An ideal gas is a convenient physical model with which it is possible to successfully solve many practical problems of real gases. In this article, we consider the questions of what is meant by the molar volume of gas and how to calculate it.
The ideal gas and its difference from the real
It should immediately be said that all the gases that are known to man are real. Nevertheless, in most cases they can be considered ideal. The latter believe that there is no interaction between atoms and molecules, and their sizes are negligible, compared with the average intermolecular distances. These conditions are met with high accuracy in the following cases:
- gas pressure is low (about 1 atmosphere);
- absolute temperature is high (300 K and above);
- Molecules and atoms constituting the gas are chemically inert, that is, they are not able to form any type of chemical bonds with each other.
An example of an ideal mixture of gases is air, which mainly consists of inert molecules N 2 and O 2 . On the contrary, water vapor at practically no pressure can not be considered an ideal gas due to the existence of hydrogen bonds between its polar molecules.
Clapeyron-Mendeleev Law
This law makes it possible to determine any thermodynamic parameter of an ideal gas system if two other parameters are known. We are talking about such thermodynamic characteristics as temperature T, volume V and pressure P. It is useful to consider the Clapeyron-Mendeleev law within the framework of this topic, since it is easy to determine the molar volume of an ideal gas with its help.
The Clapeyron-Mendeleev law is written in the form of the following equation:
P * V = n * R * T.
Some of the values have already been described above. The value n is the amount of substance in moles, the letter R denotes the universal constant for all gases (8.314 J / (mol * K)).
Avogadro principle
Studying various gases at the beginning of the 19th century, the Italian scientist Amedeo Avogadro came to an important experimental discovery. He found that the volume occupied by gases under constant conditions is directly proportional to the amount of substance and does not depend on the chemical composition. By constant conditions we mean the same temperature and pressure for all gases in the experiment.
If we put T, P = const in the Clapeyron-Mendeleev equation, then we get a mathematical formulation of the Avogadro principle or law:
n / V = const.
That is, with an increase in the number of particles in a gas system, its volume grows proportionally.
In some physics textbooks, the Avogadro law is formulated as follows: the molar volume of gases at the same temperatures and pressures is a constant value that does not depend on the chemical nature of gas particles.
From the Avogadro principle described, we can derive John Dalton’s law on the partial pressures of gas mixtures, according to which the partial pressure of a component is directly proportional to its atomic fraction in the gas mixture.
Calculation of the molar volume of gas under normal conditions
We are talking about the volume, which in space occupies 1 mole of an ideal gas under given conditions (temperature, pressure). To calculate this quantity, we use the Clapeyron-Mendeleev equation. From it we obtain the formula for the volume of the gas system:
V = n * R * T / P.
Since we calculate the molar volume, then n = 1 mol, then:
V = 8.314 * T / P.
Substituting the temperature and pressure values of interest to this formula, we can calculate the molar volume of an ideal gas. For example, under normal conditions (0 o C and 1 atm.), We get:
V = 8.314 * 273.15 / 101325 = 0.0224 m 3 .
Translating into units of volume measurement more convenient in practice, we obtain V = 22.4 liters. Note that in the formula we substituted the pressure in pascals and the temperature in kelvins. Both units are used as basic in the SI system.