Avogadro's Law and Ideal Gas Law

Avogadro's Hypothesis: Equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
Definition: When temperature (T) and pressure (P) are constant, the volume (V) of a gas is directly proportional to the number of moles (n) of gas.
Mathematical Expression: $V \propto n$ (at constant T and P) or $\frac{V<em>1}{n</em>1} = \frac{V<em>2}{n</em>2}$ .

Gas Stoichiometry: For gases at the same temperature and pressure, a liter-to-liter ratio can be used instead of a mole-to-mole ratio in balanced chemical equations (only for gases, not liquids or solids).
Molar Volume at STP: The molar volume of any gas at Standard Temperature and Pressure (STP: $273.15 \text{ K}$ or $0.00^\circ\text{C}$ and $1.00 \text{ atm}$ ) is $22.4 \text{ L/mol}$ . This applies only to gases at STP.

Combination of Gas Laws: Combines Boyle's, Charles's, and Avogadro's laws into a single equation.
Equation: $PV = nRT$
Variables:
- $P$ = pressure
- $V$ = volume
- $n$ = number of moles of gas
- $T$ = temperature
Ideal Gas Constant (R): A proportionality constant.
- Common value: $R = 0.08206 \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}}$ .
- Units for variables must be consistent with R: $P$ in atm, $V$ in L, $n$ in mol, $T$ in K.