Avogadro's Law and The Super Combined Gas Law

Avogadro's Law

• Avogadro's Law states a direct relationship between the volume of a gas and the amount of the gas, assuming temperature and pressure are held constant.

  • $V ∝ n$, where $V$ is the volume and $n$ is the number of moles.

• As the number of molecules or moles increase, the volume increases proportionally, and vice versa.

• This law is predicated on the ideal gas assumption where all gases behave identically regardless of their chemical identity.

• Avogadro's Law is particularly useful because it helps in determining the molar volumes of gases under different conditions.

• At the old STP (Standard Temperature and Pressure, 1 atmosphere and 0°C), one mole of any gas occupies 22.4 liters. This is known as the molar volume of a gas at STP.

Applying Avogadro's Law

• Avogadro's Law becomes relevant when the amount of gas changes during a chemical reaction. For example, when reactants convert to products, the number of moles of gas can change, affecting the volume.

  • Example: Consider the conversion of atmospheric oxygen (O2) to Ozone (O3) in the upper atmosphere.

• Equation: Three molecules of diatomic oxygen convert into two molecules of ozone: 3O2 —> 2O3.

• If you start with 3 moles of O2 occupying a certain volume, the reaction will produce 2 moles of O3, which will occupy a different volume, assuming constant temperature and pressure.

Super Combined Gas Law

• Avogadro's Law introduces the number of moles (n) as a variable, it can be integrated into the combined gas law to form what is sometimes called the Super Combined Gas Law.

• The super combined gas law is expressed as: {P₁V₁}/{n₁T₁} = {P₂V₂}{n₂T₂}, where:

  • $P$ is the pressure,

  • $V$ is the volume,

  • $n$ is the number of moles, and

  • $T$ is the temperature.

• This law encompasses Boyle's, Charles', Gay-Lussac's, and Avogadro's laws as special cases. By holding certain variables constant, the equation simplifies to these individual gas laws.

• For instance, if $n$ is constant (i.e., the number of moles does not change), the equation simplifies to the regular combined gas law: {P1V1}/{T1} = {P2V2}/{T2}.