Vm is the molar volume of the normal. What is molecular physics: number formulas and the molar mass of a gas

The mass of 1 mole of a substance is called the molar mass. What is the volume of 1 mole of a substance called? Obviously, it is also called the molar volume.

What is equal to molar volume water? When we measured 1 mol of water, we did not weigh 18 g of water on the scales - this is inconvenient. We used measuring utensils: a cylinder or a beaker, because we knew that the density of water is 1 g/ml. Therefore, the molar volume of water is 18 ml/mol. For liquids and solids, the molar volume depends on their density (Fig. 52, a). Another thing for gases (Fig. 52, b).

Rice. 52.
Molar volumes (n.a.):
a - liquids and solids; b - gaseous substances

If we take 1 mol of hydrogen H 2 (2 g), 1 mol of oxygen O 2 (32 g), 1 mol of ozone O 3 (48 g), 1 mol of carbon dioxide CO 2 (44 g) and even 1 mol of water vapor H 2 O (18 g) under the same conditions, for example, normal (in chemistry, it is customary to call normal conditions (n.a.) a temperature of 0 ° C and a pressure of 760 mm Hg, or 101.3 kPa), it turns out that 1 mol of any of the gases will occupy the same volume, equal to 22.4 liters, and contain the same number of molecules - 6 × 10 23.

And if we take 44.8 liters of gas, then how much of its substance will be taken? Of course, 2 mol, since the given volume is twice the molar volume. Hence:

where V is the volume of gas. From here

Molar volume is a physical quantity equal to the ratio of the volume of a substance to the amount of a substance.

The molar volume of gaseous substances is expressed in l/mol. Vm - 22.4 l/mol. The volume of one kilomol is called kilomolar and is measured in m 3 / kmol (Vm = 22.4 m 3 / kmol). Accordingly, the millimolar volume is 22.4 ml/mmol.

Task 1. Find the mass of 33.6 m 3 of ammonia NH 3 (n.a.).

Task 2. Find the mass and volume (n.s.) that 18 × 10 20 molecules of hydrogen sulfide H 2 S have.

When solving the problem, let's pay attention to the number of molecules 18 × 10 20 . Since 10 20 is 1000 times smaller than 10 23 , obviously, calculations should be made using mmol, ml/mmol and mg/mmol.

Keywords and phrases

1. Molar, millimolar and kilomolar volumes of gases.
2. The molar volume of gases (under normal conditions) is 22.4 l / mol.
3. Normal conditions.

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Questions and tasks

1. Find the mass and number of molecules at n. y. for: a) 11.2 liters of oxygen; b) 5.6 m 3 nitrogen; c) 22.4 ml of chlorine.
2. Find the volume which, at n. y. will take: a) 3 g of hydrogen; b) 96 kg of ozone; c) 12 × 10 20 nitrogen molecules.
3. Find the densities (mass of 1 liter) of argon, chlorine, oxygen and ozone at n. y. How many molecules of each substance will be contained in 1 liter under the same conditions?
4. Calculate the mass of 5 l (n.a.): a) oxygen; b) ozone; c) carbon dioxide CO 2.
5. Specify which is heavier: a) 5 liters of sulfur dioxide (SO 2) or 5 liters of carbon dioxide (CO 2); b) 2 liters of carbon dioxide (CO 2) or 3 liters carbon monoxide(CO).

The volume of 1 mol of a substance is called the Molar volume. The molar mass of 1 mol of water = 18 g/mol 18 g of water occupies a volume of 18 ml. So the molar volume of water is 18 ml. 18 g of water occupy a volume equal to 18 ml, because. the density of water is 1 g/ml CONCLUSION: The molar volume depends on the density of the substance (for liquids and solids).

1 mole of any gas under normal conditions occupies the same volume equal to 22.4 liters. Normal conditions and their designations n.o.s. (0 0 С and 760 mm Hg; 1 atm.; 101.3 kPa). The volume of gas by the amount of substance 1 mol is called the molar volume and denoted - V m

Problem solving Problem 1 Given: V(NH 3) n.o.s. \u003d 33.6 m 3 Find: m -? Solution: 1. Calculate the molar mass of ammonia: M (NH 3) \u003d \u003d 17 kg / kmol

CONCLUSIONS 1. The volume of 1 mol of a substance is called the molar volume V m 2. For liquid and solid substances, the molar volume depends on their density 3. V m = 22.4 l / mol 4. Normal conditions (n.o.): and pressure 760 mm Hg, or 101.3 k Pa 5. The molar volume of gaseous substances is expressed in l / mol, ml / mmol,

One of the basic units in the International System of Units (SI) is the unit of quantity of a substance is the mole.

mole – this is such an amount of a substance that contains as many structural units of a given substance (molecules, atoms, ions, etc.) as there are carbon atoms in 0.012 kg (12 g) of a carbon isotope 12 With .

Given that the value of the absolute atomic mass for carbon is m(C) \u003d 1.99 10  26 kg, you can calculate the number of carbon atoms N BUT contained in 0.012 kg of carbon.

A mole of any substance contains the same number of particles of this substance (structural units). The number of structural units contained in a substance with an amount of one mole is 6.02 10 23 and called Avogadro's number (N BUT ).

For example, one mole of copper contains 6.02 10 23 copper atoms (Cu), and one mole of hydrogen (H 2) contains 6.02 10 23 hydrogen molecules.

molar mass(M) is the mass of a substance taken in an amount of 1 mol.

The molar mass is denoted by the letter M and has the unit [g/mol]. In physics, the dimension [kg/kmol] is used.

In the general case, the numerical value of the molar mass of a substance numerically coincides with the value of its relative molecular (relative atomic) mass.

For example, the relative molecular weight of water is:

Mr (H 2 O) \u003d 2Ar (H) + Ar (O) \u003d 2 1 + 16 \u003d 18 a.m.u.

The molar mass of water has the same value, but is expressed in g/mol:

M (H 2 O) = 18 g/mol.

Thus, a mole of water containing 6.02 10 23 water molecules (respectively 2 6.02 10 23 hydrogen atoms and 6.02 10 23 oxygen atoms) has a mass of 18 grams. 1 mole of water contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms.

1.3.4. The relationship between the mass of a substance and its quantity

Knowing the mass of a substance and its chemical formula, and hence the value of its molar mass, one can determine the amount of a substance and, conversely, knowing the amount of a substance, one can determine its mass. For such calculations, you should use the formulas:

where ν is the amount of substance, [mol]; m is the mass of the substance, [g] or [kg]; M is the molar mass of the substance, [g/mol] or [kg/kmol].

For example, to find the mass of sodium sulfate (Na 2 SO 4) in the amount of 5 mol, we find:

1) the value of the relative molecular weight of Na 2 SO 4, which is the sum of the rounded values ​​of the relative atomic masses:

Mr (Na 2 SO 4) \u003d 2Ar (Na) + Ar (S) + 4Ar (O) \u003d 142,

2) the value of the molar mass of the substance numerically equal to it:

M (Na 2 SO 4) = 142 g/mol,

3) and, finally, a mass of 5 mol of sodium sulfate:

m = ν M = 5 mol 142 g/mol = 710 g

Answer: 710.

1.3.5. The relationship between the volume of a substance and its quantity

Under normal conditions (n.o.), i.e. at pressure R , equal to 101325 Pa (760 mm Hg), and temperature T, equal to 273.15 K (0 С), one mole of various gases and vapors occupies the same volume, equal to 22.4 l.

The volume occupied by 1 mole of gas or vapor at n.o. is called molar volumegas and has the dimension of a liter per mole.

V mol \u003d 22.4 l / mol.

Knowing the amount of gaseous substance (ν ) and molar volume value (V mol) you can calculate its volume (V) under normal conditions:

V = ν V mol,

where ν is the amount of substance [mol]; V is the volume of the gaseous substance [l]; V mol \u003d 22.4 l / mol.

Conversely, knowing the volume ( V) of a gaseous substance under normal conditions, you can calculate its amount (ν) :

Molecular physics studies the properties of bodies, guided by the behavior of individual molecules. All visible processes take place 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.

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Basic concepts

Molecular physics is sometimes seen as a theoretical extension of thermodynamics. Originating much earlier, thermodynamics was engaged in the study of the transfer of heat into work, pursuing purely practical goals. She did not produce a theoretical substantiation, describing only the results of experiments. The basic concepts of molecular physics emerged later, in the 19th century.

It studies the interaction of bodies at the molecular level, guided by a statistical method that determines the patterns in the chaotic movements of minimal particles - molecules. Molecular physics and thermodynamics complement each other, considering processes from different points of view. At the same time, thermodynamics does not deal with atomic processes, dealing only with macroscopic bodies, while 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.

Amount of substance

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

Attention! One mole always contains the same number of minimal particles. This number is called Avogadro's number (or constant) and is equal to 6.02×1023.

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.

The formula for determining the amount of a substance:

The calculation of the amount of substance is carried out in different occasions, 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 value. Consider the formula for gas pressure used in molecular physics, with explanations necessary for a better understanding.

To formulate the formula, some simplifications will have to be made. Molecules are complex systems having a multistage structure. For simplicity, consider gas particles in a certain vessel as elastic homogeneous balls that do not interact with each other (ideal gas).

The speed of motion of minimal particles will also be assumed to be the same. By introducing such simplifications that do not change the true situation much, 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 as 1/6 part.

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

The formula looks like this:

where P - gas pressure;

n is the concentration of molecules;

K - Boltzmann's 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 is the absolute temperature.

Gas volume formula

The volume of a gas is the space it occupies given quantity gas under certain conditions. Unlike solids, having a constant volume, practically independent of environmental conditions, gas can change volume with pressure or temperature.

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

PV=nRT

where P - gas pressure;

V is the volume of gas;

n is the number of moles of gas;

R is the universal gas constant;

T is the gas temperature.

By simple permutations, 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 a phase transition of a substance from a liquid to a solid state, i.e. the reverse process of melting. The process of crystallization occurs with the release of heat, which is required to 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, in fact, two sides of the same process. For a substance to crystallize, must be cooled down to melting temperature., and then remove the amount of heat equal to the product of mass and specific heat melting point (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. On the 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

It is easiest to determine the number of particles contained in a given mass of a substance 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. Then it is multiplied by the Avogadro number, resulting in the number of structural units. For compounds, the calculation is carried out by summing the atomic weight of the components. Consider a simple example:

Determine the number of water molecules in 3 grams. The formula (H2O) contains two atoms and one . General atomic weight the minimum particle of water will be: 1 + 1 + 16 \u003d 18 g / mol.

Amount of substance in 3 grams of water:

Number of molecules:

1/6 x 6 x 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, their magnitude 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 coefficient of proportionality;

Mr- atomic mass substances.

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

pV=mRT/M,

from which you can deduce:

M=mRT/pV

Thus, molar mass 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 pressure of the gas and its volume.

Attention! It should be noted that the molar mass of a gas as an element may differ from a 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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Conclusion

The formulas contained in molecular physics and thermodynamics make it possible to calculate the quantitative values ​​of all processes that occur with solids and gases. Such calculations are necessary both in theoretical research and in practice, since they contribute to the solution of practical problems.

The volume of a gram-molecule of a gas, as well as the mass of a gram-molecule, is a derived unit of measurement and is expressed as the ratio of units of volume - liters or milliliters to a mole. Therefore, the dimension of the gram-molecular volume is l / mol or ml / mol. Since the volume of a gas depends on temperature and pressure, the gram-molecular volume of a gas varies depending on the conditions, but since the gram-molecules of all substances contain the same number of molecules, the gram-molecules of all substances under the same conditions occupy the same volume. under normal conditions. = 22.4 l/mol, or 22400 ml/mol. Recalculation of the gram-molecular volume of gas under normal conditions per volume under given conditions of production. is calculated according to the equation: J-t-tr from which it follows that where Vo is the gram-molecular volume of gas under normal conditions, Umol is the desired gram-molecular volume of gas. Example. Calculate the gram-molecular volume of the gas at 720 mm Hg. Art. and 87°C. Decision. The most important calculations related to the gram-molecular volume of a gas a) Converting the volume of gas to the number of moles and the number of moles per volume of gas. Example 1. Calculate how many moles are contained in 500 liters of gas under normal conditions. Decision. Example 2. Calculate the volume of 3 mol of gas at 27 * C 780 mm Hg. Art. Decision. We calculate the gram-molecular volume of gas under the specified conditions: V - ™ ** RP st. - 22.A l / mol. 300 deg \u003d 94 p. -273 vrad 780 mm Hg "ap.--24" ° Calculate the volume of 3 mol GRAM MOLECULAR VOLUME OF GAS V \u003d 24.0 l / mol 3 mol \u003d 72 l b) Conversion of the mass of gas to its volume and volume of a gas per its mass. In the first case, the number of moles of gas is first calculated from its mass, and then the volume of gas is calculated from the found number of moles. In the second case, the number of moles of gas is first calculated from its volume, and then, from the found number of moles, the mass of the gas. Example 1, Calculate the volume (at N.C.) of 5.5 g of carbon dioxide CO * Solution. |icoe ■= 44 g/mol V = 22.4 l/mol 0.125 mol 2.80 l Example 2. Calculate the mass of 800 ml (at n.a.) carbon monoxide CO. Decision. | * co \u003d 28 g / mol m "28 g / lnm 0.036 did * \u003d" 1.000 g If the mass of the gas is expressed not in grams, but in kilograms or tons, and its volume is expressed not in liters or milliliters, but in cubic meters , then a twofold approach to these calculations is possible: either split higher measures into lower ones, or the calculation of ae with moles is known, and with kilogram-molecules or ton-molecules, using the following ratios: under normal conditions, 1 kilogram-molecule-22,400 l / kmol , 1 ton-molecule - 22,400 m*/tmol. Units: kilogram-molecule - kg/kmol, ton-molecule - t/tmol. Example 1. Calculate the volume of 8.2 tons of oxygen. Decision. 1 ton-molecule Oa » 32 t/tmol. We find the number of ton-molecules of oxygen contained in 8.2 tons of oxygen: 32 t/tmol ** 0.1 Calculate the mass of 1000 -k * ammonia (at n.a.). Decision. We calculate the number of ton-molecules in the specified amount of ammonia: "-stay5JT-0.045 t/mol Calculate the mass of ammonia: 1 ton-molecule NH, 17 t/mol tyv, = 17 t/mol 0.045 t/mol * 0.765 t General principle of calculation, related to gas mixtures, is that the calculations related to the individual components are performed separately, and then the results are summed.Example 1. Calculate what volume a gas mixture consisting of 140 g of nitrogen and 30 e of hydrogen will occupy under normal conditions. Solution Calculate the number of moles of nitrogen and hydrogen contained in the mixture (No. "= 28 u/mol; cn, = 2 g/mol): 140 £ 30 in 28 g/mol W Total 20 mol. GRAM MOLECULAR VOLUME OF GAS Calculate the volume of the mixture : Ueden in 22 "4 AlnoAb 20 mol " 448 l Example 2. Calculate the mass of 114 mixture (at n.a.) of carbon monoxide and carbon dioxide, the volume composition of which is expressed by the ratio: /lso: /iso, = 8:3. Decision. According to the indicated composition, we find the volumes of each gas by the method of proportional division, after which we calculate the corresponding number of moles: t / II l "8 Q" "11 J 8 Q Ksoe 8 + 3 8 * Va> "a & + & * VCQM grfc - 0 "36 ^-grfc "" 0.134 jas * Calculating! the mass of each of the gases from the found number of moles of each of them. 1 "co 28 g / mol; jico. \u003d 44 g / mol moo" 28 e! mol 0.36 mol "South tco. \u003d 44 e / zham" - 0.134 "au> - 5.9 g By adding the found masses of each of the components, we find the mass of the mixture: gas by gram-molecular volume Above was considered the method of calculating the molecular weight of a gas by relative density.Now we will consider the method of calculating the molecular weight of a gas by gram-molecular volume.In the calculation, it is assumed that the mass and volume of the gas are directly proportional to each other.It follows "that the volume of a gas and its mass are related to each other as the gram-molecular volume of a gas is to its gram-molecular mass, which in mathematical which form is expressed as follows: V_ Ushts / i (x where Un * "- gram-molecular volume, p - gram-molecular weight. Hence _ Huiol t p? Let's consider the calculation technique on a specific example. "Example. The mass of 34 $ ju gas at 740 mm Hg, spi and 21 ° C is 0.604 g. Calculate the molecular weight of the gas. Solution. To solve, you need to know the gram-molecular volume of the gas. Therefore, before proceeding with the calculations, you need to stop at some specific gram-molecular volume of gas.You can use the standard gram-molecular volume of gas, which is equal to 22.4 l / mol. Then the volume of gas indicated in the condition of the problem should be reduced to normal conditions. But it is possible, on the contrary, to calculate the gram-molecular volume of a gas under the conditions specified in the problem. With the first method of calculation, the following design is obtained: at 740 * mrt.st .. 340 ml - 273 deg ^ Q ^ 0 760 mm Hg. Art. 294 deg ™ 1 l.1 - 22.4 l / mol 0.604 in _ s, ypya. -m-8 \u003d 44 g, M0Ab In the second method, we find: V - 22»4 A! mol No. mm Hg. st.-29A deg 0A77 l1ylv. Uiol 273 vrad 740 mmHg Art. ~ R * 0 ** In both cases, we calculate the mass of the gram molecule, but since the gram molecule is numerically equal to the molecular mass, we thereby find the molecular mass.