The diameter of a water molecule. Basic provisions of molecular-kinetic theory. Molecule sizes - Knowledge hypermarket. Solution instructions

When two or more atoms enter into chemical bonds with each other, molecules are formed. It does not matter whether these atoms are the same or whether they are completely different from each other both in shape and size. We will figure out what the size of the molecules is and what it depends on.

What are molecules?

For millennia, scientists have speculated about the mystery of life, about what exactly happens at its origin. According to the most ancient cultures, life and everything in this world consists of the basic elements of nature - earth, air, wind, water and fire. However, over time, many philosophers began to put forward the idea that all things are made up of tiny, indivisible things that cannot be created and destroyed.

It wasn't until the advent of atomic theory and modern chemistry, however, that scientists began to postulate that particles taken together gave rise to the basic building blocks of all things. This is how the term appeared, which in the context modern theory particles refers to the smallest units of mass.

By its classical definition, a molecule is the smallest particle of a substance that helps to maintain its chemical and physical properties. It consists of two or more atoms, as well as groups of the same or different atoms held together by chemical forces.

What is the size of the molecules? In the 5th grade, natural history (a school subject) gives only general idea about sizes and shapes, this issue is studied in more detail in high school at chemistry lessons.

Molecule examples

Molecules can be simple or complex. Here are some examples:

H 2 O (water);
N 2 (nitrogen);
O 3 (ozone);
CaO (calcium oxide);
C 6 H 12 O 6 (glucose).

Molecules made up of two or more elements are called compounds. So, water, calcium oxide and glucose are composite. Not all compounds are molecules, but all molecules are compounds. How big can they be? What is the size of a molecule? It is a known fact that almost everything around us consists of atoms (except light and sound). Their total weight will be the mass of the molecule.

Molecular mass

When talking about the size of molecules, most scientists start from molecular weight. This is the total weight of all its constituent atoms:

Water, which is made up of two hydrogen atoms (having one atomic mass unit each) and one oxygen atom (16 atomic mass units), has a molecular weight of 18 (more precisely, 18.01528).
Glucose has a molecular weight of 180.
DNA that is very long can have a molecular weight that is around 1010 (the approximate weight of one human chromosome).

Measurement in nanometers

In addition to mass, we can also measure how large molecules are in nanometers. A unit of water is about 0.27 Nm across. DNA is up to 2 nm across and can stretch up to several meters in length. It is hard to imagine how such dimensions can fit in one cell. The length-to-thickness ratio of DNA is amazing. It is 1/100,000,000, which is like a human hair the length of a football field.

Shapes and sizes

What is the size of the molecules? They are different forms and sizes. Water and carbon dioxide are among the smallest, proteins are among the largest. Molecules are elements made up of atoms that are connected to each other. Understanding appearance molecules are traditionally part of chemistry. Apart from their incomprehensibly strange chemical behavior, one of the important characteristics of molecules is their size.

Where can it be especially useful to know how large molecules are? The answer to this and many other questions helps in the field of nanotechnology, as the concept of nanorobots and smart materials necessarily deals with the effects of molecular size and shape.

What is the size of the molecules?

In the 5th grade, natural history on this topic gives only general information that all molecules are made up of atoms that are in constant random motion. In high school, you can already see structural formulas in chemistry textbooks that resemble the actual shape of molecules. However, it is impossible to measure their length with an ordinary ruler, and to do this, you need to know that molecules are three-dimensional objects. Their image on paper is a projection onto a two-dimensional plane. The length of a molecule is changed by the bonds of the lengths of its angles. There are three main ones:

The angle of a tetrahedron is 109° when all bonds of this atom to all other atoms are single (only one dash).
The angle of a hexagon is 120° when one atom has one double bond with another atom.
The line angle is 180° when an atom has either two double bonds or one triple bond with another atom.

Actual angles often differ from these angles because a variety of effects must be taken into account, including electrostatic interactions.

How to imagine the size of molecules: examples

What is the size of the molecules? In grade 5, the answers to this question, as we have already said, are of a general nature. Schoolchildren know that the size of these connections is very small. For example, if you turn a sand molecule in a single grain of sand into a whole grain of sand, then under the resulting mass you could hide a house with five floors. What is the size of the molecules? The short answer, which is also more scientific, is as follows.

Molecular weight is equated to the ratio of the mass of the whole substance to the number of molecules in the substance, or the ratio of the molar mass to the Avogadro constant. The unit of measurement is kilogram. Average molecular mass is 10 -23 -10 -26 kg. Let's take water, for example. Its molecular weight will be 3 x 10 -26 kg.

How does the size of a molecule affect attractive forces?

Responsible for the attraction between molecules is the electromagnetic force, which manifests itself through the attraction of opposite and repulsion of similar charges. The electrostatic force that exists between opposite charges dominates the interactions between atoms and between molecules. Gravitational force is so small in this case that it can be neglected.

In this case, the size of the molecule affects the force of attraction through the electron cloud of random distortions that occur during the distribution of the electrons of the molecule. In the case of non-polar particles exhibiting only weak van der Waals interactions or dispersion forces, the size of the molecules has a direct effect on the size of the electron cloud surrounding the specified molecule. The larger it is, the larger the charged field that surrounds it.

A larger electron cloud means that more electronic interactions can occur between neighboring molecules. As a result, one part of the molecule develops a temporary positive partial charge, while the other part develops a negative one. When this happens, the molecule can polarize the electron cloud of the neighboring one. Attraction occurs because partial positive side one molecule is attracted to a partial negative side another.

Conclusion

So what is the size of the molecules? In natural science, as we found out, one can only find a figurative idea of the mass and size of these smallest particles. But we know that there are simple and complex compounds. And the second can include such a thing as a macromolecule. This is very large unit, for example a protein, which is usually created by the polymerization of smaller subunits (monomers). They are usually made up of thousands of atoms or more.

Molecules have sizes and various shapes. For clarity, we will depict a molecule in the form of a ball, imagining that it is covered by a spherical surface, inside which are the electron shells of its atoms (Fig. 4, a). According to modern concepts, molecules do not have a geometrically defined diameter. Therefore, it was agreed to take the distance between the centers of two molecules (Fig. 4b) as the diameter d of the molecule, so close that the forces of attraction between them are balanced by the forces of repulsion.

From the course of chemistry "it is known that a kilogram-molecule (kilomole) of any substance, regardless of its state of aggregation, contains the same number of molecules, called Avogadro's number, namely N A \u003d 6.02 * 10 26 molecules.

Now let's estimate the diameter of a molecule, for example water. To do this, we divide the volume of a kilomole of water by the Avogadro number. A kilomole of water has a mass 18 kg. Assuming that water molecules are located close to each other and its density 1000 kg / m 3, we can say that 1 kmol water occupies a volume V \u003d 0.018 m 3. Volume per molecule of water

Taking the molecule as a ball and using the ball volume formula, we calculate the approximate diameter, otherwise the linear size of the water molecule:

Copper molecule diameter 2.25*10 -10 m. The diameters of gas molecules are of the same order. For example, the diameter of a hydrogen molecule 2.47 * 10 -10 m, carbon dioxide - 3.32*10 -10 m. So the molecule has a diameter of the order 10 -10 m. On length 1 cm 100 million molecules can be located nearby.

Let's estimate the mass of a molecule, for example sugar (C 12 H 22 O 11). To do this, you need a mass of kilomoles of sugar (μ = 342.31 kg/kmol) divided by the Avogadro number, i.e., by the number of molecules in

The size of a molecule is a conditional value. It is valued like this. Between the molecules, along with the forces of attraction, there are also repulsive forces, so the molecules can approach each other only up to a certain distance. d(Fig. 1).

The distance of the closest approach of the centers of two molecules is called effective diameter molecules d(in this case, it is assumed that the molecules have a spherical shape).

Currently, there are many methods for determining the size of molecules. The simplest, although not the most accurate, is as follows. In solids and liquids, molecules are located very close to each other, almost back to back. Therefore, we can assume that the volume V occupied by a body of some mass m, approximately is equal to the sum volumes of all its molecules.

Then the volume of one molecule will be \(V_(0) =\frac(V)(N),\) where V- body volume, \(N=\frac(m)(M) \cdot N_(A)\) - number of molecules in the body. Consequently,

\(V_(0) =\frac(V\cdot M)(m\cdot N_(A)).\)

Since \(\frac(m)(V) =\rho,\) where ρ is the density of matter, then

\(V_(0) =\frac(M)(\rho \cdot N_(A)).\) (6.5)

Assuming that the molecule is a small ball, the diameter of which is d = 2r, where r- radius, we have

\(V_(0) = \frac(4)(3) \pi \cdot r^(3) = \frac(\pi \cdot d^(3))(6).\)

Substituting the value here V 0 (6.5), we get

\(\frac(\pi \cdot d^(3))(6) = \frac(M)(\rho \cdot N_(A)).\)

\(d = \sqrt[(3)](\frac(6M)(\pi \cdot \rho \cdot N_(A))).\)

Yes, for water.

\(d = \sqrt[(3)](\frac(6\cdot 18\cdot 10^(-3))(3,14 \cdot 10^(3) \cdot 6,02 \cdot 10^(23 ))) = 3.8 \cdot 10^(-10)\) m.

Molecule sizes various substances are not the same, but they are all about 10 -10 m, i.e. very small.

Literature

Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 125-126.

Molecular-kinetic theory of ideal gases

In physics, two main methods are used to describe thermal phenomena: molecular-kinetic (statistical) and thermodynamic.

Molecular kinetic method (statistical) is based on the idea that all substances are composed of molecules in random motion. Since the number of molecules is huge, it is possible, by applying the laws of statistics, to find certain patterns for the entire substance as a whole.

Thermodynamic method proceeds from the basic experimental laws, called the laws of thermodynamics. The thermodynamic method approaches the study of phenomena like classical mechanics, which is based on Newton's experimental laws. This approach does not consider internal structure substances.

Basic Provisions of Molecular Kinetic Theory

And their experimental justification. Brownian motion.

Mass and size of molecules.

theory that studies thermal phenomena in macroscopic bodies and explains the dependence of the internal properties of bodies on the nature of the movement and interaction between the particles that make up the bodies, called molecular kinetic theory ( MKT for short ) or just molecular physics.

The molecular kinetic theory is based on three major provisions:

According to the first provision of the MKT , in All bodies are made up of huge amount particles (atoms and molecules) between which there are gaps .

Atom is an electrically neutral microparticle consisting of a positively charged nucleus and its surrounding electron shell. A group of atoms of the same type is called chemical element . In the natural state, atoms of 90 chemical elements are found in nature, the heaviest of which is uranium. When approaching, atoms can combine into stable groups. Systems of a small number of atoms connected to each other are called molecule . For example, a water molecule consists of three atoms (Fig.): two hydrogen atoms (H) and one oxygen atom (O), so it is designated H 2 O. Molecules are the smallest stable particles of a given substance that have its main chemical properties. For example, the smallest particle of water is a water molecule, the smallest particle of sugar is a sugar molecule.

About substances consisting of atoms that are not united into molecules, they say that they are in atomic state; otherwise, talk about molecular state. In the first case, the smallest particle of a substance is an atom (for example, He), in the second case, a molecule (for example, H 2 O).

If two bodies consist of the same number of particles, then these bodies are said to contain the same amount of substance . The amount of a substance is denoted by the Greek letter ν (nu) and is measured in moles. For 1 mole take the amount of substance in 12 g of carbon. Since 12 g of carbon contains approximately 6∙10 23 atoms, then for the amount of substance (i.e., the number of moles) in a body consisting of N particles, we can write

If you enter the notation N A = 6∙10 23 mol -1.

then relation (1) will take the form of the following simple formula:

In this way, amount of substance is the ratio of the number N of molecules (atoms) in a given macroscopic body to the number N A of atoms in 0.012 kg of carbon atoms:

1 mole of any substance contains N A = 6.02 10 23 molecules. The number N A is called constant Avogadro. The physical meaning of the Avogadro constant lies in the fact that its value shows the number of particles (atoms in an atomic substance, molecules in a molecular substance) contained in 1 mole of any substance.

The mass of one mole of a substance is called molar mass . If the molar mass is denoted by the letter μ, then for the amount of substance in a body of mass m, we can write:

From formulas (2) and (3) it follows that the number of particles in any body can be determined by the formula:

The molar mass is determined by the formula

M=M g 10 -3 kg/mol

Here M r denotes relative molecular (atomic) mass of a substance, measured in a.u.m. (atomic mass units), which in molecular physics is usually used to characterize the mass of molecules (atoms). Relative molecular mass M g can be determined if the average mass of a molecule (m m) of a given substance is divided by 1/12 of the mass of the carbon isotope 12 C:

1/12 m 12 C \u003d 1a.u.m \u003d 1.66 10 -27 kg.

When solving problems, this value is found using the periodic table. This table lists the relative atomic masses of the elements. Folding them according to chemical formula molecules of a given substance, and get a relative molecular M g . For example, for

carbon (C) M g \u003d 12 10 -3 kg / mol

water (H 2 O) M g \u003d (1 2 + 16) \u003d 18 10 -3 kg / mol.

Similarly, it is defined relative atomic mass.

A mole of gas under normal conditions occupies a volume V 0 = 22.4 10 23 m 3

Therefore, in 1 m 3 of any gas at normal conditions (determined by pressure P = 101325 Pa = 10 5 Pa = 1 atm; temperature 273ºK (0ºС), volume 1 mol ideal gas V 0 \u003d 22.4 10 -3 m 3) contains the same number of molecules:

This number is called a constant. Loshmidt.

Molecules (like atoms) do not have clear boundaries. The dimensions of the molecules of solids can be approximately estimated as follows:

where is the volume per 1 molecule, is the volume of the whole body,

m and ρ are its mass and density, N is the number of molecules in it.

Atoms and molecules cannot be seen with the naked eye or with an optical microscope. Therefore, the doubts of many scientists of the late XIX century. in the reality of their existence can be understood. However, in the XX century. the situation has changed. Now, with the help of an electron microscope, as well as holographic microscopy, it is possible to observe images not only of molecules, but even of individual atoms.

X-ray diffraction data show that the diameter of any atom is of the order of d = 10 -8 cm (10 -10 m). Molecules are larger than atoms. Since molecules are made up of several atoms, the greater the number of atoms in a molecule, the larger its size. The sizes of molecules range from 10 -8 cm (10 -10 m) to 10 -5 cm (10 -7 m).

The masses of individual molecules and atoms are very small, for example, the absolute value of the mass of a water molecule is about 3·10 -26 kg. The mass of individual molecules is experimentally determined using a special device - a mass spectrometer.

In addition to direct experiments that make it possible to observe atoms and molecules, many other indirect data speak in favor of their existence. Such, for example, are the facts concerning the thermal expansion of bodies, their compressibility, the dissolution of certain substances in others, and so on.

According to the second position of the molecular kinetic theory, particles move continuously and chaotically (randomly).

This position is confirmed by the existence of diffusion, evaporation, gas pressure on the walls of the vessel, as well as the phenomenon of Brownian motion.

The randomness of motion means that the molecules do not have any preferred paths and their movements have random directions.

Diffusion (from the Latin diffusion - spreading, spreading) - a phenomenon when, as a result of the thermal movement of a substance, spontaneous penetration of one substance into another occurs (if these substances are in contact). According to molecular kinetic theory, such mixing occurs as a result of the fact that randomly moving molecules of one substance penetrate into the gaps between the molecules of another substance. The depth of penetration depends on the temperature: the higher the temperature, the greater the speed of movement of the particles of the substance and the faster the diffusion. Diffusion is observed in all states of matter - in gases, liquids and solids. Diffusion occurs most rapidly in gases (which is why the smell spreads so quickly in the air). Diffusion in liquids is slower than in gases. This is due to the fact that the liquid molecules are located much denser, and therefore it is much more difficult to "wade" through them. Diffusion occurs most slowly in solids. In one of the experiments, smoothly polished plates of lead and gold were placed one on top of the other and squeezed with a load. Five years later, gold and lead penetrated into each other by 1 mm. Diffusion in solids ensures the connection of metals during welding, soldering, chrome plating, etc. Diffusion has great importance in the life processes of humans, animals and plants. For example, it is thanks to diffusion that oxygen from the lungs penetrates into the human blood, and from the blood into the tissues.

Brownian motion called the random movement of small particles of another substance suspended in a liquid or gas. This movement was discovered in 1827 by the English botanist R. Brown, who observed the movement of flower pollen suspended in water through a microscope. Nowadays, small pieces of gummigut paint, which does not dissolve in water, are used for such observations. In a gas, Brownian motion is performed, for example, by particles of dust or smoke suspended in the air. The Brownian motion of a particle arises because the impulses with which the molecules of a liquid or gas act on this particle do not compensate each other. The molecules of the medium (that is, the molecules of a gas or liquid) move randomly, so their impacts lead the Brownian particle into random motion: the Brownian particle quickly changes its speed in direction and magnitude (Fig. 1).

During the study of Brownian motion, it was found that its intensity: a) increases with increasing temperature of the medium; b) increases with a decrease in the size of the Brownian particles themselves; c) decreases in a more viscous liquid; and d) is completely independent of the material (density) of the Brownian particles. In addition, it was found that this movement is universal (since it is observed in all substances suspended in a sprayed state in a liquid), continuous (in a cuvette closed on all sides, it can be observed for weeks, months, years) and chaotic (randomly).

According to third provision of the ICT , particles of matter interact with each other: they attract at small distances and repel when these distances decrease.

The presence of forces of intermolecular interaction (forces of mutual attraction and repulsion) explains the existence of stable liquid and solid bodies.

The same reasons explain the low compressibility of liquids and the ability of solids to resist compressive and tensile deformations.

The forces of intermolecular interaction are electromagnetic in nature and are reduced to two types: attraction and repulsion. These forces manifest themselves at distances comparable to the size of molecules. The reason for these forces is that molecules and atoms are composed of charged particles with opposite signs of charge - negative electrons and positively charged atomic nuclei. In general, molecules are electrically neutral. In Figure 2.2, using arrows, it is shown that the nuclei of atoms, inside which there are positively charged protons, repel each other, and negatively charged electrons behave the same way. But between the nuclei and electrons, there are forces of attraction.

The dependence of the interaction forces of molecules on the distance between them qualitatively explains the molecular mechanism of the appearance of elastic forces in solids. When a solid body is stretched, the particles move away from each other. At the same time, attractive forces of molecules appear, which return the particles to their original position. When a solid body is compressed, the particles move closer together. This leads to an increase in repulsive forces, which return the particles to their original position and prevent further compression.

Therefore, at small deformations (millions of times greater than the size of molecules), Hooke's law is fulfilled, according to which the elastic force is proportional to the deformation. For large displacements, Hooke's law does not apply.

The validity of this provision is evidenced by the resistance of all bodies to compression, and also (with the exception of gases) to their tension.

MKT is easy!

"Nothing exists but atoms and empty space..." - Democritus
"Any body can divide indefinitely" - Aristotle

The main provisions of the molecular kinetic theory (MKT)

Purpose of the ICB- this is an explanation of the structure and properties of various macroscopic bodies and thermal phenomena occurring in them, by the movement and interaction of the particles that make up the bodies.
macroscopic bodies- These are large bodies, consisting of a huge number of molecules.
thermal phenomena- phenomena associated with heating and cooling bodies.

Main statements of the ILC

1. A substance consists of particles (molecules and atoms).
2. There are gaps between the particles.
3. Particles move randomly and continuously.
4. Particles interact with each other (attract and repel).

MKT confirmation:

1. experimental
- mechanical crushing of the substance; dissolution of a substance in water; compression and expansion of gases; evaporation; body deformation; diffusion; Brigman's experiment: oil is poured into a vessel, a piston presses on the oil from above, at a pressure of 10,000 atm, the oil begins to seep through the walls of a steel vessel;

Diffusion; Brownian motion of particles in a liquid under the impact of molecules;

Poor compressibility of solid and liquid bodies; significant effort to break solids; coalescence of liquid droplets;

2. straight
- photography, particle size determination.

Brownian motion

Brownian motion is the thermal motion of suspended particles in a liquid (or gas).

Brownian motion has become evidence of the continuous and chaotic (thermal) motion of the molecules of matter.
- discovered by the English botanist R. Brown in 1827
- given theoretical explanation based on the MKT by A. Einstein in 1905
- experimentally confirmed by the French physicist J. Perrin.

Mass and size of molecules

Particle sizes

The diameter of any atom is about cm.

Number of molecules in a substance

where V is the volume of the substance, Vo is the volume of one molecule

Mass of one molecule

where m is the mass of the substance,
N is the number of molecules in the substance

Mass unit in SI: [m]= 1 kg

In atomic physics, mass is usually measured in atomic mass units (a.m.u.).
Conventionally, it is considered to be 1 a.m.u. :

Relative molecular weight of a substance

For the convenience of calculations, a quantity is introduced - the relative molecular weight of the substance.
The mass of a molecule of any substance can be compared with 1/12 of the mass of a carbon molecule.

where the numerator is the mass of the molecule and the denominator is 1/12 of the mass of the carbon atom

This quantity is dimensionless, i.e. has no units

Relative atomic mass chemical element

where the numerator is the mass of the atom and the denominator is 1/12 of the mass of the carbon atom

The quantity is dimensionless, i.e. has no units

The relative atomic mass of each chemical element is given in the periodic table.

Another way to determine the relative molecular weight of a substance

The relative molecular mass of a substance is equal to the sum of the relative atomic masses of the chemical elements that make up the molecule of the substance.
Relative atomic mass we take any chemical element from the periodic table!)