The molar mass of a substance is equal to the mass of the substance. The relationship between the volume of a substance and its quantity

In the International System of Units (SI), the unit of quantity of a substance is the mole.

Mole - this is the amount of a substance containing as many structural units (molecules, atoms, ions, electrons, etc.) as there are atoms in 0.012 kg of the carbon isotope 12 C.

Knowing the mass of one carbon atom (1.93310 -26 kg), we can calculate the number of N A atoms in 0.012 kg of carbon

N A = 0.012/1.93310 -26 = 6.0210 23 mol -1

6.0210 23 mol -1 is called Avogadro's constant(designation N A, dimension 1/mol or mol -1). It shows the number of structural units in a mole of any substance.

Molar mass– a value equal to the ratio of the mass of a substance to the amount of substance. It has the dimension kg/mol or g/mol. It is usually designated M.

In general, the molar mass of a substance, expressed in g/mol, is numerically equal to the relative atomic (A) or relative molecular mass (M) of this substance. For example, the relative atomic and molecular masses of C, Fe, O 2, H 2 O are respectively 12, 56, 32, 18, and their molar masses are respectively 12 g/mol, 56 g/mol, 32 g/mol, 18 g /mol.

It should be noted that mass and quantity of a substance are different concepts. Mass is expressed in kilograms (grams), and the amount of substance is expressed in moles. There are simple relationships between the mass of a substance (m, g), the amount of substance (ν, mol) and the molar mass (M, g/mol)

m = νM; ν = m/M; M = m/v.

Using these formulas, it is easy to calculate the mass of a certain amount of a substance, or determine the number of moles of a substance in a known mass, or find the molar mass of a substance.

Relative atomic and molecular masses

In chemistry, they traditionally use relative rather than absolute mass values. Since 1961, the atomic mass unit (abbreviated a.m.u.), which is 1/12 of the mass of a carbon-12 atom, that is, the isotope of carbon 12 C, has been adopted as a unit of relative atomic masses since 1961.

Relative molecular weight(M r) of a substance is a value equal to the ratio of the average mass of a molecule of the natural isotopic composition of the substance to 1/12 of the mass of a carbon atom 12 C.

The relative molecular mass is numerically equal to the sum of the relative atomic masses of all atoms that make up the molecule, and is easily calculated using the formula of the substance, for example, the formula of the substance is B x D y C z, then

M r = xA B + yA D + zA C.

Molecular mass has the dimension a.m.u. and is numerically equal to the molar mass (g/mol).

Gas laws

The state of a gas is completely characterized by its temperature, pressure, volume, mass and molar mass. The laws that connect these parameters are very close for all gases, and absolutely accurate for ideal gas , in which there is completely no interaction between particles, and whose particles are material points.

The first quantitative studies of reactions between gases belonged to the French scientist Gay-Lussac. He is the author of the laws on the thermal expansion of gases and the law of volumetric relations. These laws were explained in 1811 by the Italian physicist A. Avogadro. Avogadro's Law - one of the important basic principles of chemistry, which states that “ equal volumes of different gases taken at the same temperature and pressure contain the same number of molecules».

Consequences from Avogadro's law:

1) the molecules of most simple atoms are diatomic (H 2 , ABOUT 2 etc.);

2) the same number of molecules of different gases under the same conditions occupy the same volume.

3) under normal conditions, one mole of any gas occupies a volume equal to 22.4 dm 3 (l). This volume is called molarvolume of gas(V o) (normal conditions - t o = 0 °C or

T o = 273 K, P o = 101325 Pa = 101.325 kPa = 760 mm. Hg Art. = 1 atm).

4) one mole of any substance and an atom of any element, regardless of the conditions and state of aggregation, contains the same number of molecules. This Avogadro's number (Avogadro's constant) - it has been experimentally established that this number is equal to

N A = 6,02213∙10 23 (molecules).

Thus: for gases 1 mol – 22.4 dm 3 (l) – 6.023∙10 23 molecules – M, g/mol ;

for substance 1 mole – 6.023∙10 23 molecules – M, g/mol.

Based on Avogadro's law: at the same pressure and the same temperatures, the masses (m) of equal volumes of gases are related as their molar masses (M)

m 1 /m 2 = M 1 /M 2 = D,

where D is the relative density of the first gas relative to the second.

According to law of R. Boyle – E. Mariotte , at a constant temperature, the pressure produced by a given mass of gas is inversely proportional to the volume of the gas

P o /P 1 = V 1 /V o or PV = const.

This means that as pressure increases, the volume of gas decreases. This law was first formulated in 1662 by R. Boyle. Since the French scientist E. Marriott was also involved in its creation, in other countries except England, this law is called by a double name. It represents a special case ideal gas law(describing a hypothetical gas that ideally obeys all the laws of gas behavior).

By J. Gay-Lussac's law : at constant pressure, the volume of gas changes in direct proportion to the absolute temperature (T)

V 1 /T 1 = V o /T o or V/T = const.

The relationship between gas volume, pressure and temperature can be expressed by a general equation combining the Boyle-Mariotte and Gay-Lussac laws ( united gas law)

PV/T=P o V o /T o,

where P and V are the pressure and volume of gas at a given temperature T; P o and V o - pressure and volume of gas under normal conditions (n.s.).

Mendeleev-Clapeyron equation (equation of state of an ideal gas) establishes the relationship between the mass (m, kg), temperature (T, K), pressure (P, Pa) and volume (V, m 3) of a gas with its molar mass (M, kg/mol)

where R is the universal gas constant, equal to 8,314 J/(mol K). In addition, the gas constant has two more values: P – mmHg, V - cm 3 (ml), R = 62400 ;

R – atm, V – dm 3 (l), R = 0,082 .

Partial pressure (lat. partialis- partial, from lat. pars- part) - the pressure of an individual component of the gas mixture. The total pressure of a gas mixture is the sum of the partial pressures of its components.

The partial pressure of a gas dissolved in a liquid is the partial pressure of the gas that would be formed in the gas formation phase in a state of equilibrium with the liquid at the same temperature. The partial pressure of a gas is measured as the thermodynamic activity of the gas molecules. Gases will always flow from an area of ​​high partial pressure to an area of ​​lower pressure; and the greater the difference, the faster the flow will be. Gases dissolve, diffuse and react according to their partial pressure and are not necessarily dependent on the concentration in the gas mixture. The law of addition of partial pressures was formulated in 1801 by J. Dalton. At the same time, the correct theoretical justification, based on the molecular kinetic theory, was made much later. Dalton's laws - two physical laws that determine the total pressure and solubility of a mixture of gases and were formulated by him at the beginning of the 19th century.

Molecular physics studies the properties of bodies based on the behavior of individual molecules. All visible processes occur at the level of interaction of the smallest particles; what we see with the naked eye is only a consequence of these subtle deep connections.

In contact with

Basic Concepts

Molecular physics is sometimes seen as a theoretical complement to thermodynamics. Having emerged much earlier, thermodynamics dealt with the study of the transition of heat into work, pursuing purely practical goals. She did not provide a theoretical justification, describing only the results of experiments. The basic concepts of molecular physics emerged later, in the 19th century.

She studies the interaction of bodies at the molecular level, guided by a statistical method that determines patterns in the chaotic movements of minimal particles - molecules. Molecular physics and thermodynamics complement each other, looking at processes from different points of view. At the same time, thermodynamics does not concern atomic processes, dealing only with macroscopic bodies, and molecular physics, on the contrary, considers any process precisely from the point of view of the interaction of individual structural units.

All concepts and processes have their own designations and are described by special formulas that most clearly represent the interactions and dependencies of certain parameters on each other. Processes and phenomena intersect in their manifestations; different formulas can contain the same quantities and be expressed in different ways.

Quantity of substance

The amount of a substance determines the relationship between (mass) and the number of molecules that mass contains. The fact is that different substances with the same mass have different numbers of minimal particles. Processes taking place at the molecular level can only be understood by considering precisely the number of atomic units participating in the interactions. Unit of measurement of the amount of substance, adopted in the SI system, - mole.

Attention! One mole always contains the same number of minimal particles. This number is called Avogadro's number (or constant) and is equal to 6.02x1023.

This constant is used in cases where calculations require taking into account the microscopic structure of a given substance. Dealing with the number of molecules is difficult, since you have to operate with huge numbers, so the mole is used - a number that determines the number of particles per unit mass.

Formula determining the amount of a substance:

The calculation of the amount of a substance is made in different cases, is used in many formulas and is an important value in molecular physics.

Gas pressure

Gas pressure is an important quantity that has not only theoretical but also practical significance. Let's look at the gas pressure formula used in molecular physics, with explanations necessary for better understanding.

To compile the formula, you will have to make some simplifications. Molecules are complex systems, having a multi-stage structure. For simplicity, we consider gas particles in a certain vessel as elastic homogeneous balls that do not interact with each other (ideal gas).

The speed of movement of minimal particles will also be considered the same. By introducing such simplifications, which do not greatly change the true position, we can derive the following definition: gas pressure is the force exerted by the impacts of gas molecules on the walls of vessels.

At the same time, taking into account the three-dimensionality of space and the presence of two directions of each dimension, it is possible to limit the number of structural units acting on the walls to 1/6.

Thus, bringing together all these conditions and assumptions, we can deduce gas pressure formula under ideal conditions.

The formula looks like this:

where P is gas pressure;

n is the concentration of molecules;

K - Boltzmann constant (1.38×10-23);

Ek - gas molecules.

There is another version of the formula:

P = nkT,

where n is the concentration of molecules;

T - absolute temperature.

Gas volume formula

The volume of a gas is the space that a given amount of gas occupies under certain conditions. Unlike solids, which have a constant volume, practically independent of environmental conditions, gas can change volume depending on pressure or temperature.

The formula for gas volume is the Mendeleev-Clapeyron equation, which looks like this:

PV = nRT

where P is gas pressure;

V - volume of gas;

n is the number of moles of gas;

R - universal gas constant;

T - gas temperature.

By simple rearrangements we obtain the formula for the volume of gas:

Important! According to Avogadro's law, equal volumes of any gases placed in exactly the same conditions - pressure, temperature - will always contain an equal number of minimal particles.

Crystallization

Crystallization is the phase transition of a substance from a liquid to a solid state, i.e. process is the reverse of melting. The crystallization process occurs with the release of heat, which must be removed from the substance. The temperature coincides with the melting point, the whole process is described by the formula:

Q = λm,

where Q is the amount of heat;

λ - heat of fusion;

This formula describes both crystallization and melting, since they are essentially two sides of the same process. In order for a substance to crystallize, it must be cooled to its melting point, and then remove an amount of heat equal to the product of mass and specific heat of fusion (λ). During crystallization, the temperature does not change.

There is another way to understand this term - crystallization from supersaturated solutions. In this case, the reason for the transition is not only the achievement of a certain temperature, but also the degree of saturation of the solution with a certain substance. At a certain stage, the number of solute particles becomes too large, which causes the formation of small single crystals. They attach molecules from solution, producing layer-by-layer growth. Depending on the growth conditions, the crystals have different shapes.

Number of molecules

The easiest way to determine the number of particles contained in a given mass of a substance is using the following formula:

It follows that the number of molecules is equal to:

That is, it is necessary first of all to determine the amount of substance per certain mass. It is then multiplied by Avogadro's number, resulting in the number of structural units. For compounds, the calculation is carried out by summing the atomic weights of the components. Let's look at a simple example:

Let's determine the number of water molecules in 3 grams. The formula (H2O) contains two atoms and one . The total atomic weight of the minimum particle of water will be: 1+1+16 = 18 g/mol.

Amount of substance in 3 grams of water:

Number of molecules:

1/6 × 6 × 1023 = 1023.

Molecule mass formula

One mole always contains the same number of minimal particles. Therefore, knowing the mass of a mole, we can divide it by the number of molecules (Avogadro’s number), resulting in the mass of a system unit.

It should be noted that this formula applies only to inorganic molecules. Organic molecules are much larger in size, their size or weight have completely different meanings.

Molar mass of gas

Molar mass is mass in kilograms of one mole of a substance. Since one mole contains the same number of structural units, the molar mass formula looks like this:

M = κ × Mr

where k is the proportionality coefficient;

Mr is the atomic mass of the substance.

The molar mass of a gas can be calculated using the Mendeleev-Clapeyron equation:

pV = mRT / M,

from which we can deduce:

M = mRT / pV

Thus, the molar mass of a gas is directly proportional to the product of the mass of the gas and the temperature and the universal gas constant and inversely proportional to the product of the gas pressure and its volume.

Attention! It should be taken into account that the molar mass of a gas as an element may differ from the gas as a substance, for example, the molar mass of the element oxygen (O) is 16 g/mol, and the mass of oxygen as a substance (O2) is 32 g/mol.

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Physics in 5 minutes - molecular physics

Conclusion

Formulas contained in molecular physics and thermodynamics allow one to calculate the quantitative values ​​of all processes occurring with solids and gases. Such calculations are necessary both in theoretical research and in practice, since they contribute to solving practical problems.

Molecular mass is one of the basic concepts in modern chemistry. Its introduction became possible after the scientific substantiation of Avogadro’s statement that many substances consist of tiny particles - molecules, each of which, in turn, consists of atoms. Science owes this judgment largely to the Italian chemist Amadeo Avogadro, who scientifically substantiated the molecular structure of substances and gave chemistry many of the most important concepts and laws.

Units of mass of elements

Initially, the hydrogen atom was taken as the basic unit of atomic and molecular mass as the lightest element in the Universe. But atomic masses were mostly calculated based on their oxygen compounds, so it was decided to choose a new standard for determining atomic masses. The atomic mass of oxygen was taken to be 15, the atomic mass of the lightest substance on Earth, hydrogen, was 1. In 1961, the oxygen system for determining weight was generally accepted, but it created certain inconveniences.

In 1961, a new scale of relative atomic masses was adopted, the standard for which was the carbon isotope 12 C. The atomic mass unit (abbreviated as amu) is 1/12 of the mass of this standard. Currently, atomic mass is the mass of an atom, which must be expressed in amu.

Mass of molecules

The mass of a molecule of any substance is equal to the sum of the masses of all the atoms that form this molecule. Hydrogen has the lightest molecular weight of a gas; its compound is written as H 2 and has a value close to two. A water molecule consists of an oxygen atom and two hydrogen atoms. This means that its molecular mass is 15.994 + 2*1.0079=18.0152 amu. The largest molecular weights are those of complex organic compounds - proteins and amino acids. The molecular weight of a protein structural unit ranges from 600 to 10 6 and higher, depending on the number of peptide chains in this macromolecular structure.

Mole

Along with the standard units of mass and volume, a completely special system unit is used in chemistry - the mole.

A mole is the amount of a substance that contains as many structural units (ions, atoms, molecules, electrons) as is contained in 12 grams of the 12 C isotope.

When using a measure of the amount of a substance, it is necessary to indicate which structural units are meant. As follows from the concept of “mole”, in each individual case it is necessary to indicate exactly what structural units we are talking about - for example, a mole of H + ions, a mole of H 2 molecules, etc.

Molar and molecular mass

The mass of 1 mole of a substance is measured in g/mol and is called molar mass. The relationship between molecular and molar mass can be written as the equation

ν = k × m/M, where k is the proportionality coefficient.

It is easy to say that for any ratio the proportionality coefficient will be equal to one. Indeed, the carbon isotope has a relative molecular mass of 12 amu, and, according to definition, the molar mass of this substance is 12 g/mol. The ratio of molecular mass to molar mass is 1. From this we can conclude that molar and molecular mass have the same numerical values.

Gas volumes

As you know, all the substances around us can be in a solid, liquid or gaseous state of aggregation. For solids, the most common basic measure is mass, for solids and liquids - volume. This is due to the fact that solids retain their shape and finite dimensions. Liquid and gaseous substances do not have finite dimensions. The peculiarity of any gas is that between its structural units - molecules, atoms, ions - the distance is many times greater than the same distances in liquids or solids. For example, one mole of water under normal conditions occupies a volume of 18 ml - approximately the same amount as one tablespoon. The volume of one mole of finely crystalline table salt is 58.5 ml, and the volume of 1 mole of sugar is 20 times greater than a mole of water. Gases require even more space. One mole of nitrogen under normal conditions occupies a volume 1240 times larger than one mole of water.

Thus, the volumes of gaseous substances differ significantly from the volumes of liquid and solid substances. This is due to the difference in distances between molecules of substances in different states of aggregation.

Normal conditions

The state of any gas depends greatly on temperature and pressure. For example, nitrogen at a temperature of 20 °C occupies a volume of 24 liters, and at 100 °C at the same pressure - 30.6 liters. Chemists took this dependence into account, so it was decided to reduce all operations and measurements with gaseous substances to normal conditions. All over the world the parameters of normal conditions are the same. For gaseous chemicals this is:

• Temperature at 0°C.
• Pressure 101.3 kPa.

For normal conditions, a special abbreviation has been adopted - no. Sometimes this designation is not written in problems, then you should carefully re-read the conditions of the problem and bring the given gas parameters to normal conditions.

Calculation of the volume of 1 mole of gas

As an example, it is not difficult to calculate one mole of any gas, such as nitrogen. To do this, you first need to find the value of its relative molecular mass:

M r (N 2) = 2×14 = 28.

Since the relative molecular mass of a substance is numerically equal to the molar mass, then M(N 2)=28 g/mol.

It was found experimentally that under normal conditions the density of nitrogen is 1.25 g/liter.

Let's substitute this value into the standard formula, known from a school physics course, where:

• V is the volume of gas;
• m is gas mass;
• ρ is the gas density.

We find that the molar volume of nitrogen under normal conditions

V(N 2) = 25 g/mol: 1.25 g/liter = 22.4 l/mol.

It turns out that one mole of nitrogen occupies 22.4 liters.

If you perform such an operation with all existing gas substances, you can come to an amazing conclusion: the volume of any gas under normal conditions is 22.4 liters. Regardless of what kind of gas we are talking about, what its structure and physical and chemical characteristics are, one mole of this gas will occupy a volume of 22.4 liters.

The molar volume of a gas is one of the most important constants in chemistry. This constant makes it possible to solve many chemical problems related to measuring the properties of gases under normal conditions.

Results

The molecular weight of gaseous substances is important in determining the amount of a substance. And if the researcher knows the amount of substance of a particular gas, he can determine the mass or volume of such gas. For the same portion of a gaseous substance, the following conditions are simultaneously satisfied:

ν = m/ M ν= V/ V m.

If we remove the constant ν, we can equate these two expressions:

This way you can calculate the mass of one portion of a substance and its volume, and the molecular mass of the substance under study also becomes known. Using this formula, you can easily calculate the volume-mass ratio. When this formula is reduced to the form M= m V m /V, the molar mass of the desired compound will become known. In order to calculate this value, it is enough to know the mass and volume of the gas under study.

It should be remembered that a strict correspondence between the real molecular weight of a substance and that found using the formula is impossible. Any gas contains a lot of impurities and additives that make certain changes in its structure and affect the determination of its mass. But these fluctuations introduce changes to the third or fourth decimal place in the found result. Therefore, for school problems and experiments, the results found are quite plausible.

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Introduction

When studying chemistry and physics, such concepts as “atom”, “relative atomic and molar mass of a chemical element” play an important role. It would seem that nothing new has been discovered in this area for a long time. However, the International Union of Pure and Applied Chemistry (IUPAC) annually updates the values ​​of the atomic masses of chemical elements. Over the past 20 years, the atomic masses of 36 elements have been adjusted, 18 of which have no isotopes.

Taking part in the All-Russian full-time round of the Olympiad in natural science, we were offered the following task: “Suggest a way to determine the molar mass of a substance in a school laboratory.”

This task was purely theoretical and I successfully completed it. So I decided to experimentally, in a school laboratory, calculate the molar mass of a substance.

Target:

Determine experimentally the molar mass of a substance in a school laboratory.

Tasks:

Study scientific literature that describes methods for calculating relative atomic and molar mass.

Experimentally determine the molar mass of a substance in the gaseous and solid states using physical methods.

Draw conclusions.

II. Main part

Basic concepts:

Relative atomic mass is the mass of a chemical element expressed in atomic mass units (amu). For 1 a.u.m. 1/12 of the mass of a carbon isotope with an atomic weight of 12 is accepted. 1 amu = 1.6605655·10 -27 kg.

Relative atomic mass - shows how many times the mass of a given atom of a chemical element is greater than 1/12 of the mass of the 12 C isotope.

Isotopes- atoms of the same chemical element that have different numbers of neutrons and the same number of protons in the nucleus, therefore, having different relative atomic masses.

Molar mass of the substance - this mass of a substance taken in an amount of 1 mol.

1 mole - This is the amount of substance that contains the same number of atoms (molecules) as there are in 12g of carbon.

Specific heat capacity of a substance is a physical quantity that shows how much heat must be imparted to a 1 kg object in order to change its temperature by 1 0 C.

Heat capacity- It is the product of the specific heat capacity of a substance and its mass.

History of determining the atomic masses of chemical elements:

Having analyzed various sources of literature on the history of determining the relative atomic masses of various chemical elements, I decided to summarize the data in a table, which is quite convenient, because In various literature sources the information is given vaguely:

Knowing the relative atomic mass of an atom, we can determine the molar mass of a substance: M= Ar·10̄ ³ kg/mol

Methods for determining the molecular masses of elements:

Atomic and molecular mass can be determined either by physical or chemical methods. Chemical methods differ in that at one stage they involve not the atoms themselves, but their combinations.

Physical methods:

1 way. Dulog and Petit's law

In 1819, Dulong, together with A.T. Petit, established the law of heat capacity of solids, according to which the product of the specific heat capacities of simple solids and the relative atomic mass of the constituent elements is an approximately constant value (in modern units of measurement equal to approximately Сv·Аr = 25.12 J/(g.K)); Nowadays this relationship is called the “Dulong-Petit law”. The law of specific heat capacity, which remained unnoticed by contemporaries for quite a long time, subsequently served as the basis for a method for approximate estimation of the atomic masses of heavy elements. From Dulong and Petit's law it follows that by dividing 25.12 by the specific heat capacity of a simple substance, which is easily determined experimentally, one can find the approximate value of the relative atomic mass of a given element. And knowing the relative atomic mass of an element, you can determine the molar mass of the substance.

М=Мr·10̵ ³ kg/mol

At the initial stage of development of physics and chemistry, the specific heat capacity of an element was easier to determine than many other parameters, therefore, using this law, approximate values ​​​​of the RELATIVE ATOMIC MASS were established.

Means, Ar=25.12/s

c is the specific heat capacity of the substance

To determine the specific heat capacity of a solid, we perform the following experiment:

1. 1. 1. Let's pour hot water into the calorimeter and determine its mass and initial temperature.

         Let's determine the mass of a solid body made of an unknown substance, the relative atomic mass of which we need to determine. We will also determine its initial temperature (its initial temperature is equal to room air temperature, since the body was in this room for a long time).

         Let's lower a solid body into a calorimeter with hot water and determine the temperature established in the calorimeter.

         Having made the necessary calculations, we determine the specific heat capacity of the solid.

Q1=c1m1(t-t1), where Q1 is the amount of heat given off by water as a result of heat exchange, c1 is the specific heat capacity of water (tabular value), m1 is the mass of water, t is the final temperature, t 1 is the initial temperature of water, Q2=c2m2(t-t2), where Q2 is the amount of heat received by a solid body as a result of heat exchange, c2 is the specific heat capacity of the substance (to be determined), m2 is the mass of the substance, t 2 is the initial temperature of the body under study, because The heat balance equation has the form: Q1 + Q2 = 0 ,

Then c2 = c1m1(t-t1) /(- m2(t-t2))

Average value relative atomic mass substances turned out

Ar = 26.5 amu

Hence, molar mass a is equal to M =0.0265 kg/mol.

Solid body - aluminum bar

Method 2. Let's calculate the molar mass of air.

Using the equilibrium condition of the system, you can also calculate the molar mass of a substance, for example a gas, for example air.

Fa = Fstrand(the Archimedes force acting on the balloon is balanced by the total force of gravity acting on the shell of the balloon, the gas in the balloon, and the load suspended from the balloon.). Of course, considering that the ball is suspended in the air (it does not rise or fall).

Fa- Archimedes force acting on a ball in the air

Fa =ρвg Vш

ρв - air density

F1- the force of gravity acting on the shell of the ball and the gas (helium) located inside the ball

F1=mob g + mgel g

F2- the force of gravity acting on the load

F2=mg g

We get the formula: ρвg Vш= mob g + mgel g + mg g (1)

Let's use the Mendeleev-Clapeyron formula to calculate the molar mass of air:

Let's express the molar mass of air:

In equation (3) we substitute equation (2) instead of air density. So, we have a formula for calculating the molar mass of air:

Therefore, to find the molar mass of air, you need to measure:

1) weight of the load

2) helium mass

3) shell mass

4) air temperature

5) air pressure (atmospheric pressure)

6) volume of the ball

R- universal gas constant, R=8.31 ​​J/(mol K)

The barometer showed atmospheric pressure

equal ra =96000Pa

Room temperature:

T=23 +273=297K

We determined the mass of the load and the mass of the shell of the ball using electronic scales:

mgr =8.02g

mass of the ball shell:

mob = 3.15 g

We determined the volume of the ball in two ways:

a) our ball turned out to be round. By measuring the circumference of the ball in several places, we determined the radius of the ball. And then its volume: V=4/3·πR³

L=2πR, Lav= 85.8cm= 0.858m, therefore R=0.137m

Vsh= 0.0107m³

b) poured water into the bucket to the very edge, after placing it with a tray to drain the water. We lowered the balloon completely into the water, some of the water poured into the bath under the bucket, measuring the volume of water poured out of the bucket, we determined the volume of the balloon: Vwater=Vsh= 0.011m³

(The ball in the picture was closer to the camera, so it seems larger)

So, for the calculation we took the average value of the volume of the ball:

Vsh= 0.0109m³

We determine the mass of helium using the Mendeleev-Clapeyron equation, taking into account that the temperature of helium is equal to the air temperature, and the pressure of helium inside the ball is equal to atmospheric pressure.

Molar mass of helium 0.004 kg/mol:

mgel = 0.00169 kg

Substituting all measurement results into formula (4), we obtain the value of the molar mass of air:

M= 0.030 kg/mol

(table molar mass value

air 0.029 kg/mol)

Conclusion: In a school laboratory, you can determine the relative atomic mass of a chemical element and the molar mass of a substance using physical methods. After doing this work, I learned a lot about how to determine relative atomic mass. Of course, many methods are inaccessible to a school laboratory, but, nevertheless, even using elementary equipment, I was able to experimentally determine the relative atomic mass of a chemical element and the molar mass of a substance using physical methods. Consequently, I accomplished the goal and objectives set in this work.

List of used literature

alhimik.ru

alhimikov.net

https://ru.wikipedia.org/wiki/Molar_mass

G. I. Deryabina, G. V. Kantaria. 2.2.Mole, molar mass. Organic chemistry: web textbook.

http://kf.info.urfu.ru/glavnaja/

https://ru.wikipedia.org/wiki/Molar_mass h

In practical and theoretical chemistry, two concepts exist and are of practical importance: molecular (it is often replaced by the concept of molecular weight, which is not correct) and molar mass. Both of these quantities depend on the composition of a simple or complex substance.

How to determine or molecular? Both of these physical quantities cannot (or almost cannot) be found by direct measurement, for example, by weighing a substance on a scale. They are calculated based on the chemical formula of the compound and the atomic masses of all elements. These quantities are numerically equal, but differ in dimension. expressed in atomic mass units, which are a conventional quantity and are designated a. e.m., as well as another name - “dalton”. The units of molar mass are expressed in g/mol.

The molecular masses of simple substances, the molecules of which consist of one atom, are equal to their atomic masses, which are indicated in the periodic table of Mendeleev. For example, for:

• sodium (Na) - 22.99 a. eat.;
• iron (Fe) - 55.85 a. eat.;
• sulfur (S) - 32.064 a. eat.;
• argon (Ar) - 39.948 a. eat.;
• potassium (K) - 39.102 a. eat.

Also, the molecular weights of simple substances, the molecules of which consist of several atoms of a chemical element, are calculated as the product of the atomic mass of the element by the number of atoms in the molecule. For example, for:

• oxygen (O2) - 16. 2 = 32 a. eat.;
• nitrogen (N2) - 14.2 = 28 a. eat.;
• chlorine (Cl2) - 35. 2 = 70 a. eat.;
• ozone (O3) - 16. 3 = 48 a. eat.

Molecular masses are calculated by summing the product of the atomic mass and the number of atoms for each element included in the molecule. For example, for:

• (HCl) - 2 + 35 = 37 a. eat.;
• (CO) - 12 + 16 = 28 a. eat.;
• carbon dioxide (CO2) - 12 + 16. 2 = 44 a. eat.

But how to find the molar mass of substances?

This is not difficult to do, since it is the mass of a unit amount of a particular substance, expressed in moles. That is, if the calculated molecular mass of each substance is multiplied by a constant value equal to 1 g/mol, then its molar mass will be obtained. For example, how do you find the molar mass (CO2)? It follows (12 + 16.2).1 g/mol = 44 g/mol, that is, MCO2 = 44 g/mol. For simple substances, molecules that contain only one atom of the element, this indicator, expressed in g/mol, numerically coincides with the atomic mass of the element. For example, for sulfur MS = 32.064 g/mol. How to find the molar mass of a simple substance, the molecule of which consists of several atoms, can be considered using the example of oxygen: MO2 = 16. 2 = 32 g/mol.

Examples have been given here for specific simple or complex substances. But is it possible and how to find the molar mass of a product consisting of several components? Like the molecular mass, the molar mass of a multicomponent mixture is an additive quantity. It is the sum of the products of the molar mass of a component and its share in the mixture: M = ∑Mi. Xi, that is, both the average molecular and average molar mass can be calculated.

Using the example of air, which contains approximately 75.5% nitrogen, 23.15% oxygen, 1.29% argon and 0.046% carbon dioxide (the remaining impurities, which are contained in smaller quantities, can be neglected): Mair = 28. 0.755 + 32. 0.2315 + 40 . 0.129 + 44 . 0.00046 = 29.08424 g/mol ≈ 29 g/mol.

How to find the molar mass of a substance if the accuracy of determining the atomic masses indicated in the periodic table is different? For some elements it is indicated with an accuracy of tenths, for others with an accuracy of hundredths, for others to thousandths, and for such elements as radon - to whole ones, for manganese to ten-thousandths.

When calculating molar mass, it does not make sense to carry out calculations with greater accuracy than up to tenths, since they have practical applications when the purity of the chemical substances or reagents themselves will introduce a large error. All these calculations are approximate. But where chemists require greater accuracy, appropriate corrections are made using certain procedures: the titer of the solution is established, calibrations are made using standard samples, etc.