note

• fully clauded cos idk how to do this chapter just do more practices

Checklist (what you must be able to do)

1. Compare the properties of solids, liquids and gases
2. Describe the molecular structure of each state, linking properties to forces, distances and motion of particles
3. Infer from Brownian motion that molecules are moving
4. Describe the link between motion of molecules and temperature
5. Explain gas pressure in terms of particle motion
6. Explain Boyle's Law using the kinetic model
7. Apply Boyle's Law to problems

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1. States of Matter

Key points

• In a liquid, particles are still in contact with one another.
• You may say "particles" for most substances, but you must use "molecules" for water.

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2. Brownian Motion

Setup: Smoke particles in a chamber, observed under a microscope.

Observations

• Smoke particles appear as bright specks (they scatter light).
• They move in a random, erratic (zig-zag) path.
• They rarely hit each other, but seem to be continuously struck by invisible air molecules.
• Larger smoke particles move less vigorously.

Definition to know

Brownian motion is the random and continuous movement of small particles suspended in a fluid (liquid or gas).

Explanation phrasing

The smoke particles move randomly because they are constantly and unevenly bombarded by air molecules that are in continuous random motion.

Conclusion (what it proves)

This is evidence that air molecules are in constant, random motion, supporting the kinetic particle model of matter.

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3. Kinetic Particle Model of Matter

Statement

Matter is made up of a large number of tiny particles that are always in continuous random motion.

Solid model (spring model)

• Particles carry positive and negative charges, so they exert forces on each other.
• Forces are represented by springs (attractive forces pull particles together).
• When energy is transferred in, particles vibrate more vigorously.
• Internal energy = sum of the kinetic and potential energy of all the particles.

Misconception about the spring model: Real intermolecular forces weaken with increasing distance and do not act indefinitely. If particles are pulled too far apart, the forces cannot restore the structure, unlike an ideal spring.

Temperature and particle motion

• One component of internal energy is random kinetic energy (from the random motion of particles, NOT from movement of the whole container).

The average random kinetic energy of the particles is directly proportional to the temperature of an ideal gas (in kelvin).

• Heating an ideal gas increases internal energy, so temperature increases, so particles move faster on average.

Ideal gas assumptions

1. Large number of identical molecules
2. Negligible volume of molecules compared to the container
3. Constant, random, straight-line motion in all directions
4. Perfectly elastic collisions (no loss of kinetic energy)
5. No intermolecular forces except during collisions
6. Collision time negligible compared to time between collisions

Enrichment: Maxwell-Boltzmann distribution

• Higher temperature: curve flattens and shifts right.
• Greater fraction of particles have high kinetic energy; smaller fraction have low kinetic energy.
• So average random kinetic energy increases.

Light vs heavy particles (PhET applet)

• Light particles move faster than heavy particles.
• At the same temperature, their average kinetic energy is the same.

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4. Pressure

$P = \frac{F}{A}$

• P in pascal (Pa), F in N, A in m²
• Pressure is the force per unit area acting perpendicular to a surface.
• Gas pressure acts in all directions.

Pressure exerted by a gas (key explanation)

Gas particles move randomly and collide with the walls of the container. Each collision exerts a force on the wall. The many continuous collisions produce a net force on the walls, and the force per unit area is the gas pressure.

Temperature and pressure (constant volume)

When temperature increases, the average kinetic energy of the particles increases, so they move faster. They hit the walls more frequently and with greater force, so the average force per unit area on the walls increases, and pressure increases.

Atmospheric pressure

• Caused by air molecules' weight and constant collisions with surfaces.
• Standard atmospheric pressure at sea level ≈ 101 kPa.
• We are not crushed because it acts equally in all directions and is balanced.

Bottle activity (sealed bottle descending a mountain)

Phrasing: At lower altitude, there are more air molecules per unit volume outside, so they collide more frequently with the outer surface of the bottle. External pressure becomes greater than internal pressure, giving a net inward force that squashes the bottle. (No mountain spirit involved.)

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5. Boyle's Law

Experiment: Trapped air in a syringe/cylinder, weights added to the piston to increase pressure, volume recorded, temperature kept constant.

Statement (memorise)

For a fixed quantity of gas, the pressure is inversely proportional to the volume at constant temperature.

$PV = \text{constant} \qquad P_1V_1 = P_2V_2$

Graphs

• P against V: a curve (hyperbola) called an isotherm (same temperature at every point; PV constant).
• P against 1/V: a straight line through the origin.

Kinetic model explanation of Boyle's Law

When the volume decreases at constant temperature, the same number of particles occupy a smaller space, so there are more particles per unit volume. The particles collide with the walls more frequently. Since temperature is constant, their average speed (and kinetic energy) is unchanged, so the average force per unit area on the walls increases, and the pressure increases.

(Reverse it for a volume increase: fewer collisions per unit area per unit time, so pressure decreases.)

Fizzy drink bubbles

• As a bubble rises, the liquid pressure on it decreases, so its volume increases.
• Yes, it is an example of Boyle's Law (assuming constant temperature): inverse pressure-volume relationship.

Worked example

Pressure 2.0 × 10⁵ Pa, volume 9.0 × 10⁻⁴ m³. Pressure increased to 6.0 × 10⁵ Pa at constant temperature. Find new volume.

$P_1V_1 = P_2V_2$ $(2.0\times10^5)(9.0\times10^{-4}) = (6.0\times10^5)V_2$ $V_2 = 3.0\times10^{-4}\ \text{m}^3$

Exam tips for Boyle's Law questions

• Always state "fixed mass of gas" and "constant temperature".
• Units of P and V just need to be consistent on both sides.
• If pressure triples, volume becomes one third.