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 periodic table 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 molecular weight will be equal to:

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 the number with high accuracy structural units(molecules, atoms, ions...) contained in 1 mole of a substance 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 the number of grams equal to atomic mass 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

Atomic mass unit. 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 convenience 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? (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 the molecule, expressed in atomic units mass is called relative molecular weight .

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

12 a.u.m. = 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 a molecule of a given substance contains 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 base unit of measurement in SI.

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

Knowing the amount of a substance in moles and Avogadro's number, it is very easy to calculate how many molecules are contained in this substance. Simply multiply Avogadro's number by the amount of substance.

N=N A *ν

And if you come to the clinic to take tests, let’s say, blood sugar, knowing Avogadro’s number, you can easily count the number of sugar molecules in your blood. Well, for example, the analysis showed 5 mol. Let's multiply this result by Avogadro's number and get 3,010,000,000,000,000,000,000,000 pieces. Looking at this figure, it becomes clear why they stopped measuring molecules in pieces and began measuring them in moles.

Molar mass (M).

If the amount of a substance is unknown, then it can be found by dividing the mass of the substance by its molar mass.

N=N A * m / M .

The only question that may arise here is: “what is molar mass?” No, this is not a mass of painter, as it might seem!!! Molar mass is the mass of one mole of a substance. Everything is simple here, if one mole contains N A particles (those. equal to the number Avogadro), then, multiplying the mass of one such particle m 0 by Avogadro's number, we get the molar mass.

M=m 0 *N A .

Molar mass is the mass of one mole of a substance.

And it’s good if it’s known, but what if it’s not? We will have to calculate the mass of one molecule m 0 . But this is not a problem either. You only need to know it chemical formula and have the periodic table at hand.

Relative molecular weight (Mr).

If the number of molecules in a substance is very large, then the mass of one molecule m0, on the contrary, is very small. Therefore, for the convenience of calculations, we introduced relative molecular mass (M r). This is the ratio of the mass of one molecule or atom of a substance to 1/12 of the mass of a carbon atom. But don’t let this scare you, for atoms it is indicated in the periodic table, and for molecules it is calculated as the sum of the relative molecular masses of all atoms included in the molecule. Relative molecular weight is measured in atomic mass units (a.u.m), in terms of kilograms 1 amu = 1.67 10 -27 kg. Knowing this, we can easily determine the mass of one molecule by multiplying the relative molecular mass by 1.67 10 -27.

m 0 = M r *1.67*10 -27 .

Relative molecular weight- the ratio of the mass of one molecule or atom of a substance to 1/12 of the mass of a carbon atom.

Relationship between molar and molecular mass.

Let us recall the formula for finding the molar mass:

M=m 0 *N A .

Because m 0 = M r * 1.67 10 -27, we can express molar mass as:

M=M r *N A *1.67 10 -27 .

Now if we multiply Avogadro's number N A by 1.67 10 -27, we get 10 -3, that is, to find out the molar mass of a substance, it is enough just to multiply its molecular mass by 10 -3.

M=M r *10 -3

But don’t rush to do all this by calculating the number of molecules. If we know the mass of a substance m, then dividing it by the mass of the molecule m 0, we get the number of molecules in this substance.

N=m / m 0

Of course, it is a thankless task to count molecules; not only are they small, they are also constantly moving. Just in case you get lost, you'll have to count again. But in science, as in the army, there is such a word “must”, and therefore even atoms and molecules were counted...

Every schoolchild who begins to study chemistry encounters the concept of “mole.” With more complex concepts, such as concentration, molarity of the solvent, are difficult to figure out without knowing what a mole is. We can conclude that mole is one of the most important concepts in chemistry. Many problems cannot be solved without determining the number of moles.

Definition

So what is a mole in chemistry? The explanation is quite simple: this is a unit in which the amount of a substance is expressed, one of the SI units. The definition of what a mole is in chemistry can be formulated this way: 1 mole is equivalent to the structural particles contained in 12 g of carbon-12.

It was found that 12 g of this isotope contains a number of atoms numerically equal to Avogadro’s constant.

Origin of the concept

Having understood a little about what a mole is in chemistry with the help of definitions, let’s turn to the history of this concept. As is commonly believed, the term "mole" was introduced by the German chemist Wilhelm Oswald, who received Nobel Prize in 1909. The word "mole" obviously comes from the word "molecule".

An interesting fact is that Avogadro’s hypothesis that under the same conditions the same volumes of different gases contain the same amount of substance was put forward long before Oswald, and the constant itself was calculated by Avogadro back in early XIX century. That is, although the concept of “mole” did not exist, the very idea of ​​the amount of substance already existed.

Basic formulas

The amount of substance is found differently, depending on the data of the problem. This is the most common formula, in which this quantity is expressed as the ratio of mass to molar mass:

It is worth saying that the amount of a substance is an additive quantity. That is, in order to calculate the value of this quantity for a mixture, you must first determine the amount of substance for each of its elements and add them up.

Another formula is applied if the number of particles is known:

If the problem specifies that the process occurs when normal conditions, you can use the following rule: under normal conditions, any gas occupies an invariant volume - 22.4 liters. Then you can use the following expression:

The amount of substance is expressed from the Clapeyron equation:

Knowledge of what a mole is in chemistry and basic formulas to determine the number of moles of a substance, makes it possible to solve many problems much faster. If the amount of a substance is known, mass, volume, density and other parameters can be found.

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 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 amount (ν) can be calculated :