Gay-Lussac's Laws

laws describing certain properties of gases; discovered by J. L. Gay-Lussac in the early 19th century.

(1) The law of thermal expansion of gases states that the change in the volume of a given weight of gas under a constant pressure is directly proportional to the change in its temperature:

(v₂ — v₁)/v₁ =αΔt

or

v₂ = v₁(1 + αΔt)

where v₁ is the volume of the gas at initial temperature t₁ v₂ is the volume at final temperature t₂; Δt = t₂ — t1₁ and α is the coefficient of thermal expansion of gases under constant pressure. The value of α for all gases under ordinary conditions is approximately the same, and when the temperature of a gas is measured in degrees C, α = 1/273.15 (or 0.00367). Combining this law with the Boyle-Mariotte law, E. Clapeyron derived the equation linking p, v, and T for the state of an ideal gas.

(2) The law of combining volumes states that the volumes of gases participating in a chemical reaction are in simple relationships to one another and to the volumes of the gaseous products of the reaction. In other words, the relationship of the volumes in which gases participate in a reaction is a small whole-number ratio. Measuring the volumes of hydrogen, chlorine, and hydrogen chloride under identical conditions, Gay-Lussac found that one volume of hydrogen and one volume of chlorine when combined yield two volumes of hydrogen chloride—that is, the ratio of the volumes is 1:1:2. A similar situation occurs in other reactions involving gases.

This law has played an important role in developing the theory of atoms and molecules. It provided the impetus for the discovery of Avogadro’s law, by means of which Avogadro first drew the correct conclusion concerning the composition of molecules of simple gases (H₂, Cl₂, N₂, and others) and strictly delineated the concepts of atom and molecule. When the molecular formulas of all gases are precisely known, complicated measurements will no longer be needed to find the relationship of volumes of gases involved in a reaction. Thus, from the equation for synthesis of hydrogen chloride from hydrogen and chloride, H₂ + Cl₂ = 2HCl, it is easy to see that the relationship of the volumes of the gases in this case is 1:1:2.