AP Chemistry — Unit 3: Properties of Substances and Mixtures
Gas laws
All the named gas laws are one equation, PV = nRT, with something held constant. In the cylinder below the piston is free to move, so it settles wherever the gas pressure matches the applied pressure. Change one slider at a time: move only the pressure and you are doing Boyle's law; move only the temperature and you are doing Charles's law. Watch PV/nT — it never budges.
What to take away: temperature must be in kelvin — V ∝ T only works from absolute zero, which is why 20 °C to 40 °C does not double the volume. Boyle (PV constant) and Charles (V/T constant) are not separate rules to memorise; each is PV = nRT with one variable pinned.
Solution dilution
Diluting a solution adds solvent, never solute. That single fact is the whole of M₁V₁ = M₂V₂.
What to take away: the number of solute particles is identical before and after — only the volume they are spread through changes, so the concentration falls by exactly the factor the volume rose by. Take 25 mL of 1.00 M and dilute to 100 mL: the volume went up 4×, so the concentration drops 4× to 0.250 M, while the 25 mmol of solute stays 25 mmol throughout.