Mass and size of molecules. Basic Provisions of Molecular Kinetic Theory
The molecular-kinetic theory of the structure of matter is based on three positions, each of which has been proven through experiments: a substance consists of particles; these particles move randomly; particles interact with each other.
The properties and behavior of bodies, ranging from the rarefied gases of the upper atmosphere and ending with solid bodies on Earth, as well as the superdense cores of planets and stars, are determined by the movement of interacting particles that make up all bodies - molecules, atoms, or even smaller formations - elementary particles.
Estimation of the sizes of molecules. For complete confidence in the reality of the existence of molecules, it is necessary to determine their sizes.
Let us consider a relatively simple method for estimating the size of molecules. It is known that it is impossible to force a drop of olive oil to spread on the surface of the water so that it occupies an area of more than 1. It can be assumed that when the oil spreads over the maximum area, it forms a layer with a thickness of only one molecule. It is easy to determine the thickness of this layer and thus estimate the size of the olive oil molecule.
Let us mentally cut a cube of volume into square layers of area each so that they can cover the area (Fig. 2). The number of such layers will be equal to: The thickness of the oil layer, and hence the size of the olive oil molecule, can be found by dividing the edge of a cube of 0.1 cm by the number of layers: cm.
Ionic projector. At present, there is no need to enumerate all possible ways of proving the existence of atoms and molecules. Modern instruments make it possible to observe images of individual atoms and molecules. In the physics textbook for grade VI, there is a photograph taken with an electron microscope, in which you can see the arrangement of individual atoms on the surface of a gold crystal.
But the electron microscope is a very complex device. We will get acquainted with a much simpler device that allows us to obtain images of individual atoms and estimate their size. This device is called an ion projector or an ion microscope. It is arranged as follows: in the center of a spherical vessel with a radius of about 10 cm, the point of a tungsten needle is located (Fig. 3). The radius of curvature of the tip is made as small as possible with modern metalworking technology - about 5-10 6 cm. The inner surface of the sphere is covered with a thin conductive layer that can, like a television tube screen, glow under the impact of fast particles. A voltage of several hundred volts is created between the positively charged tip and the negatively charged conductive layer. The vessel is filled with helium at a low pressure of 100 Pa (0.75 mm Hg).
The tungsten atoms on the surface of the point form microscopic "bumps" (Fig. 4). When approaching randomly
moving helium atoms with tungsten atoms, an electric field, especially strong near atoms on the surface of the tip, tears off electrons from helium atoms and turns these atoms into ions. Helium ions are repelled from the positively charged tip and move at high speed along the radii of the sphere. Colliding with the surface of the sphere, the ions cause it to glow. As a result, an enlarged picture of the arrangement of tungsten atoms on the tip appears on the screen (Fig. 5). The bright spots on the screen are images of individual atoms.
The magnification of the projector - the ratio of the distance between the images of atoms to the distance between the atoms themselves - turns out to be equal to the ratio of the radius of the vessel to the radius of the tip and reaches two million. That is why it is possible to see individual atoms.
The diameter of a tungsten atom, determined using an ion projector, turns out to be approximately cm. The sizes of atoms found by other methods turn out to be approximately the same. The sizes of molecules consisting of many atoms are naturally larger.
With each inhalation, you capture so many molecules into your lungs that if all of them were evenly distributed in the Earth’s atmosphere after exhalation, then every inhabitant of the planet would receive two molecules during inhalation that visited your lungs.
>>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.
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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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Molecular-kinetic theory - the doctrine of the structure and properties of matter, using the concept of the existence of atoms and molecules as the smallest particles of a chemical substance. The MCT is based on three statements strictly proven by experiments:
The substance consists of particles - atoms and molecules, between which there are gaps;
These particles are in chaotic motion, the speed of which is affected by temperature;
Particles interact with each other.
The fact that a substance really consists of molecules can be proved by determining their size: A drop of oil spreads over the surface of water, forming a layer whose thickness is equal to the diameter of the molecule. A drop with a volume of 1 mm 3 cannot spread more than 0.6 m 2:
Modern instruments (electron microscope, ion projector) make it possible to see individual atoms and molecules.
Forces of interaction of molecules. a) the interaction is electromagnetic in nature; b) short-range forces are found at distances comparable to the size of molecules; c) there is such a distance when the forces of attraction and repulsion are equal (R 0), if R> R 0, then the forces of attraction prevail if R The action of forces of molecular attraction is revealed in an experiment with lead cylinders sticking together after cleaning their surfaces. Molecules and atoms in a solid make random oscillations about positions in which the forces of attraction and repulsion from neighboring atoms are balanced. In a liquid, the molecules not only oscillate around the equilibrium position, but also jump from one equilibrium position to the next, these molecular jumps are the cause of the liquid fluidity, its ability to take the form of a vessel. In gases, usually the distances between atoms and molecules are, on average, much larger than the dimensions of the molecules; repulsive forces do not act at large distances, so gases are easily compressed; there are practically no attractive forces between gas molecules, therefore gases have the property of expanding indefinitely. Any substance consists of particles, therefore the amount of a substance is considered to be proportional to the number of particles. The unit of quantity of a substance is the mole. A mole is equal to the amount of substance of a system containing as many particles as there are atoms in 0.012 kg of carbon. The ratio of the number of molecules to the amount of substance is called the Avogadro constant: The Avogadro constant is . It shows how many atoms or molecules are contained in one mole of a substance. The amount of a substance can be found as the ratio of the number of atoms or molecules of a substance to the Avogadro constant: Molar mass is a quantity equal to the ratio of the mass of a substance to the amount of a substance: The molar mass can be expressed in terms of the mass of the molecule: To determine the mass of molecules, you need to divide the mass of a substance by the number of molecules in it: Brownian motion is the thermal motion of particles suspended in a gas or liquid. English botanist Robert Brown (1773 - 1858) in 1827 discovered the random movement of solid particles visible through a microscope in a liquid. This phenomenon has been called Brownian motion. This movement does not stop; with increasing temperature, its intensity increases. Brownian motion is the result of pressure fluctuations (a noticeable deviation from the mean value). The reason for the Brownian motion of a particle is that the impacts of liquid molecules on the particle do not cancel each other out. In a rarefied gas, the distance between molecules is many times greater than their size. In this case, the interaction between molecules is negligible and the kinetic energy of the molecules is much greater than the potential energy of their interaction. To explain the properties of a substance in a gaseous state, instead of a real gas, its physical model is used - an ideal gas. The model assumes: the distance between the molecules is slightly greater than their diameter; molecules are elastic balls; there are no attractive forces between molecules; when molecules collide with each other and with the walls of the vessel, repulsive forces act; Molecular motion obeys the laws of mechanics. The basic equation of the MKT of an ideal gas is: The basic equation of the MKT makes it possible to calculate the pressure of a gas if the mass of the molecule, the average value of the square of the velocity, and the concentration of the molecules are known. The pressure of an ideal gas lies in the fact that the molecules, when colliding with the walls of the vessel, interact with them according to the laws of mechanics as elastic bodies. When a molecule collides with the wall of the vessel, the projection of the velocity v x of the velocity vector on the axis OX, perpendicular to the wall, changes its sign to the opposite, but remains constant in absolute value. During the collision, according to Newton's third law, the molecule acts on the wall with a force F 2 equal in absolute value to the force F 1 and directed oppositely. Equation of state of an ideal gas (Mendeleev-Clapeyron equation). Universal gas constant: Based on the dependence of gas pressure on the concentration of its molecules and temperature, an equation can be obtained that relates all three macroscopic parameters: pressure, volume and temperature, which characterize the state of a given mass of a sufficiently rarefied gas. This equation is called the ideal gas equation of state. Where is the universal gas constant for a given mass of gas, therefore Clapeyron equation. Quantitative relationships between two gas parameters for a fixed value of the third parameter are called gas laws. And the processes occurring at a constant value of one of the parameters are isoprocesses. Isothermal process - the process of changing the state of the thermodynamic system of macroscopic bodies at a constant temperature. For a gas of a given mass, the product of the pressure of the gas and its volume is constant if the temperature of the gas does not change. - Boyle's law - Mariotte. Isochoric process - the process of changing the state of the thermodynamic system of macroscopic bodies at a constant volume. For a gas of a given mass, the ratio of pressure to temperature is constant if the volume of the gas does not change. Charles' law. Isobaric process - the process of changing the state of the thermodynamic system of macroscopic bodies at constant pressure. For a gas of a given mass, the ratio of volume to temperature is constant if the pressure of the gas does not change. - Gay-Lussac's law. 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. 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 of modern particle theory refers to the smallest units of mass. By its classical definition, a molecule is the smallest particle of a substance that helps 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 a general idea of sizes and shapes, this issue is studied in more detail in high school chemistry lessons. Molecules can be simple or complex. Here are some examples: 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. When talking about the size of molecules, most scientists start from molecular weight. This is the total weight of all its constituent atoms: 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. What is the size of the molecules? They come in different shapes 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 the appearance of molecules is 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. In grade 5, 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: Actual angles often differ from these angles because a variety of effects must be taken into account, including electrostatic interactions. 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. The average molecular weight is 10 -23 -10 -26 kg. Let's take water, for example. Its molecular weight will be 3 x 10 -26 kg. 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. The 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 indicated 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 the partial positive side of one molecule is attracted to the partial negative side of the other. 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. It is a very large unit, such as a protein, which is usually created by the polymerization of smaller subunits (monomers). They are usually made up of thousands of atoms or more. 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. I.e 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. 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. 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).2. Mass and size of molecules. Avogadro constant
3. Brownian motion and ideal gas
What are molecules?
Molecule examples
Molecular mass
Measurement in nanometers
Shapes and sizes
What is the size of the molecules?
How to imagine the size of molecules: examples
How does the size of a molecule affect attractive forces?
Conclusion
mole of substance
Avogadro constant