Molecules come in different sizes and shapes. For clarity, we will depict the molecule in the form of a ball, imagining that it is covered by a spherical surface, inside which are the electronic 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 diameter d of the molecule as the distance between the centers of two molecules (Fig. 4, b), which are so close that the attractive forces between them are balanced by the repulsive forces.
From the chemistry course 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 = 6.02*10 26 molecules.
Now let's estimate the diameter of a molecule, for example water. To do this, divide the volume of a kilomole of water by Avogadro's 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/m3, we can say that 1 kmol water takes up volume V = 0.018 m3. One molecule of water accounts for the volume
Taking the molecule as a ball and using the formula for the volume of a ball, we calculate the approximate diameter, otherwise the linear size of a 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. This means that the molecule has a diameter of the order of 10 -10 m. At 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 Avogadro's number, i.e. by the number of molecules in
>>Physics: Basic principles of molecular kinetic theory. Molecular sizes
Molecules are very small, but look 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 consists of particles; these particles move randomly; particles interact with each other. Each statement is strictly proven through 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 molecular sizes. To be completely sure of the existence of molecules, their sizes must be determined.
The easiest way to do this is to watch a drop of oil, such as olive oil, spread across the surface of the water. Oil will never cover the entire surface if the vessel is large ( Fig.8.1). It is impossible to force a droplet with a volume of 1 mm 3 to 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 only one molecule thick - a “monomolecular layer”. The thickness of this layer is easy to determine and thereby estimate the size of the olive oil molecule.
Volume V layer of oil is equal to the product of its surface area S by thickness d layer, i.e. V=Sd. Therefore, the size of the olive oil molecule is:
There is no need to list now all the possible ways to prove 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.
The sizes of molecules, including olive oil, are larger than the sizes of atoms. The diameter of any atom is approximately 10 -8 cm. These dimensions are so small that they are difficult to imagine. In such cases, they resort to comparisons.
Here's one of them. If you clench your fingers into a fist and enlarge it 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 molecular sizes, their number in any macroscopic body is enormous. Let's 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. Considering that each water molecule, when the molecules are tightly packed, occupies a volume (3 10 -8 cm) 3, you can find the number of molecules in a drop by dividing the volume of the drop (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 were in your lungs when inhaling.
Atom sizes are small: .
The three main provisions of the molecular kinetic theory will be discussed repeatedly.
???
1. What measurements need to be made to estimate the size of the olive oil molecule?
2. If an atom were increased to the size of a poppy seed (0.1 mm), what size of body would the grain reach with the same magnification?
3. List the evidence known to you for the existence of molecules that is not mentioned in the text.
G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics 10th grade
Lesson content lesson notes supporting frame lesson presentation acceleration methods interactive technologies Practice tasks and exercises self-test workshops, trainings, cases, quests homework discussion questions rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures, graphics, tables, diagrams, humor, anecdotes, jokes, comics, parables, sayings, crosswords, quotes Add-ons abstracts articles tricks for the curious cribs textbooks basic and additional dictionary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in a textbook, elements of innovation in the lesson, replacing outdated knowledge with new ones Only for teachers perfect lessons calendar plan for the year; methodological recommendations; discussion program Integrated LessonsIf you have corrections or suggestions for this lesson,
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) based on the idea that all substances consist of molecules in chaotic motion. Since the number of molecules is huge, it is possible, using the laws of statistics, to find certain patterns for the entire substance as a whole.
Thermodynamic method comes from basic experimental laws called the laws of thermodynamics. The thermodynamic method approaches the study of phenomena similar to classical mechanics, which is based on Newton's experimental laws. This approach does not consider the internal structure of matter.
Basic principles of molecular kinetic theory
And their experimental justification. Brownian motion.
Mass and size of molecules.
A theory that studies thermal phenomena in macroscopic bodies and explains the dependence of the internal properties of bodies on the nature of motion and interaction between the particles that make up the bodies is called molecular kinetic theory ( abbreviated MKT ) or simply molecular physics.
The molecular kinetic theory is based on three most important principles:
According to first position MKT , V All bodies consist of a huge number of particles (atoms and molecules), between which there are spaces .
Atom is an electrically neutral microparticle consisting of a positively charged nucleus and an electron shell surrounding it. A collection of atoms of the same type is called chemical element . In their natural state, atoms of 90 chemical elements occur in nature, the heaviest of which is uranium. When brought closer together, atoms can unite into stable groups. Systems of a small number of atoms bound together 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 basic chemical properties. For example, the smallest particle of water is a water molecule, the smallest particle of sugar is a sugar molecule.
Substances consisting of atoms that are not united into molecules are said to be in atomic state; otherwise they talk about molecular state. In the first case, the smallest particle of a substance is an atom (for example, He), in the second case, it is a molecule (for example, H 2 O).
If two bodies consist of the same number of particles, then they are said to contain the same amount of substance . The amount of 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 we enter the notation N A = 6∙10 23 mol -1.
then relation (1) will take the form of the following simple formula:
Thus, 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 Avogadro's constant. Physical meaning of Avogadro's constant is 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:
Molar mass is determined by the formula
M=M g 10 -3 kg/mol
Here M g is denoted relative molecular (atomic) mass of a substance, measured in a.m.u. (atomic mass units), which in molecular physics usually characterizes the mass of molecules (atoms). Relative molecular mass M g can be determined if the average molecular mass (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 = 1 a.u.m = 1.66 10 -27 kg.
When solving problems, this value is found using the periodic table. This table shows the relative atomic masses of the elements. Adding them in accordance with the chemical formula of the molecule of a given substance, and obtaining the relative molecular M g .
For example, for
carbon (C) M g =12·10 -3 kg/mol
water (H 2 O) M g = (1·2+16)=18·10 -3 kg/mol.
Similarly 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 (0ºC), volume of 1 mole of ideal gas V 0 = 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 sizes of molecules of solids can be approximately estimated as follows:
where is the volume per 1 molecule, is the volume of the entire 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 19th century. in the reality of their existence one can understand. However, in the 20th century. the situation became different. Now, with the help of an electron microscope, as well as holographic microscopy, it is possible to observe images of not only molecules, but even 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. These are, for example, facts concerning the thermal expansion of bodies, their compressibility, the dissolution of some substances in others, etc.
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.
Random motion means that molecules do not have any preferred paths and their movements have random directions.
Diffusion (from 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 come into contact). According to the molecular kinetic theory, such mixing occurs as a result of the randomly moving molecules of one substance penetrating into the spaces between the molecules of another substance. The depth of penetration depends on temperature: the higher the temperature, the greater the speed of movement of the particles of the substance and the faster the diffusion occurs. Diffusion is observed in all states of matter - in gases, liquids and solids. Diffusion occurs most quickly in gases (which is why odor spreads so quickly in the air). Diffusion occurs more slowly in liquids than in gases. This is explained by the fact that the molecules of the liquid are located much denser, and therefore it is much more difficult to “get through” them. Diffusion occurs most slowly in solids. In one experiment, smoothly polished plates of lead and gold were placed one on top of the other and squeezed with a weight. After five years, gold and lead penetrated each other by 1mm. Diffusion in solids ensures the connection of metals during welding, soldering, chrome plating, etc. Diffusion is of great importance in the life processes of humans, animals and plants. For example, it is thanks to diffusion that oxygen penetrates from the lungs 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 through a microscope the movement of pollen suspended in water. Nowadays, for such observations, small parts of gummigut paint are used, which does not dissolve in water. In a gas, Brownian motion is performed, for example, by particles of dust or smoke suspended in the air. Brownian motion of a particle occurs because the impulses with which the molecules of a liquid or gas act on this particle do not compensate each other. Molecules of the medium (that is, molecules of gas or liquid) move chaotically, 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 discovered that its intensity: a) increases with increasing temperature of the environment; b) increases as the size of the Brownian particles themselves decreases; c) decreases in a more viscous liquid and d) is completely independent of the material (density) of 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 the third provision of the IKT , particles of matter interact with each other: they are attracted at short distances and repel when these distances decrease.
The presence of intermolecular interaction forces (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 come down 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 consist of charged particles with opposite signs of charges - 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 of which there are positively charged protons, repel each other, and negatively charged electrons behave the same way. But there are attractive forces between nuclei and electrons.
The dependence of the interaction forces between 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. In this case, 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 the molecules), Hooke's law is satisfied, according to which the elastic force is proportional to the deformation. At large displacements, Hooke's law does not apply
The validity of this position is evidenced by the resistance of all bodies to compression, as well as (with the exception of gases) to their stretching.
Kikoin A.K. A simple way to determine the size of molecules // Quantum. - 1983. - No. 9. - P.29-30.
By special agreement with the editorial board and editors of the journal "Kvant"
In molecular physics, the main “actors” are molecules, the unimaginably small particles that make up all substances in the world. It is clear that to study many phenomena it is important to know what molecules they are. In particular, what are their sizes.
When people talk about molecules, they are usually thought of as small, elastic, hard balls. Therefore, knowing the size of molecules means knowing their radius.
Despite the smallness of molecular sizes, physicists have been able to develop many ways to determine them. Physics 9 talks about two of them. One takes advantage of 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.
There is, however, a very simple, although not the most accurate, method of calculating 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 tightly adjacent to each other. In this case, for a rough estimate, we can assume that the volume V some mass m of a substance is simply equal to the sum of the volumes of the molecules it contains. Then we get the volume of one molecule by dividing the volume V per number of molecules N.
Number of molecules in a body weighing m equals, as is known, \(~N_a \frac(m)(M)\), 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
\(~V_0 = \frac(V)(N) = \frac(V M)(m N_A)\) .
This expression includes the ratio of the volume of a substance to its mass. The inverse relation \(~\frac(m)(V) = \rho\) is the density of the substance, so
\(~V_0 = \frac(M)(\rho N_A)\) .
The density of almost any substance can be found in tables accessible to everyone. Molar mass is easy to determine if the chemical formula of a substance is known.
\(~\frac(4)(3) \pi r^3 = \frac(M)(\rho N_A)\) .
from which we obtain the expression for the radius of the molecule:
\(~r = \sqrt (\frac(3M)(4 \pi \rho N_A)) = \sqrt (\frac(3)(4 \pi N_A)) \sqrt (\frac(M)(\rho) )\) .
The first of these two roots is a constant value equal to ≈ 7.4 10 -9 mol 1/3, so the formula for r pretends
\(~r \approx 7.4 \cdot 10^(-9) \sqrt (\frac(M)(\rho)) (m)\) .
For example, the radius of a water molecule calculated using this formula is equal to r B ≈ 1.9 · 10 -10 m.
The described method for determining the radii of molecules cannot be accurate simply because the balls cannot be placed so that there are no gaps between them, even if they are in contact with each other. In addition, with such a “packing” of molecules-balls, molecular movements would be impossible. Nevertheless, calculations of the sizes of molecules using the formula given above give results that almost coincide with the results of other methods, which are incomparably more accurate.
Municipal educational institution
"Basic secondary school No. 10"
Determination of molecular diameter
Laboratory work
Performer: Masaev Evgeniy
7th grade "A"
Head: Reznik A.V.
Guryevsky district
Introduction
This school year I started studying physics. I learned that the bodies that surround us consist of tiny particles - molecules. I was interested in the size of the molecules. Due to their very small size, 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 molecules of different substances differ from each other, but 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 considering it alone turned out to be a difficult task and I had to study the literature on methods for determining the diameter of molecules.
ChapterI. Molecules
1.1 From the theory of the issue
A molecule in the modern sense is the smallest particle of a substance that has all its chemical properties. The molecule is capable of independent existence. It can consist of identical atoms, for example, oxygen O 2, ozone O 3, nitrogen N 2, phosphorus P 4, sulfur S 6, etc., or of 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 so-called high molecular weight 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 while studying Brownian motion. It, as Perrin showed, is the result of the thermal movement of molecules - and nothing else.
The essence of a molecule can 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, which are shared between 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 2.7 x 10 19 molecules.
To understand how large this number is, you can imagine that the molecule is a “brick”. Then if you take a number of bricks equal to the number of molecules in 1 cm 3 of gas under normal conditions, and densely lay them on the land surface of the entire globe, they would cover the surface with a layer 120 m high, which is almost 4 times the height of a 10-story building. The huge number of molecules per unit volume indicates the very small size of the molecules themselves. For example, the mass of a water molecule is m=29.9 x 10 -27 kg. The sizes of the molecules are correspondingly small. The diameter of a molecule is considered to be the minimum distance to which repulsive forces allow them to approach. However, the concept of molecular size is conditional, since at molecular distances the concepts 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 move from one state to another forcedly (under the influence of external influences) or spontaneously. All molecules of a given type are characterized by a certain set of states, which can serve to identify the molecules. As an independent formation, a molecule has in each state a certain set of physical properties; these properties are preserved to one degree or another during the transition from molecules to the 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 up into molecules with fewer atoms, and also enter into other types of chemical reactions. Therefore, chemistry studies substances and their transformations in inextricable connection with the structure and state of molecules.
An electrically neutral particle is usually called a molecule. In a substance, positive ions always coexist with negative ones.
Based on the number of atomic nuclei included in the molecule, molecules are distinguished as diatomic, triatomic, etc. 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 a molecule is considered the molecular mass. Based on molecular weight, all substances are conventionally divided into low- and high-molecular.
1.2 Methods for measuring the diameter of molecules
In molecular physics, the main “actors” are molecules, the unimaginably small particles that make up all substances in the world. It is clear that to study many phenomena it is important to know what molecules they are. In particular, what are their sizes.
When people talk about molecules, they are usually thought of as small, elastic, hard balls. Therefore, knowing the size of molecules means knowing their radius.
Despite the smallness of molecular sizes, physicists have been able to develop many ways to determine them. Physics 7 talks about two of them. One takes advantage of 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 studies the scattering of electrons by a beam of molecules in the gas phase, allows one to calculate geometric configuration parameters 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. In addition to the above information, X-ray studies 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 determined by the set of states and corresponding energy levels characteristic of each molecule. These methods allow for 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, 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, studies transitions between vibrational-rotational states and is widely used for spectral and analytical purposes, since many vibrational frequencies of certain structural fragments of molecules are characteristic and change slightly when moving from one molecule to another. At the same time, infrared spectroscopy 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 the 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.
Unique information about the details of the electronic structure of molecules is provided by photo- and X-ray photoelectron spectra, as well as Auger spectra, which make it possible to evaluate the type of symmetry of molecular orbitals and the features of the electron density distribution. Laser spectroscopy (in various frequency ranges), characterized by exceptionally high excitation selectivity, has opened up wide possibilities for studying individual states of molecules. Pulsed laser spectroscopy allows one to analyze the structure of short-lived molecules and their transformations in an electromagnetic field.
A variety of information about the structure and properties of molecules is obtained by studying their behavior in external electric and magnetic fields.
There is, however, a very simple, although not the most accurate, method of calculating 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 tightly adjacent to each other. In this case, for a rough estimate, we can assume that the volume V some mass m of a substance is simply equal to the sum of the volumes of the molecules it contains. Then we get the volume of one molecule by dividing the volume V per number of molecules N.
Number of molecules in a body weighing m equally, as is 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 is true
