined Gas Law (PV/T = constant).
• Real gases deviate from ideal behavior at high pressure/low temperature due to IMF and particle volume.

1. States of Matter: Definitions and Properties

All matter exists in three primary states: solid, liquid, and gas. A fourth state, plasma, exists at extremely high temperatures (e.g., lightning, stars) but is not covered in Class 11.

Key Differences

Why does ice float on water?

• Density anomaly: Water expands when freezing (ice has open hexagonal structure with hydrogen bonds), making it less dense than liquid water.
• IMFs: Hydrogen bonds in ice are fixed in space, creating empty spaces between molecules.

2. Intermolecular Forces (IMFs): The "Glue" Between Particles

IMFs determine whether a substance is solid, liquid, or gas at room temperature. They are weaker than covalent/ionic bonds but stronger than van der Waals forces in some cases.

Types of IMFs

graph TD
    A["Intermolecular Forces"] --> B["1. Hydrogen Bonding"]
    A --> C["2. Dipole-Dipole Forces"]
    A --> D["3. London Dispersion Forces (LDF)"]
    B --> E["Strongest IMF\nOccurs in H-F, H-O, H-N bonds"]
    C --> F["Polar molecules\n+ve end attracts -ve end"]
    D --> G["Weakest IMF\nPresent in all molecules\nCaused by temporary dipoles"]

Examples and Strengths

Worked Example 1: Predicting Physical States Which of the following is a gas at room temperature? A) CH₄ (methane) B) H₂O (water) C) NaCl (sodium chloride) D) Fe (iron)

Solution:

• CH₄: Only London dispersion forces (very weak) → gas.
• H₂O: Strong hydrogen bonding → liquid.
• NaCl: Ionic bonds (strong) → solid.
• Fe: Metallic bonding → solid.

Answer: A (CH₄)

3. Kinetic Theory of Gases

Explains the behavior of gases based on particle motion and collisions.

Postulates of Kinetic Theory

1. Gases consist of tiny particles (atoms/molecules) in random motion.
2. Particle volume is negligible compared to the container.
3. Particles collide elastically (no energy lost).
4. No intermolecular forces (ideal gas assumption).
5. Average kinetic energy (KE) depends only on temperature: $$K{E}_{avg}=\frac{3}{2}{k}_{B}T\text{(where }{k}_B=\text{Boltzmann constant)}$$

Real vs. Ideal Gases

Why does CO₂ not behave ideally at high pressure?

• At high pressure, CO₂ molecules are forced closer, so their own volume and IMFs become significant.

4. Phase Changes (Physical Changes)

Substances change states by absorbing or releasing energy (but not changing chemically).

Types of Phase Changes

flowchart TD
    A["Phase Changes"] --> B["Melting (Solid → Liquid)"]
    A --> C["Freezing (Liquid → Solid)"]
    A --> D["Vaporization (Liquid → Gas)"]
    A --> E["Condensation (Gas → Liquid)"]
    A --> F["Sublimation (Solid → Gas)"]
    A --> G["Deposition (Gas → Solid)"]
    B -->|"+Energy"| H["Endothermic"]
    C -->|"-Energy"| H
    D -->|"+Energy"| H
    E -->|"-Energy"| H
    F -->|"+Energy"| H
    G -->|"-Energy"| H

Energy Changes During Phase Transitions

• Endothermic: Absorbs heat (melting, boiling, sublimation).
• Exothermic: Releases heat (freezing, condensation, deposition).

Worked Example 2: Heating Curve of Water Sketch the heating curve for ice → water → steam at 1 atm, labeling all regions and plateaus.

Solution:

Key Points:

1. 0–10°C: Ice warms up (temperature rises).
2. 10–20°C: Ice melts at 0°C (plateau = latent heat of fusion, 334 J/g).
3. 20–30°C: Water warms up.
4. 30°C+: Water boils at 100°C (plateau = latent heat of vaporization, 2260 J/g).

5. Gas Laws: Relationships Between P, V, and T

Gases follow predictable laws when conditions change.

Boyle’s Law (Pressure-Volume Relationship)

• Inverse relationship: At constant temperature, P ∝ 1/V.
• Equation: $P_1{V}_1=P_2{V}_2$

Worked Example 3: Boyle’s Law A gas occupies 2.0 L at 760 mmHg. What is its volume at 380 mmHg?

Solution: $$\begin{gathered} P_1{V}_1=P_2{V}_2 \\ 760\times 2.0=380\times V_2 \\ {V}_2=\frac{760\times 2.0}{380}=4.0\text{ L} \end{gathered}$$

Charles’s Law (Volume-Temperature Relationship)

• Direct relationship: At constant pressure, V ∝ T (in Kelvin).
• Equation: $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Worked Example 4: Charles’s Law A balloon has a volume of 500 mL at 27°C. What is its volume at 127°C?

Solution: Convert to Kelvin: $$T_1=27+273=300\text{ K},T_2=127+273=400\text{ K}$$ $$\begin{gathered} \frac{V_1}{T_1}=\frac{V_2}{T_2} \\ \frac{500}{300}=\frac{V_2}{400} \\ {V}_2=\frac{500\times 400}{300}=666.7\text{ mL} \end{gathered}$$

Gay-Lussac’s Law (Pressure-Temperature Relationship)

• Direct relationship: At constant volume, P ∝ T (in Kelvin).
• Equation: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Combined Gas Law

Combines all three laws: $$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$$

Worked Example 5: Combined Gas Law A gas at 750 mmHg, 300 K, and 2.0 L is compressed to 1.0 L and heated to 350 K. What is the new pressure?

Solution: $$\begin{gathered} \frac{750\times 2.0}{300}=\frac{P_2\times 1.0}{350} \\ {P}_2=\frac{750\times 2.0\times 350}{300\times 1.0}=1750\text{ mmHg} \end{gathered}$$

6. Real-World Applications

Exam Tip: How to Score Full Marks in NEB Exams

1. Diagrams are mandatory: Always draw heating/cooling curves, kinetic theory particle diagrams, and phase change cycles.

   • Example: For a question on "Explain the heating curve of ice," sketch the graph with sloped lines (temperature rise) and plateaus (phase changes).

2. Use equations correctly:

   • Write the full equation (e.g., $P_1{V}_1=P_2{V}_2$) and substitute values with units.
   • Show step-by-step calculations (e.g., converting °C to K).

3. Compare states clearly:

   • Use tables or bullet points to contrast solids/liquids/gases (e.g., "Solids have fixed shape due to strong IMFs...").

4. Explain real-world examples:

   • NEB loves applications (e.g., "Why does a spray can explode in fire?" → Charles’s Law: temperature ↑ → pressure ↑).

5. Common mistakes to avoid:

   • Forgetting to convert °C to K in gas laws.
   • Confusing endothermic/exothermic (e.g., melting is endothermic because it absorbs heat).
   • Ignoring units in calculations (e.g., mmHg vs. atm).

NEB Board-Style Questions (Practice)

Short Answer (5 marks)

1. Explain the difference between intermolecular forces and intramolecular forces with examples.
2. Sketch the cooling curve of water vapor → liquid → ice, labeling all regions and energy changes.
3. A gas occupies 1.5 L at 300 K. What volume will it occupy at 600 K if pressure is constant?

Long Answer (10 marks)

4. a) State Boyle’s Law and Charles’s Law. How are they different? b) A sample of gas has a volume of 500 mL at 700 mmHg. Calculate its new volume if pressure is reduced to 350 mmHg. c) Explain why water has a higher boiling point than methane (CH₄).

Structured Question (7 marks)

5. a) Draw a kinetic theory diagram showing gas particles at:
   • Low temperature
   • High temperature b) Why do real gases deviate from ideal behavior at high pressure? c) Give one industrial application of each:
   • Boyle’s Law
   • Charles’s Law

Answers to Practice Questions

1. IMFs (between molecules, e.g., H-bonding in H₂O) vs. intramolecular forces (within molecules, e.g., covalent bonds in H₂O).
2. Cooling curve: Sloped lines for temperature drop, plateaus at 100°C (condensation) and 0°C (freezing).
3. Charles’s Law: $$\frac{V_1}{T_1}=\frac{V_2}{T_2}\Rightarrow V_2=\frac{1.5\times 600}{300}=3.0\text{ L}$$
4. b) $V_2=\frac{500\times 350}{700}=250\text{ mL}$ c) Water has hydrogen bonding (strong IMF), while CH₄ has only London dispersion forces (weak).
5. a) Particles move slower at low T, faster at high T. b) At high P, particle volume and IMFs become significant. c)
   • Boyle’s Law: Scuba diving (pressure changes with depth).
   • Charles’s Law: Hot air balloons (air expands when heated).