Diameter of a water molecule in mm. Kvant

>>Physics: Fundamentals of molecular kinetic theory. Molecule sizes

Molecules are very small, but see how easy it is to estimate their size and mass. One observation and a couple of simple calculations are enough. True, we still need to figure out how to do this.
The molecular-kinetic theory of the structure of matter is based on three statements: matter is made up of particles; these particles move randomly; particles interact with each other. Each assertion is rigorously proven by experiments.
The properties and behavior of all bodies without exception, from ciliates to stars, are determined by the movement of particles interacting with each other: molecules, atoms, or even smaller formations - elementary particles.
Estimation of the sizes of molecules. To be completely sure of the existence of molecules, it is necessary to determine their sizes.
The easiest way to do this is to observe the spreading of a drop of oil, such as olive oil, on the surface of the water. Oil will never occupy the entire surface if the vessel is large ( fig.8.1). It is impossible to make a droplet of 1 mm 3 spread out so that it occupies a surface area of ​​more than 0.6 m 2 . It can be assumed that when the oil spreads over the maximum area, it forms a layer with a thickness of only one molecule - a “monomolecular layer”. It is easy to determine the thickness of this layer and thus estimate the size of the olive oil molecule.

Volume V oil layer is equal to the product of its surface area S for thickness d layer, i.e. V=Sd. Therefore, the size of an olive oil molecule is:

There is no need to enumerate now all possible ways of proving the existence of atoms and molecules. Modern instruments make it possible to see images of individual atoms and molecules. Figure 8.2 shows a micrograph of the surface of a silicon wafer, where the bumps are individual silicon atoms. Such images were first learned to be obtained in 1981 using not ordinary optical, but complex tunneling microscopes.

Molecules, including olive oil, are larger than atoms. The diameter of any atom is approximately equal to 10 -8 cm. These dimensions are so small that it is difficult to imagine them. In such cases, comparisons are used.
Here is one of them. If the fingers are clenched into a fist and enlarged to the size of the globe, then the atom, at the same magnification, will become the size of a fist.
Number of molecules. With very small sizes of molecules, the number of them in any macroscopic body is enormous. Let us calculate the approximate number of molecules in a drop of water with a mass of 1 g and, therefore, a volume of 1 cm 3 .
The diameter of a water molecule is approximately 3 10 -8 cm. Assuming that each water molecule with a dense packing of molecules occupies a volume (3 10 -8 cm) 3, you can find the number of molecules in a drop by dividing the drop volume (1 cm 3) by the volume, per molecule:

With each inhalation, you capture so many molecules that if all of them were evenly distributed in the Earth's atmosphere after exhalation, then every inhabitant of the planet would receive two or three molecules that had been in your lungs during inhalation.
The dimensions of the atom are small: .
The three main provisions of the molecular-kinetic theory will be discussed repeatedly.

???
1. What measurements should be taken to estimate the size of an olive oil molecule?
2. If an atom were to increase to the size of a poppy seed (0.1 mm), then what size of a body would the grain reach at the same magnification?
3. List the proofs of the existence of molecules known to you that are not mentioned in the text.

G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics Grade 10

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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 efforts 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
- A theoretical explanation based on the MKT was given 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 of a 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.
We take the relative atomic mass of any chemical element from the periodic table!)

Amount of substance

The amount of substance (ν) determines the relative number of molecules in the body.

where N is the number of molecules in the body and Na is Avogadro's constant

Unit of measurement of the amount of a substance in the SI system: [ν] = 1 mol

1 mol- this is the amount of a substance that contains as many molecules (or atoms) as there are atoms in carbon with a mass of 0.012 kg.

Remember!
1 mole of any substance contains the same number of atoms or molecules!

But!
The same amount of a substance for different substances has a different mass!

Avogadro constant

The number of atoms in 1 mole of any substance is called Avogadro's number or Avogadro's constant:

Molar mass

Molar mass (M) is the mass of a substance taken in one mole, or otherwise, it is the mass of one mole of a substance.

Molecule mass
- Avogadro's constant

Molar mass unit: [M]=1 kg/mol.

Formulas for solving problems

These formulas are obtained by substituting the above formulas.

The mass of any amount of matter

Many experiments show that molecule size very small. The linear size of a molecule or atom can be found in various ways. For example, with the help of an electron microscope, photographs of some large molecules were taken, and with the help of an ion projector (ion microscope), one can not only study the structure of crystals, but also determine the distance between individual atoms in a molecule.

Using the achievements of modern experimental technology, it was possible to determine the linear dimensions of simple atoms and molecules, which are about 10-8 cm. The linear dimensions of complex atoms and molecules are much larger. For example, the size of a protein molecule is 43*10 -8 cm.

To characterize atoms, the concept of atomic radii is used, which makes it possible to approximately estimate the interatomic distances in molecules, liquids or solids, since atoms do not have clear boundaries in their size. That is atomic radius- this is a sphere in which the main part of the electron density of an atom is enclosed (at least 90 ... 95%).

The size of a molecule is so small that it can only be represented by comparisons. For example, a water molecule is many times smaller than a large apple, how many times an apple is smaller than the globe.

mole of substance

The masses of individual molecules and atoms are very small, so it is more convenient to use relative rather than absolute mass values ​​in calculations.

Relative molecular weight(or relative atomic mass) substances M r is the ratio of the mass of a molecule (or atom) of a given substance to 1/12 of the mass of a carbon atom.

M r \u003d (m 0) : (m 0C / 12)

where m 0 is the mass of a molecule (or atom) of a given substance, m 0C is the mass of a carbon atom.

The relative molecular (or atomic) mass of a substance shows how many times the mass of a substance molecule is greater than 1/12 of the mass of the C 12 carbon isotope. Relative molecular (atomic) mass is expressed in atomic mass units.

Atomic mass unit is 1/12 of the mass of the carbon isotope C 12. Precise measurements showed that the atomic mass unit is 1.660 * 10 -27 kg, that is

1 amu = 1.660 * 10 -27 kg

The relative molecular mass of a substance can be calculated by adding the relative atomic masses of the elements that make up the molecule of the substance. The relative atomic mass of chemical elements is indicated in the periodic system of chemical elements by D.I. Mendeleev.

In the periodic system D.I. Mendeleev for each element is indicated atomic mass, which is measured in atomic mass units (amu). For example, the atomic mass of magnesium is 24.305 amu, that is, magnesium is twice as heavy as carbon, since the atomic mass of carbon is 12 amu. (this follows from the fact that 1 amu = 1/12 of the mass of the carbon isotope that makes up the majority of the carbon atom).

Why measure the mass of molecules and atoms in amu, if there are grams and kilograms? Of course, you can use these units, but it will be very inconvenient for writing (too many numbers will have to be used in order to write down the mass). To find the mass of an element in kilograms, multiply the atomic mass of the element by 1 amu. The atomic mass is found according to the periodic table (written to the right of the letter designation of the element). For example, the weight of a magnesium atom in kilograms would be:

m 0Mg = 24.305 * 1 a.e.m. = 24.305 * 1.660 * 10 -27 = 40.3463 * 10 -27 kg

The mass of a molecule can be calculated by adding the masses of the elements that make up the molecule. For example, the mass of a water molecule (H 2 O) will be equal to:

m 0H2O \u003d 2 * m 0H + m 0O \u003d 2 * 1.00794 + 15.9994 \u003d 18.0153 a.e.m. = 29.905 * 10 -27 kg

mole is equal to the amount of substance of the system, which contains as many molecules as there are atoms in 0.012 kg of carbon C 12. That is, if we have a system with some substance, and in this system there are as many molecules of this substance as there are atoms in 0.012 kg of carbon, then we can say that in this system we have 1 mole of substance.

Avogadro constant

Amount of substanceν is equal to the ratio of the number of molecules in a given body to the number of atoms in 0.012 kg of carbon, that is, the number of molecules in 1 mole of a substance.

ν = N / N A

where N is the number of molecules in a given body, N A is the number of molecules in 1 mole of the substance that makes up the body.

N A is Avogadro's constant. The amount of a substance is measured in moles.

Avogadro constant is the number of molecules or atoms in 1 mole of a substance. This constant got its name in honor of the Italian chemist and physicist Amedeo Avogadro (1776 – 1856).

1 mole of any substance contains the same number of particles.

N A \u003d 6.02 * 10 23 mol -1

Molar mass is the mass of a substance taken in the amount of one mole:

μ = m 0 * N A

where m 0 is the mass of the molecule.

Molar mass is expressed in kilograms per mole (kg/mol = kg*mol -1).

Molar mass is related to relative molecular mass by the relationship:

μ \u003d 10 -3 * M r [kg * mol -1]

The mass of any amount of substance m is equal to the product of the mass of one molecule m 0 by the number of molecules:

m = m 0 N = m 0 N A ν = μν

The amount of a substance is equal to the ratio of the mass of the substance to its molar mass:

ν = m / μ

The mass of one molecule of a substance can be found if the molar mass and the Avogadro constant are known:

m 0 = m / N = m / νN A = μ / N A

A more accurate determination of the mass of atoms and molecules is achieved using a mass spectrometer - a device in which a beam of charged particles separates in space depending on their charge mass using electric and magnetic fields.

For example, let's find the molar mass of a magnesium atom. As we found out above, the mass of a magnesium atom is m0Mg = 40.3463 * 10 -27 kg. Then the molar mass will be:

μ \u003d m 0Mg * N A \u003d 40.3463 * 10 -27 * 6.02 * 10 23 \u003d 2.4288 * 10 -2 kg / mol

That is, 2.4288 * 10 -2 kg of magnesium “fits” in one mole. Well, or about 24.28 grams.

As you can see, the molar mass (in grams) is almost equal to the atomic mass indicated for the element in the periodic table. Therefore, when they indicate the atomic mass, they usually do this:

The atomic mass of magnesium is 24.305 amu. (g/mol).

Municipal educational institution

"Basic secondary school No. 10"

Determining the diameter of molecules

Laboratory work

Artist: Masaev Evgeniy

7th grade "A"

Head: Reznik A.V.

Guryevsky district

Introduction

This academic year I started studying physics. I learned that the bodies that surround us are made up of tiny particles - molecules. I was wondering what the size of the molecules are. Due to their very small size, the molecules cannot be seen with the naked eye or with an ordinary microscope. I read that molecules can only be seen with an electron microscope. Scientists have proven that the molecules of different substances differ from each other, and the molecules of the same substance are the same. I wanted to measure the diameter of a molecule in practice. But unfortunately, the school curriculum does not provide for the study of problems of this kind, and it turned out to be a difficult task to consider it alone and I had to study the literature on methods for determining the diameter of molecules.

ChapterI. molecules

1.1 From the theory of the question

A molecule in the modern sense is the smallest particle of a substance that has all of its chemical properties. The molecule is capable of independent existence. It can consist of both identical atoms, for example, oxygen O 2, ozone O 3, nitrogen N 2, phosphorus P 4, sulfur S 6, etc., and from different atoms: this includes molecules of all complex substances. The simplest molecules consist of one atom: these are molecules of inert gases - helium, neon, argon, krypton, xenon, radon. In the so-called macromolecular compounds and polymers, each molecule can consist of hundreds of thousands of atoms.

The experimental proof of the existence of molecules was first most convincingly given by the French physicist J. Perrin in 1906 when studying Brownian motion. It, as Perrin showed, is the result of the thermal motion of molecules - and nothing else.

The essence of a molecule can also be described from another point of view: a molecule is a stable system consisting of atomic nuclei (identical or different) and surrounding electrons, and the chemical properties of the molecule are determined by the electrons of the outer shells in the atoms. Atoms are combined into molecules in most cases by chemical bonds. Typically, such a bond is created by one, two, or three pairs of electrons shared by two atoms.

Atoms in molecules are connected to each other in a certain sequence and distributed in space in a certain way. Bonds between atoms have different strengths; it is estimated by the amount of energy that must be expended to break interatomic bonds.

Molecules are characterized by a certain size and shape. It has been determined by various methods that 1 cm 3 of any gas under normal conditions contains about 2.7x10 19 molecules.

To understand how large this number is, we can imagine that the molecule is a "brick". Then if we take the number of bricks equal to the number of molecules in 1 cm 3 of gas under normal conditions, and tightly lay the surface of the entire globe with them, then they would cover the surface with a layer 120 m high, which is almost 4 times higher than the height of a 10-story building. A huge number of molecules per unit volume indicates a very small size of the molecules themselves. For example, the mass of a water molecule is m=29.9 x 10 -27 kg. Accordingly, the size of the molecules is also small. The diameter of a molecule is considered to be the minimum distance at which the repulsive forces allow them to approach each other. However, the concept of the size of a molecule is conditional, since at molecular distances the ideas of classical physics are not always justified. The average size of molecules is about 10-10 m.

A molecule as a system consisting of interacting electrons and nuclei can be in different states and pass from one state to another forcedly (under the influence of external influences) or spontaneously. For all molecules of this type, a certain set of states is characteristic, which can serve to identify molecules. As an independent formation, a molecule has a certain set of physical properties in each state, these properties are preserved to one degree or another during the transition from molecules to a substance consisting of them and determine the properties of this substance. During chemical transformations, molecules of one substance exchange atoms with molecules of another substance, break down into molecules with a smaller number of atoms, and also enter into chemical reactions of other types. Therefore, chemistry studies substances and their transformations in close connection with the structure and state of molecules.

A molecule is usually called an electrically neutral particle. In matter, positive ions always coexist with negative ones.

According to the number of atomic nuclei included in the molecule, diatomic, triatomic, etc. molecules are distinguished. If the number of atoms in a molecule exceeds hundreds and thousands, the molecule is called a macromolecule. The sum of the masses of all the atoms that make up the molecule is considered as the molecular weight. According to the molecular weight, all substances are conditionally divided into low and high molecular weight.

1.2 Methods for measuring the diameter of molecules

In molecular physics, the main "actors" are molecules, unimaginably small particles that make up all the substances in the world. It is clear that for the study of many phenomena it is important to know what they are, molecules. In particular, what are their sizes.

When talking about molecules, they are usually thought of as small, elastic, hard balls. Therefore, to know the size of molecules means to know their radius.

Despite the smallness of molecular sizes, physicists have managed to develop many ways to determine them. Physics 7 talks about two of them. One exploits the property of some (very few) liquids to spread in the form of a film one molecule thick. In another, the particle size is determined using a complex device - an ion projector.

The structure of molecules is studied by various experimental methods. Electron diffraction, neutron diffraction, and X-ray structural analysis provide direct information about the structure of molecules. Electron diffraction, a method that investigates the scattering of electrons by a beam of molecules in the gas phase, makes it possible to calculate the parameters of the geometric configuration for isolated, relatively simple molecules. Neutron diffraction and X-ray structural analysis are limited to the analysis of the structure of molecules or individual ordered fragments in the condensed phase. X-ray studies, in addition to the indicated information, make it possible to obtain quantitative data on the spatial distribution of electron density in molecules.

Spectroscopic methods are based on the individuality of the spectra of chemical compounds, which is due to the set of states characteristic of each molecule and the corresponding energy levels. These methods make it possible to carry out qualitative and quantitative spectral analysis of substances.

Absorption or emission spectra in the microwave region of the spectrum make it possible to study transitions between rotational states, to determine the moments of inertia of molecules, and on their basis, bond lengths, bond angles, and other geometric parameters of molecules. Infrared spectroscopy, as a rule, investigates transitions between vibrational-rotational states and is widely used for spectral-analytical purposes, since many vibrational frequencies of certain structural fragments of molecules are characteristic and change little when passing from one molecule to another. At the same time, infrared spectroscopy also makes it possible to judge the equilibrium geometric configuration. The spectra of molecules in the optical and ultraviolet frequency ranges are associated mainly with transitions between electronic states. The result of their research is data on the features of potential surfaces for various states and the values ​​of molecular constants that determine these potential surfaces, as well as the lifetimes of molecules in excited states and the probabilities of transitions from one state to another.

On the details of the electronic structure of molecules, unique information is provided by photo- and X-ray electron spectra, as well as Auger spectra, which make it possible to estimate the type of symmetry of molecular orbitals and the features of the electron density distribution. Laser spectroscopy (in various frequency ranges), which is distinguished by exceptionally high selectivity of excitation, has opened up wide possibilities for studying individual states of molecules. Pulsed laser spectroscopy makes it possible to analyze the structure of short-lived molecules and their transformation into an electromagnetic field.

A variety of information about the structure and properties of molecules is provided by the study of their behavior in external electric and magnetic fields.

There is, however, a very simple, although not the most accurate, way to calculate the radii of molecules (or atoms). It is based on the fact that the molecules of a substance, when it is in a solid or liquid state, can be considered to be tightly adjacent to each other. In this case, for a rough estimate, we can assume that the volume V some mass m substance is simply equal to the sum of the volumes of the molecules contained in it. Then we get the volume of one molecule by dividing the volume V per number of molecules N.

The number of molecules in a body of mass m as well as known

, where M- molar mass of the substance N A is Avogadro's number. Hence the volume V 0 of one molecule is determined from the equality .

This expression includes the ratio of the volume of a substance to its mass. The opposite relationship

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 the Avogadro 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