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 the amount of a substance that contains as many structural units of a given substance (molecules, atoms, ions, etc.) as there are carbon atoms contained in 0.012 kg (12 g) of a carbon isotope 12 WITH .

Considering that the value of the absolute atomic mass for carbon is equal to m(C) = 1.99 10  26 kg, the number of carbon atoms can be calculated N A, 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 is called Avogadro's number (N A ).

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 mole.

Molar mass is designated by the letter M and has the dimension [g/mol]. In physics they use the unit [kg/kmol].

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:

Мr(Н 2 О) = 2Аr (Н) + Аr (O) = 2∙1 + 16 = 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. Water, with an amount of substance of 1 mole, contains 2 moles of hydrogen atoms and one 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 therefore the value of its molar mass, you can determine the amount of the substance and, conversely, knowing the amount of the substance, you can determine its mass. For such calculations you should use the formulas:

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

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

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

Мr(Na 2 SO 4) = 2Аr(Na) + Аr(S) + 4Аr(O) = 142,

2) a numerically equal value of the molar mass of the substance:

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

3) and, finally, the 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.s.), 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 different gases and vapors occupies the same volume equal to 22.4 l.

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

V mol = 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 – volume of gaseous substance [l]; V mol = 22.4 l/mol.

And, conversely, knowing the volume ( V) of a gaseous substance under normal conditions, its quantity (ν) can be calculated :

In order to find out the composition of any gaseous substances, you must be able to operate with concepts such as molar volume, molar mass and density of the substance. In this article, we will look at what molar volume is and how to calculate it?

Quantity of substance

Quantitative calculations are carried out in order to actually carry out a particular process or to find out the composition and structure of a certain substance. These calculations are inconvenient to perform with absolute values ​​of the mass of atoms or molecules due to the fact that they are very small. Relative atomic masses also cannot be used in most cases, since they are not related to generally accepted measures of mass or volume of a substance. Therefore, the concept of quantity of a substance was introduced, which is denoted by the Greek letter v (nu) or n. The amount of a substance is proportional to the number of structural units (molecules, atomic particles) contained in the substance.

The unit of quantity of a substance is the mole.

A mole is an amount of substance that contains the same number of structural units as there are atoms in 12 g of carbon isotope.

The mass of 1 atom is 12 a. e.m., therefore the number of atoms in 12 g of carbon isotope is equal to:

Na= 12g/12*1.66057*10 to the power-24g=6.0221*10 to the power of 23

The physical quantity Na is called Avogadro's constant. One mole of any substance contains 6.02 * 10 to the power of 23 particles.

Rice. 1. Avogadro's law.

Molar volume of gas

The molar volume of a gas is the ratio of the volume of a substance to the amount of that substance. This value is calculated by dividing the molar mass of a substance by its density using the following formula:

where Vm is the molar volume, M is the molar mass, and p is the density of the substance.

Rice. 2. Molar volume formula.

In the international C system, the molar volume of gaseous substances is measured in cubic meters per mole (m 3 /mol)

The molar volume of gaseous substances differs from substances in liquid and solid states in that a gaseous element with an amount of 1 mole always occupies the same volume (if the same parameters are met).

The volume of gas depends on temperature and pressure, so when calculating, you should take the volume of gas under normal conditions. Normal conditions are considered to be a temperature of 0 degrees and a pressure of 101.325 kPa. The molar volume of 1 mole of gas under normal conditions is always the same and equal to 22.41 dm 3 /mol. This volume is called the molar volume of an ideal gas. That is, in 1 mole of any gas (oxygen, hydrogen, air) the volume is 22.41 dm 3 /m.

Rice. 3. Molar volume of gas under normal conditions.

Table "molar volume of gases"

The following table shows the volume of some gases:

Gas	Molar volume, l
H 2	22,432
O2	22,391
Cl2	22,022
CO2	22,263
NH 3	22,065
SO 2	21,888
Ideal	22,41383

Before solving problems, you should know the formulas and rules for how to find the volume of gas. We should remember Avogadro's law. And the volume of gas itself can be calculated using several formulas, choosing the appropriate one from them. When selecting the required formula, environmental conditions, in particular temperature and pressure, are of great importance.

Avogadro's law

It says that at the same pressure and the same temperature, the same volumes of different gases will contain the same number of molecules. The number of gas molecules contained in one mole is Avogadro's number. From this law it follows that: 1 Kmol (kilomol) of an ideal gas, any gas, at the same pressure and temperature (760 mm Hg and t = 0*C) always occupies one volume = 22.4136 m3.

How to determine gas volume

• The formula V=n*Vm can most often be found in problems. Here, the volume of gas in liters is V, Vm is the molar volume of gas (l/mol), which under normal conditions = 22.4 l/mol, and n is the amount of substance in moles. When the conditions do not have the amount of a substance, but there is a mass of the substance, then we proceed this way: n=m/M. Here M is g/mol (molar mass of the substance), and the mass of the substance in grams is m. In the periodic table it is written under each element, as its atomic mass. Let's add up all the masses and get what we are looking for.
• So, how to calculate the volume of gas. Here is the task: dissolve 10 g of aluminum in hydrochloric acid. Question: how much hydrogen can be released at u.? The reaction equation looks like this: 2Al+6HCl(g)=2AlCl3+3H2. At the very beginning, we find the aluminum (quantity) that reacted according to the formula: n(Al)=m(Al)/M(Al). We take the mass of aluminum (molar) from the periodic table M(Al) = 27 g/mol. Let's substitute: n(Al)=10/27=0.37 mol. From the chemical equation it can be seen that 3 moles of hydrogen are formed when 2 moles of aluminum are dissolved. It is necessary to calculate how much hydrogen will be released from 0.4 moles of aluminum: n(H2)=3*0.37/2=0.56mol. Let's substitute the data into the formula and find the volume of this gas. V=n*Vm=0.56*22.4=12.54l.

P1V1=P2V2, or, which is the same, PV=const (Boyle-Mariotte law). At constant pressure, the ratio of volume to temperature remains constant: V/T=const (Gay-Lussac's law). If we fix the volume, then P/T=const (Charles’ law). Combining these three laws gives a universal law that states that PV/T=const. This equation was established by the French physicist B. Clapeyron in 1834.

The value of the constant is determined only by the amount of substance gas. DI. Mendeleev derived an equation for one mole in 1874. So it is the value of the universal constant: R=8.314 J/(mol∙K). So PV=RT. In the case of an arbitrary quantity gasνPV=νRT. The amount of a substance itself can be found from mass to molar mass: ν=m/M.

Molar mass is numerically equal to relative molecular mass. The latter can be found from the periodic table; it is indicated in the cell of the element, as a rule, . The molecular weight is equal to the sum of the molecular weights of its constituent elements. In the case of atoms of different valences, an index is required. On at mer, M(N2O)=14∙2+16=28+16=44 g/mol.

Normal conditions for gases at It is commonly assumed that P0 = 1 atm = 101.325 kPa, temperature T0 = 273.15 K = 0°C. Now you can find the volume of one mole gas at normal conditions: Vm=RT/P0=8.314∙273.15/101.325=22.413 l/mol. This table value is the molar volume.

Under normal conditions conditions quantity relative to volume gas to molar volume: ν=V/Vm. For arbitrary conditions you need to use the Mendeleev-Clapeyron equation directly: ν=PV/RT.

Thus, to find the volume gas at normal conditions, you need the amount of substance (number of moles) of this gas multiply by the molar volume equal to 22.4 l/mol. Using the reverse operation, you can find the amount of a substance from a given volume.

To find the volume of one mole of a substance in a solid or liquid state, find its molar mass and divide by its density. One mole of any gas under normal conditions has a volume of 22.4 liters. If conditions change, calculate the volume of one mole using the Clapeyron-Mendeleev equation.

You will need

• Periodic table of Mendeleev, table of density of substances, pressure gauge and thermometer.

Instructions

Determining the volume of one mole or solid
Determine the chemical formula of the solid or liquid you are studying. Then, using the periodic table, find the atomic masses of the elements that are included in the formula. If one is included in the formula more than once, multiply its atomic mass by that number. Add up the atomic masses and get the molecular mass of what the solid or liquid is made of. It will be numerically equal to the molar mass measured in grams per mole.

Using the table of substance densities, find this value for the material of the body or liquid being studied. After this, divide the molar mass by the density of the substance, measured in g/cm³ V=M/ρ. The result is the volume of one mole in cm³. If the substance remains unknown, it will be impossible to determine the volume of one mole of it.