Formulas for calculating the mass of a molecule, an example of a problem

2024 Author: Angel Austin | [email protected]. Last modified: 2023-12-17 05:14

Every person knows that the bodies around us are made up of atoms and molecules. They have different shapes and structures. When solving problems in chemistry and physics, it is often necessary to find the mass of a molecule. Consider in this article several theoretical methods for solving this problem.

General information

Before considering how to find the mass of a molecule, you should get acquainted with the concept itself. Here are some examples.

A molecule is usually called a set of atoms that are united with each other by one or another type of chemical bond. Also, they should and can be considered as a whole in various physical and chemical processes. These bonds can be ionic, covalent, metallic, or van der Waals.

The well-known water molecule has the chemical formula H₂O. The oxygen atom in it is connected by means of polar covalent bonds with two hydrogen atoms. This structure determines many of the physical and chemical properties of liquid water, ice and steam.

Natural gas methane is another bright representative of a molecular substance. Its particles are formeda carbon atom and four hydrogen atoms (CH₄). In space, the molecules have the shape of a tetrahedron with carbon in the center.

Air is a complex mixture of gases, which mainly consists of oxygen molecules O₂ and nitrogen N₂. Both types are connected by strong double and triple covalent non-polar bonds, which makes them highly chemically inert.

Determining the mass of a molecule through its molar mass

The periodic table of chemical elements contains a large amount of information, among which there are atomic mass units (amu). For example, a hydrogen atom has an amu equal to 1, and an oxygen atom has an amu of 16. Each of these numbers indicates the mass in grams that a system containing 1 mole of atoms of the corresponding element will have. Recall that the unit of measurement of the amount of substance 1 mole is the number of particles in the system, corresponding to the Avogadro number N_A, it is equal to 6.0210²³.

When considering a molecule, they use the concept not of amu, but of molecular weight. The latter is a simple sum of a.m.u. for the atoms that make up the molecule. For example, the molar mass for H₂O would be 18 g/mol, and for O₂ 32 g/mol. Having a general concept, then you can proceed to the calculations.

The molar mass M is easy to use to calculate the mass of a molecule m₁. To do this, use a simple formula:

m₁=M/N_A.

In some tasksthe mass of the system m and the amount of matter in it n can be given. In this case, the mass of one molecule is calculated as follows:

m₁=m/(nN_A).

Ideal gas

This concept is called such a gas, the molecules of which randomly move in different directions at high speeds, do not interact with each other. The distances between them far exceed their own sizes. For such a model, the following expression is true:

PV=nRT.

It is called the Mendeleev-Clapeyron law. As you can see, the equation relates the pressure P, the volume V, the absolute temperature T and the amount of substance n. In the formula, R is the gas constant, numerically equal to 8.314. The written law is called universal because it does not depend on the chemical composition of the system.

If three thermodynamic parameters are known - T, P, V and the value m of the system, then the mass of an ideal gas molecule m₁is not difficult to determine by the following formula:

m₁=mRT/(N_APV).

This expression can also be written in terms of gas density ρ and Boltzmann constant k_B:

m₁=ρk_BT/P.

Example problem

It is known that the density of some gas is 1.225 kg/m³at atmospheric pressure 101325 Pa and temperature 15 ^oC. What is the mass of a molecule? What gas are you talking about?

Because we are given pressure, density and temperaturesystem, then you can use the formula obtained in the previous paragraph to determine the mass of one molecule. We have:

m₁=ρk_BT/P;

m₁ =1, 2251, 3810^-23288, 15/101325=4, 807 10^-26 kg.

To answer the second question of the problem, let's find the molar mass M of the gas:

M=m₁N_A;

M=4.80710^-266.0210²³=0.029 kg/mol.

The obtained value of the molar mass corresponds to the gas air.