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 substance that contains so much structural units of a given substance (molecules, atoms, ions, etc.), how many carbon atoms are 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 general numerical value 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 quantity 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 :

Atomic unit masses. Avogadro's number

Matter consists of molecules. By molecule we will mean smallest particle of this substance, preserving Chemical properties of this substance.

Reader: In what units is the mass of molecules measured?

Author: The mass of a molecule can be measured in any units of mass, for example in tons, but since the masses of molecules are very small: ~10–23 g, then for comfort introduced a special unit - atomic mass unit(a.e.m.).

Atomic mass unitis called a value equal to the th mass of the carbon atom 6 C 12.

The notation 6 C 12 means: a carbon atom having a mass of 12 amu. and nuclear charge – 6 elementary charges. Similarly, 92 U 235 is a uranium atom with a mass of 235 amu. and the charge of the nucleus is 92 elementary charges, 8 O 16 is an oxygen atom with a mass of 16 amu and the charge of the nucleus is 8 elementary charges, etc.

Reader: Why was it chosen as the atomic unit of mass? (but not or ) part of the mass of an atom and specifically carbon, and not oxygen or plutonium?

It has been experimentally established that 1 g » 6.02×10 23 amu.

The number showing how many times the mass of 1 g is greater than 1 amu is called Avogadro's number: N A = 6.02×10 23.

From here

N A × (1 amu) = 1 g (5.1)

Neglecting the mass of electrons and the difference in the masses of a proton and a neutron, we can say that Avogadro’s number approximately shows how many protons (or, which is almost the same thing, hydrogen atoms) must be taken to form a mass of 1 g (Fig. 5.1).

Mole

The mass of a molecule, expressed in atomic mass units, is called relative molecular weight .

Designated M r(r– from relative – relative), for example:

12 a.m.u. = 235 a.m.u.

A portion of a substance that contains the same number of grams of a given substance as the number of atomic mass units contained in a molecule of a given substance is called pray(1 mol).

For example: 1) relative molecular weight of hydrogen H2: therefore, 1 mole of hydrogen has a mass of 2 g;

2) relative molecular weight carbon dioxide CO 2:

12 amu + 2×16 a.m.u. = 44 amu

therefore, 1 mole of CO 2 has a mass of 44 g.

Statement. One mole of any substance contains the same number of molecules: N A = 6.02×10 23 pcs.

Proof. Let the relative molecular mass of a substance M r(a.m.) = M r× (1 amu). Then, according to the definition, 1 mole of a given substance has a mass M r(d) = M r×(1 g). Let N is the number of molecules in one mole, then

N×(mass of one molecule) = (mass of one mole),

The mole is the SI base unit of measurement.

Comment. A mole can be defined differently: 1 mole is N A = = 6.02×10 23 molecules of this substance. Then it is easy to understand that the mass of 1 mole is equal to M r(G). Indeed, one molecule has a mass M r(a.u.m.), i.e.

(mass of one molecule) = M r× (1 amu),

(mass of one mole) = N A ×(mass of one molecule) =

= N A × M r× (1 amu) = .

The mass of 1 mole is called molar mass of this substance.

Reader: If you take the mass T some substance molar mass which is equal to m, then how many moles will it be?

Let's remember:

Reader: In what SI units should m be measured?

, [m] = kg/mol.

For example, the molar mass of hydrogen

Mole- one of the most important concepts in chemistry, this is a kind of link for the transition from the microworld of atoms and molecules to the ordinary macroworld of grams and kilograms.

In chemistry we often have to count large quantities atoms and molecules. For quick and efficient calculation, it is customary to use the weighing method. But you need to know the weight individual atoms and molecules. In order to find out the molecular mass, you need to add up the mass of all the atoms included in the compound.

Let's take a water molecule H 2 O, which consists of one oxygen atom and two hydrogen atoms. From the periodic table of Mendeleev we learn that one hydrogen atom weighs 1.0079 amu. ; one oxygen atom - 15.999 amu. Now, to calculate the molecular mass of water, we need to add up the atomic masses of the components of the water molecule:

H 2 O = 2 1.0079 + 1 15.999 = 18.015 amu

For example, for ammonium sulfate the molecular weight will be:

Al 2 (SO 4) 3 = 2 26.982 + 3 32.066 + 12 15.999 = 315.168 amu.

Let's return again to Everyday life, in which we are accustomed to using such concepts as pair, ten, dozen, hundred. These are all unique units of measurement. certain objects: a pair of shoes, a dozen eggs, a hundred paper clips. A similar unit of measurement in chemistry is MOL.

Modern science has determined with high accuracy the number of structural units (molecules, atoms, ions...) that are contained in 1 mole of a substance - this is 6.022 10 23 - Avogadro's constant, or Avogadro's number.

All of the above about the pier refers to the microcosm. Now we need to connect the concept of mole with the everyday macrocosm.

The whole nuance is that 12 grams of the carbon isotope 12 C contains 6.022·10 23 carbon atoms, or exactly 1 mole. Thus, for any other element, a mole is expressed by a number of grams equal to the atomic mass of the element. For chemical compounds A mole is expressed in a number of grams equal to the molecular weight of a compound.

A little earlier we found out that the molecular weight of water is 18.015 amu. Taking into account the knowledge gained about the mole, we can say that the mass of 1 mole of water = 18.015 g (since a mole of a compound is the number of grams equal to its molecular weight). In other words, we can say that 18.015 g of water contains 6.022 10 23 molecules of H 2 O, or 1 mole of water = 1 mole of oxygen + 2 moles of hydrogen.

From the above example, the connection between the microcosm and the macrocosm through a mole is clear:

• n - quantity of substance, mol;
• N - number of particles;
• N A - Avogadro number, mol -1

Here are a few practical examples mole uses:

Task #1: How many water molecules are there in 16.5 moles of H2O?

Solution: 16.5 6.022 10 23 = 9.93 10 24 molecules.

Task #2: How many moles are there in 100 grams of H 2 O?

Solution:(100 g/1)·(1 mol/18.015 g) = 5.56 mol.

Task #3: How many molecules does 5 g of carbon dioxide contain?

Solution:

1. Determine the molecular weight of CO 2: CO 2 = 1 12.011 + 2 15.999 = 44.01 g/mol
2. Find the number of molecules: (5g/1)·(1mol/44.01g)·(6.022·10 23 /1mol) = 6.84·10 22 CO 2 molecules

The concept mole is used to measure chemical substances. Let us find out the features of this quantity, give examples of calculation tasks with its participation, and determine the importance this term.

Definition

The mole in chemistry is a unit of calculation. It represents the quantity a certain substance, which contains as many structural units (atoms, molecules) as are contained in 12 grams of a carbon atom.

Avogadro's number

The amount of substance is related to Avogadro's number, which is 6*10^23 1/mol. For substances molecular structure It is believed that one mole includes precisely Avogadro's number. If you need to count the number of molecules contained in 2 moles of water, then you need to multiply 6*10^23 by 2, we get 12*10^23 pieces. Let's look at the role moths play in chemistry.

Quantity of substance

A substance that consists of atoms contains Avogadro's number. For example, for a sodium atom it is 6*10*23 1/mol. What is its designation? Mole in chemistry means Greek letter"nude" or Latin "n". For mathematical calculations associated with the amount of substance, use the mathematical formula:

n=N/N(A), where n is the amount of substance, N(A) is Avogadro’s number, N is the number of structural particles of the substance.

If necessary, you can calculate the number of atoms (molecules):

The actual mass of a mole is called the molar mass. If the amount of a substance is determined in moles, then the molar mass has units of g/mol. IN numerically it corresponds to the relative molecular mass value, which can be determined by summing the relative atomic masses of the individual elements.

For example, in order to determine the molar mass of a carbon dioxide molecule, it is necessary to carry out the following calculations:

M (CO2)=Ar(C)+2Ar(O)=12+2*16=44

When calculating the molar mass of sodium oxide we obtain:

M (Na2O)=2*Ar(Na)+Ar(O)=2*23+16=62

When determining the molar mass of sulfuric acid, we sum up the two relative atomic masses of hydrogen with one atomic mass of sulfur and four relative atomic masses oxygen. Their meanings can always be found in periodic table Mendeleev. As a result we get 98.

The mole in chemistry allows for a variety of calculations related to chemical equations. All typical calculation problems in inorganic and organic chemistry, which involve finding the mass and volume of substances, are solved precisely through moles.

Examples of calculation problems

The molecular formula of any substance indicates the number of moles of each element included in its composition. For example, one mole of phosphoric acid contains three moles of hydrogen atoms, one mole of phosphorus atoms and four moles of oxygen atoms. Everything is quite simple. The mole in chemistry is a transition from the microworld of molecules and atoms to the macrosystem with kilograms and grams.

Task 1. Determine the number of water molecules contained in 16.5 moles.

To solve, we use the relationship between Avogadro’s number (amount of substance). We get:

16.5*6.022*1023 = 9.9*1024 molecules.

Task 2. Calculate the number of molecules contained in 5 g of carbon dioxide.

First, you need to calculate the molar mass of a given substance using its relationship with relative molecular mass. We get:

N=5/44*6.023*1023=6.8*1023 molecules.

Algorithm for chemical equation problems

When calculating the mass or reaction products using the equation, use specific algorithm actions. First, determine which starting materials in short supply. To do this, find their number in moles. Next, they compose an equation for the process, and be sure to set up the stereochemical coefficients. The initial data is written above the substances, below them the amount of the substance taken in moles (according to the coefficient) is indicated. If necessary, convert units of measurement using formulas. Next, they make up a proportion and solve it mathematically.

If more is offered difficult task, then preliminarily calculate the mass pure substance, removing impurities, then begin to determine its amount (in moles). Not a single problem in chemistry related to the reaction equation can be solved without such a quantity as the mole. In addition, using this term, you can easily determine the number of molecules or atoms, using for such calculations constant number Avogadro. Calculation tasks included in test questions in chemistry for graduates of basic and secondary schools.