**What is Gay-Lussac’s law?**

The Gay-Lussac law or Gay-Lussac law of combination volumes can be stated as follows:

*In reactions between gases, to form a given compound, the ratio between the volumes that combine (measured at equal pressure and temperature) are in a constant ratio of single integers.*

**Gay-Lussac experiment**

It answers the question **what happens to the pressure and temperature of an ideal gas when we keep the volume constant?**

Gay-Lussac investigated the volume of oxygen (O_{2}) contained in air and performed, under the same conditions of pressure and temperature, numerous experiments with other gases.

Gay-Lussac observed that pressure and temperature are directly proportional quantities; the ratio P/T remains constant for the same volume.

P/T = cte

P_{1}/T_{1} = P_{2}/T_{2}

*When a gas undergoes a transformation at constant volume, the ratio of the pressure exerted to the temperature of the gas remains constant.*

Thus, when an ideal gas in a plunger passes from state 1 to state 2, keeping the volume constant, the pressure will increase if the temperature also increases:

fig-1

In gas laws, temperature must be used in Kelvin, while pressure and volume can be expressed in any unit we wish, as long as we use the same unit for the two states under consideration.

From these experiments, Joseph-Louis Gay-Lussac (1778-1850) enunciated in 1809 a **general law for gases** measured at the same conditions of pressure and temperature which can be stated as:

*In reactions between gases, to form a given compound, the ratio between the volumes that combine (measured at equal pressure and temperature) are in a constant ratio of single integers.*

Gay-Lussac’s merit was to determine the volume of reactants and products in reactions between gases. It is evident that, from the experimental point of view, the work is much more complex than the measurement of masses. Masses can be measured relatively easily using balances. However, the volumes of gases depend on pressure and temperature.

**Solved exercises on Gay-Lussac’s law**

1) When hydrogen gas (H_{2}) reacts with nitrogen gas (N_{2}) to form ammonia (NH_{3}), it does so in the following proportions, all measured at equal pressure and temperature:

3 L of H_{2} react with 1 L of N_{2} to form 2 L of NH_{3}.

3H_{2} + N_{2} → 2NH_{3}

How many liters of H_{2} and N_{2} will be necessary to obtain 400 mL of NH_{3} under these conditions?

**Solution:**

400 mL of NH_{3} · (3L of H_{2}) / (2L of NH_{3}) = 600 mL of H_{2}

400 mL of NH_{3} · (1L of N_{2}) / (2L of NH_{3}) = 200 mL of N_{2}

**Limitations in Gay Lussac’s law**

Despite its simplicity, this law could not be interpreted with Dalton’s atomic theory, which was a serious drawback for the acceptance of this theory by the scientific community. It was not until 1811 that Amadeo Avogadro formulated a hypothesis explaining the experimental law of the combined volumes of gases.

When a chemical reaction takes place, a certain number of particles of one reactant interact with a certain number of particles of another reactant. These numbers are integers, the so-called stoichiometric coefficients. According to Avogadro, the number of particles in a gas is related to the volume it occupies. Therefore, the simple relationship that is established between the number of particles (between stoichiometric coefficients) can also be extended to the volumes occupied by gases.

Therefore, if, according to Avogadro, equal volumes of different gases have the same number of particles, the molar ratios (given by the stoichiometric coefficients of the chemical equations) must be equal to the volumetric ratios.