Gas has a high reactivity compared to liquid and solid bodies due to the large area of its active surface and high kinetic energy of the particles forming the system. In this case, the chemical activity of the gas, its pressure and some other parameters depend on the concentration of molecules. Let us consider in this article what this quantity is and how it can be calculated.
What kind of gas will we talk about?
In this article, the so-called ideal gases will be considered. They neglect the size of the particles and the interaction between them. The only process that occurs in ideal gases is elastic collisions between particles and the walls of the vessel. The result of these collisions is absolute pressure.
Any real gas is close in its properties to ideal, if you reduce its pressure or density and increase the absolute temperature. Nevertheless, there are chemicals that are far from ideal gas even at low densities and high temperatures. A striking and well-known example of such a substance is water vapor. The fact is that its molecules (H 2 O) are strongly polar (oxygen pulls the electron density away from hydrogen atoms). The polarity leads to the appearance of a significant electrostatic interaction between them, which is a gross violation of the ideal gas concept.
Universal Clapeyron-Mendeleev Law
To be able to calculate the concentration of molecules of an ideal gas, you should get acquainted with the law, which describes the state of any ideal gas system, regardless of its chemical composition. This law bears the names of the Frenchman Emil Clapeyron and the Russian scientist Dmitry Mendeleev. The corresponding equation has the form:
P * V = n * R * T.
Equality suggests that the product of pressure P by volume V always for an ideal gas should be directly proportional to the product of the absolute temperature T by the amount of substance n. Here R is the proportionality coefficient, which is called the universal gas constant. It shows the amount of work that 1 mol of gas performs as a result of expansion if it is heated by 1 K (R = 8.314 J / (mol * K)).
The concentration of molecules and its calculation
According to the definition, the concentration of atoms or molecules is understood as the number of particles in the system, which is per unit volume. Mathematically, you can write:
c N = N / V.
Where N is the total number of particles in the system.
Before writing down the formula for determining the concentration of gas molecules, we recall the determination of the amount of substance n and the expression that relates the value of R to the Boltzmann constant k B :
n = N / N A ;
k B = R / N A.
Using these equalities, we express the N / V ratio from the universal equation of state:
P * V = n * R * T =>
P * V = N / N A * R * T = N * k B * T =>
c N = N / V = P / (k B * T).
Thus, we obtained a formula for determining the concentration of particles in a gas. As you can see, it is directly proportional to the pressure in the system and inversely proportional to the absolute temperature.
Since the number of particles in the system is large, it is inconvenient to use the concentration c N when performing practical calculations. Instead, molar concentration c n is more often used. For an ideal gas, it is defined as follows:
c n = n / V = P / (R * T).
Task example
It is necessary to calculate the molar concentration of oxygen molecules in air under normal conditions.
To solve this problem, recall that in the air is 21% oxygen. In accordance with Dalton's law, oxygen creates a partial pressure of 0.21 * P 0 , where P 0 = 101325 Pa (one atmosphere). Normal conditions also assume a temperature of 0 o C (273.15 K).
We know all the necessary parameters for calculating the molar concentration of oxygen in the air. We get:
c n (O 2 ) = P / (R * T) = 0.21 * 101325 / (8.314 * 273.15) = 9.37 mol / m 3 .
If this concentration is brought to a volume of 1 liter, then we get a value of 0.009 mol / L.
To understand how many O 2 molecules are contained in 1 liter of air, multiply the calculated concentration by the number N A. Performing this procedure, we obtain a huge value: N (O 2 ) = 5.64 * 10 21 molecules.