Gay-Lussac's Gas Laws Experiments

Law of Combining Volumes (1808)

Joseph Louis Gay-Lussac discovered that gases combine in simple whole number ratios by volume when they react to form other gases, provided the temperature and pressure remain constant. This discovery was crucial in developing the modern understanding of molecular structure.

Key Examples of Gas Reactions:

1. Formation of water vapor:

2H2+O2→2H2O2H_2 + O_2 \rightarrow 2H_2O

2 volumes of hydrogen + 1 volume of oxygen → 2 volumes of water vapor

2. Formation of hydrogen chloride:

H2+Cl2→2HClH_2 + Cl_2 \rightarrow 2HCl

1 volume of hydrogen + 1 volume of chlorine → 2 volumes of hydrogen chloride

3. Formation of ammonia:

N2+3H2→2NH3N_2 + 3H_2 \rightarrow 2NH_3

1 volume of nitrogen + 3 volumes of hydrogen → 2 volumes of ammonia

Temperature-Volume Relationship

Gay-Lussac also established that for a fixed amount of gas at constant pressure, the volume (V) is directly proportional to its absolute temperature (T). This relationship is now known as Charles's Law (as Charles had made similar observations earlier).

The mathematical relationship can be expressed as:

V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}

or

V∝T(at constant pressure)V \propto T \quad \text{(at constant pressure)}

Pressure-Temperature Relationship

Gay-Lussac's Law states that the pressure of a fixed amount of gas at constant volume is directly proportional to its absolute temperature. This is sometimes called Amontons's Law.

P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}

or

P∝T(at constant volume)P \propto T \quad \text{(at constant volume)}

where:

  • P1,P2P_1, P_2 = initial and final pressures
  • T1,T2T_1, T_2 = initial and final temperatures (in Kelvin)

Historical Impact

These experiments were crucial in developing the modern understanding of gases and provided important evidence for atomic theory. The simple whole-number ratios observed in gas reactions supported Dalton's atomic theory and led to Avogadro's hypothesis about equal volumes of gases containing equal numbers of molecules.

The mathematical relationships discovered by Gay-Lussac form a crucial part of the ideal gas law:

PV=nRTPV = nRT

where R is the universal gas constant:

R=0.08206L⋅atmmol⋅KR = 0.08206 \frac{L\cdot atm}{mol\cdot K}