Theory Exercises

Matter can appear as solid, liquid, or gas depending on particle motion and intermolecular forces.

1. Kinetic Theory of Matter

Main ideas:

  • Matter is made of particles.
  • Particles are always moving.
  • Temperature is related to average kinetic energy.
  • Intermolecular forces and particle distance determine the state.

2. States of Matter

PropertySolidLiquidGas
Particle distanceVery smallSmall-mediumLarge
Intermolecular forceStrongMediumVery weak
ShapeDefiniteTakes container shapeFills container
VolumeDefiniteDefiniteVariable
CompressibilityVery lowLowHigh

3. Density

Density links mass and volume:

\[\rho = \frac{m}{V}\]

Useful rearrangements:

\[m = \rho V\]
\[V = \frac{m}{\rho}\]

Typical units:

  • \(\mathrm{kg/m^3}\)
  • \(\mathrm{g/cm^3}\)
  • \(\mathrm{kg/L}\)

4. Changes of State

  • Melting: solid \(\to\) liquid
  • Freezing: liquid \(\to\) solid
  • Vaporization (evaporation/boiling): liquid \(\to\) gas
  • Condensation: gas \(\to\) liquid
  • Sublimation: solid \(\to\) gas
  • Deposition: gas \(\to\) solid

During a phase change, temperature stays constant while energy is used to break or form intermolecular interactions.

5. Heating Curve

In a heating curve:

  • Rising segments: temperature increases in one state.
  • Flat segments: phase change at constant temperature.

Two important temperatures:

  • Melting point
  • Boiling point

6. Gas Laws (qualitative and quantitative)

Gas behavior depends on pressure \(P\), volume \(V\), and temperature \(T\) (in kelvin).

Boyle law (constant temperature)

\[P_1V_1 = P_2V_2\]

Charles law (constant pressure)

\[\frac{V_1}{T_1} = \frac{V_2}{T_2}\]

Gay-Lussac law (constant volume)

\[\frac{P_1}{T_1} = \frac{P_2}{T_2}\]

Combined gas law

\[\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\]

Remember temperature conversion:

\[T(\mathrm{K}) = T(^\circ\mathrm{C}) + 273.15\]

7. Everyday Examples

  • A perfume smell spreads because gas particles move and diffuse.
  • A pressure cooker increases pressure, raising boiling temperature.
  • Clothes dry below boiling point by evaporation from the surface.