AQA Trilogy Physics Particle Model of Matter and Density Study Notes

Density of Materials and the Particle Model

• The density of a material is calculated using the following equation:   $\rho = \frac{m}{V}$
  • where $\rho$ represents density.
  • where $m$ represents mass.
  • where $V$ represents volume.
• The units for density are determined by the units used for mass and volume:
  • If mass is in grams $(g)$ and volume is in cubic centimeters $(cm^3)$, density is in $g/cm^3$.
  • If mass is in kilograms $(kg)$ and volume is in cubic meters $(m^3)$, density is in $kg/m^3$.
• Density conversion factor: $1\,g/cm^3 = 1000\,kg/m^3$.
• The formula triangle for rearrangement consists of MASS $(m)$ at the top, and DENSITY $(\rho)$ and VOLUME $(V)$ at the bottom.
• Density relative to state:
  • Solids are generally the most dense.
  • Gases are significantly less dense than solids.

Properties of the States of Matter

• Matter exists in three states: solid, liquid, or gas.
• Solids:
  • Particle arrangement: Particles are closely packed together.
  • Particle motion: Particles vibrate about fixed positions.
  • Shape: Have a definite, rigid shape.
  • Volume: Have a definite volume.
• Liquids:
  • Particle arrangement: Particles are closely packed.
  • Particle motion: Particles can flow over one another.
  • Shape: No definite shape; they take the shape of their container.
  • Volume: Have a definite volume.
• Gases:
  • Particle arrangement: Particles are far apart from each other.
  • Particle motion: Particles move randomly.
  • Shape: No definite shape; they fill the shape of the container.
  • Volume: No fixed volume; they expand to fill an evacuated container.
  • Compressibility: Highly compressible due to large gaps between particles, making it easier to push them closer together compared to solids or liquids.

Differences in Density and Molecular Packing

• Solids and Liquids:
  • In both states, molecules are tightly packed, resulting in high densities that are roughly equal.
  • The primary difference is that liquid molecules have enough energy to push past one another.
• Gases:
  • Molecules are widely separated and spaced apart.
  • This arrangement results in gases having much lower densities than solids or liquids.

Required Practical 17: Determining Density

Experiment 1: Measuring Density of Regularly Shaped Objects

• Aim: Determine density using measurements of object dimensions.
• Variables:
  • Independent Variable: Type of shape or volume.
  • Dependent Variable: Mass of the object.
• Procedure:
  1. Measure the object's mass using a digital balance.
  2. Measure dimensions (width, height, length, radius) using a ruler, Vernier calipers, or a micrometer (choice depends on object size).
  3. Repeat measurements and calculate an average.
  4. Convert units where necessary: $1\,cm = 0.01\,m$ (divide by $100$).
  5. Calculate density using $\rho = \frac{m}{V}$.

Experiment 2: Measuring Density of Irregularly Shaped Objects

• Aim: Determine density using a displacement technique.
• Variables:
  • Independent Variable: Different irregular shapes or masses.
  • Dependent Variable: Volume of displaced water.
• Procedure:
  1. Measure and note the mass of the object using a digital balance.
  2. Fill a eureka can with water to just below the spout.
  3. Place an empty measuring cylinder under the spout.
  4. Carefully lower the object into the can.
  5. Measure the volume of displaced water in the cylinder; this volume equals the object's volume.
  6. Repeat and average results before calculating $\rho = \frac{m}{V}$.

Experiment 3: Measuring Density of Liquids

• Aim: Determine liquid density by finding the difference in mass.
• Variables:
  • Independent Variable: Volume of water added.
  • Dependent Variable: Mass of the cylinder.
• Procedure:
  1. Place an empty measuring cylinder on a digital balance and zero (tare) it.
  2. Fill the cylinder with liquid and record the volume.
  3. Record the new mass reading displayed on the balance.
  4. Repeat and average the results before calculating density.

Evaluation, Errors, and Safety in Density Experiments

• Systematic Errors:
  • Ensure digital balances are set to zero before any mass measurement.
  • Specifically, for liquids, the balance must be zeroed with the empty cylinder on it.
• Random Errors:
  • Length measurements are a primary source of error; minimize this by taking repeat readings and calculating an average.
  • Splashing in the displacement can leads to incorrect volume readings; lower irregular objects into the water carefully.
• Safety Considerations:
  • Glassware: Handle with care to avoid breakage.
  • Electrical/Water Hazards: Do not pour water into the measuring cylinder while it is sitting on the electric balance to avoid electric shock.
  • Spills: Stand up throughout the experiment to react quickly to any spills.

Changes of State and Internal Energy

• Reversibility: Changes of state are physical changes and are reversible.
• Conservation of Mass: Mass does not change during transitions (melting, freezing, boiling, evaporating, condensing, or sublimating) because the number of particles remains constant; only their spacing and arrangement change.
• Internal Energy:
  • Energy is stored in the atoms and molecules of a system.
  • Internal energy is defined as the total kinetic energy and potential energy of all particles in the system.

Specific Heat Capacity and Thermal Energy

• Equation for change in thermal energy:   $\Delta E = m \times c \times \Delta \theta$
  • $\Delta E$: Change in energy in Joules $(J)$.
  • $m$: Mass in kilograms $(kg)$.
  • $c$: Specific heat capacity in Joules per kilogram per degree Celsius $(J/kg\,^\circ C)$.
  • $\Delta \theta$: Change in temperature in degrees Celsius $(^\circ C)$.
• Factors affecting temperature increase:
  • Mass of the substance.
  • Type of material.
  • Energy input to the system.
• Specific Heat Capacity (SHC) Definition: The amount of energy required to raise the temperature of $1\,kg$ of a substance by $1\,^\circ C$.
• Characteristics:
  • Low SHC: Substance heats up and cools down quickly; requires less energy to change temperature.
  • High SHC: Substance heats up and cools down slowly; requires more energy to change temperature.

Heating and Cooling Graphs

• Energy usage in graph sections:
  • Origin to A: Energy increases particle kinetic energy (substance is a solid).
  • A to B: Energy overcomes intermolecular forces, increasing potential energy (substance is melting).
  • B to C: Energy increases particle kinetic energy (substance is a liquid).
  • C to D: Energy overcomes intermolecular forces, increasing potential energy (substance is boiling).
  • D to E: Energy increases particle kinetic energy (substance is a gas).
• State Change Mechanics:
  • During melting and boiling, energy input to the substance stops raising the temperature and is instead used to break the bonds/intermolecular forces.
  • Cooling processes include condensation (gas to liquid) and freezing (liquid to solid).
  • During cooling transitions, energy is transferred away, causing particles to succumb to intermolecular forces while the temperature remains constant.

Specific Latent Heat

• Equation for change of state:   $E = m \times L$
  • $E$: Energy in Joules $(J)$.
  • $m$: Mass in kilograms $(kg)$.
  • $L$: Specific Latent Heat.
• Difference between SHC and SLH:
  • Specific heat capacity determines the energy needed for a temperature change.
  • Specific latent heat determines the energy needed for a state change.

Particle Motion and Pressure in Gases

• Random Motion: Gas molecules move in constant random motion at high speeds, traveling in no specific path and changing direction upon collision with walls or other molecules.
• Brownian Motion: The random motion of tiny particles in a fluid.
• Temperature and Speed:
  • Temperature is the average kinetic energy of the particles.
  • Higher temperature implies higher average kinetic energy and higher average speeds.
• Pressure:
  • Pressure is the force exerted per unit area of the container walls.
  • High pressure is caused by more frequent and forceful collisions against container walls.
  • Increasing temperature at a constant volume increases pressure because molecules move faster and collide with the walls more often.

Boyle's Law: Pressure and Volume Relationship

• Definition: For a fixed mass of gas at a constant temperature, pressure and volume are inversely proportional.
  • If volume decreases, pressure increases.
  • If volume increases, pressure decreases.
• Formula:   $P_1 \times V_1 = P_2 \times V_2$
  • $P_1$: Initial pressure.
  • $V_1$: Initial volume.
  • $P_2$: New pressure.
  • $V_2$: New volume.
• Example Problem:
  • Given: $P_1 = 1\,atm$, $V_1 = 6\,L$, $P_2 = 3\,atm$.
  • Calculation: $1\,atm \times 6\,L = 3\,atm \times V_2$.
  • Rearranging: $V_2 = \frac{1 \times 6}{3} = 2\,L$.
• Key constraints: Boyle's Law only applies if the temperature remains constant.