A unit of measurement for the amount of a substance in chemistry. Calculations according to the equations of chemical reactions. Tasks for determining the amount of a substance using basic formulas

Instruction

To find a mole of a substance, you need to remember a very simple rule: the mass of one mole of any substance is numerically equal to its molecular weight, only expressed in other quantities. And how is it determined? Using the periodic table, you will find out the atomic mass of each element included in the molecules of a substance. Next, you need to add the atomic masses, taking into account the index of each element, and you get the answer.

Calculate its molecular weight, taking into account the index of each element: 12 * 2 + 1 * 4 + 16 * 3 = 76 a.m.u. (atomic mass units). Therefore, its molar mass (that is, the mass of one mole) is also 76, only its unit is gram/mol. Answer: one mole of ammonium nitrate weighs 76 grams.

Suppose you are given such a task. It is known that the mass of 179.2 liters of some gas is 352 grams. It is necessary to determine how much one mole of this gas weighs. It is known that under normal conditions, one mole of any gas or mixture of gases occupies a volume approximately equal to 22.4 liters. And you have 179.2 liters. Perform the calculation: 179.2 / 22.4 \u003d 8. Therefore, this volume contains 8 moles of gas.

Dividing the mass known according to the conditions of the problem by the number of moles, you get: 352/8 \u003d 44. Therefore, one mole of this gas weighs 44 grams - this is carbon dioxide, CO2.

If there is some amount of gas of mass M, enclosed in a volume V at a given temperature T and pressure P. It is required to determine its molar mass (that is, find what its mole is equal to). The universal Mendeleev-Clapeyron equation will help you solve the problem: PV \u003d MRT / m, where m is the same molar mass that we need to determine, and R is the universal gas constant, equal to 8.31. Transforming the equation, you get: m = MRT/PV. By substituting known quantities into the formula, you will find what a mole of gas is equal to.

Helpful advice

Calculations usually use rounded values. atomic weights elements. If higher precision is required, then rounding is not allowed.

A. Avogadro in 1811, at the very beginning of the development of atomic theory, made the assumption that an equal amount of ideal gases at the same pressure and temperature contains the same number of molecules. Later, this assumption was confirmed and became a necessary consequence for kinetic theory. Now this theory is called Avogadro.

Instruction

The constant Avogadro shows the number of atoms or molecules that are contained in one mole of a substance.

The number of molecules, provided that the system is one-component, and the molecules or atoms of the same type contained in it, can be found by a special formula

Related videos

First define chemical composition and state of aggregation substances. If a gas is being tested, measure its temperature, volume, and pressure, or place it under normal conditions and measure only the volume. After that, calculate the number of molecules and atoms. To determine the number of atoms in a solid or liquid, find their mass and molar mass, and then the number of molecules and atoms.

You will need

pressure gauge, thermometer, scales and periodic table, find out the Avogadro constant.

Instruction

Determining the mass of one mole from a known amount of a substance If you know the amount of a substance in moles, the molar mass of which you want to find, use the balance to find its actual mass, expressing it in grams. To determine the mass of one mole, divide the mass of a substance by its amount M=m/υ.

Determination of the mass of one mole of a substance by the mass of a molecule If the mass of one molecule of a substance, expressed in grams, is known, find the mass of one mole by multiplying the mass of this molecule by the number of molecules in one mole (Avogadro's number), which is equal to 6.022 10^23, M = m0 NA .

Determining the mass of one mole of a gas Take a sealed vessel of known volume, expressed in cubic meters. Pump out the gas from it, and weigh it on the scales. Pump gas into it, and weigh it again, the difference between the empty and filled cylinders will be equal to the mass of gas. Convert it to kilograms.
Measure the temperature of the gas in the cylinder, if you wait a little after injection, it equals the ambient temperature, and convert it to kelvins by adding the number 273 to degrees Celsius. Measure the gas pressure with a pressure gauge, in pascals. Find the molar mass of a gas (the mass of one mole) by multiplying the mass of the gas by its temperature and 8.31 (universal gas constant), and dividing the result by the pressure and volume M=m R T/(P V).

Sometimes researchers face the following problem: how to determine the number of atoms of a substance? Initially, it may seem extremely complicated, because the number of atoms even in a tiny sample of any substance is simply grandiose. How to count them?

Instruction

Suppose you need to count the number of atoms in a piece of pure - for example, copper or even gold. Yes, imagine yourself in the place of the great scientist Archimedes, to whom King Hieron gave a completely different assignment, saying: “You know, Archimedes, in vain I suspected my jeweler of fraud, the crown turned out to be pure gold! Our royal majesty is now pleased to know that there are atoms in it.

The task, of course, would have plunged the real Archimedes into a stupor, even though he was. Well, you could do it in no time. First you need to accurately weigh the crown. Suppose she weighed exactly 2 kg, that is, 2000 grams. Then, according to the periodic table, set the molar mass of gold (about 197 grams / mol.) To simplify the calculations, slightly round up a little - let it be 200 grams / mol. Therefore, there are exactly 10 moles of gold in the ill-fated crown. Well, then take the universal number of Avogadro (6.022x1023), multiply by 10 and triumphantly take the result to King Hieron.

And then use the well-known Mendeleev-Clapeyron equation: PV = MRT/m. Note that M/m is nothing more than the number of moles of a given gas, since M is its actual mass and m is its molar mass.

Substitute the values you know into the fraction PV / RT, multiply the result found by the universal Avogadro number (6.022 * 1023) and get the number of gas atoms at a given volume, pressure and temperature.

And if you want to count the number of atoms in a sample complex substance? And there is nothing particularly difficult. Weigh the sample, then write its exact chemical formula, use the periodic table to specify the molar mass of each component and calculate the exact molar mass of this complex substance (taking into account the element indices if necessary).

Well, then find out the number of moles in the sample under study (by dividing the mass of the sample by the molar mass) and multiply the result by the value of Avogadro's number.

In chemistry, the mole is used as the unit of quantity of a substance. A substance has three characteristics: mass, molar mass and amount of substance. Molar mass is the mass of one mole of a substance.

Instruction

One mole of a substance is its amount, which contains so many structural units, how many atoms are contained in 0.012 kg of an ordinary (non-radioactive) isotope. To the structural units of matter molecules, atoms, ions. When, under the conditions of the problem, it is given with the relative atomic mass Ar, from the formula of the substance, depending on the formulation of the problem, either the mass of one mole of the same substance or its molar mass is found by performing calculations. The relative atomic mass of Ar is a value equal to the ratio of the average mass of an isotope of an element to 1/12 of the mass of carbon.

The molar mass of both organic and inorganic substances. For example, calculate this parameter for water H2O and methane CH3. First, find the molar mass of water:
M(H2O)=2Ar(H)+Ar(O)=2*1+16=18 g/mol
Methane is a gas of organic origin. This means that its molecule contains hydrogen and carbon atoms. In total, one molecule of this gas contains three hydrogen atoms and one carbon atom. Calculate the molar mass of this substance as follows:
M(CH3)=Ar(C)+2Ar(H)=12+3*1=15 g/mol
Similarly, calculate the molar masses of any other substances.

Also, the mass of one mole of a substance or the molar mass is found, knowing the mass and amount of the substance. In this case, the molar mass is calculated as the ratio of the mass of a substance to its quantity. The formula then looks like this:
M=m/ν, where M is the molar mass, m is the mass, ν is the amount of substance.
The molar mass of a substance is expressed in grams or kilograms per mole. If the mass of a molecule of a particular substance is known, then, knowing the Avogadro number, one can find the mass of one mole of a substance as follows:
Mr=Na*ma, where Mr is the molar mass, Na is Avogadro's number, ma is the mass of the molecule.
So, for example, knowing the mass of a carbon atom, you can find the molar mass of this substance:
Mr=Na*ma=6.02*10^23*1.993*10^-26=12 g/mol

Related videos

Sources:

Talitsa Mendeleev

The most typical processes carried out in chemistry are chemical reactions, i.e. interactions between some initial substances, leading to the formation of new substances. Substances react in certain quantitative relations, which must be taken into account in order to obtain the desired products using the minimum amount of starting materials and not creating useless production waste. To calculate the masses of the reacting substances, it turns out that one more physical quantity, which characterizes a portion of a substance in terms of the number of structural units contained in it. In itself, the ego number is unusually large. This is obvious, in particular, from Example 2.2. Therefore, in practical calculations, the number of structural units is replaced by a special value called quantity substances.

The amount of substance is a measure of the number of structural units, determined by the expression

where N(X)- the number of structural units of the substance X in a real or mentally taken portion of a substance, N A = 6.02 10 23 - Avogadro's constant (number), widely used in science, one of the fundamental physical constants. If necessary, a more accurate value of the Avogadro constant 6.02214 10 23 can be used. A portion of a substance containing N a structural units, represents a single amount of a substance - 1 mol. Thus, the amount of a substance is measured in moles, and the Avogadro constant has a unit of 1/mol, or in another notation, mol -1.

With all sorts of reasoning and calculations related to the properties of matter and chemical reactions, the concept amount of substance completely replaces the concept number of structural units. This eliminates the need to use large numbers. For example, instead of saying "taken 6.02 10 23 structural units (molecules) of water", we say: "taken 1 mole of water."

Each portion of a substance is characterized by both mass and quantity of the substance.

The ratio of the mass of a substanceXto the amount of the substance is called the molar massM(X):

The molar mass is numerically equal to the mass of 1 mol of a substance. This is important quantitative characteristic of each substance, depending only on the mass of structural units. The Avogadro number is set in such a way that the molar mass of a substance, expressed in g / mol, numerically coincides with the relative molecular weight M g For a water molecule M g = 18. This means that the molar mass of water is M (H 2 0) \u003d 18 g / mol. Using the data of the periodic table, it is possible to calculate more accurate values M g and M(X), but in teaching tasks in chemistry this is usually not required. From all that has been said, it is clear how easy it is to calculate the molar mass of a substance - it is enough to add the atomic masses in accordance with the formula of the substance and put the unit g / mol. Therefore, formula (2.4) is practically used to calculate the amount of a substance:

Example 2.9. Calculate the molar mass of baking soda NaHC0 3 .

Decision. According to the formula of the substance M g = 23 + 1 + 12 + 3 16 = 84. Hence, by definition, M(NaIIC0 3) = 84 g/mol.

Example 2.10. What is the amount of substance in 16.8 g of baking soda? Decision. M(NaHC0 3) = 84 g/mol (see above). By formula (2.5)

Example 2.11. How many fractions (structural units) of drinking soda are in 16.8 g of a substance?

Decision. Transforming formula (2.3), we find:

AT(NaHC0 3) = N a n(NaHC0 3);

tt(NaHC0 3) = 0.20 mol (see example 2.10);

N (NaHC0 3) \u003d 6.02 10 23 mol "1 0.20 mol \u003d 1.204 10 23.

Example 2.12. How many atoms are there in 16.8 g of baking soda?

Decision. Baking soda, NaHC0 3 , is made up of sodium, hydrogen, carbon and oxygen atoms. In total, there are 1 + 1 + 1 + 3 = 6 atoms in the structural unit of matter. As was found in example 2.11, this mass of drinking soda consists of 1.204 10 23 structural units. So total number atoms in matter is

The amount of matter contained in a body is determined by the number of molecules (or atoms) in that body. Since the number of molecules in macroscopic bodies is very large, to determine the amount of matter in the body, the number of molecules in it is compared with the number of atoms in 0.012 kg of the carbon isotope \(~^(12)_6C\).

Amount of substanceν - value, equal to the ratio number of molecules (atoms) N in a given body to the number of atoms N A in 0.012 kg of carbon isotope \(~^(12)_6C\):

\(~\nu = \frac(N)(N_A) . \qquad (2)\)

In SI, the unit of quantity of a substance is the mole. 1 mol- the amount of a substance that contains the same number of structural elements (atoms, molecules, ions) as there are atoms in 0.012 kg of the carbon isotope \(~^(12)_6C\).

The number of particles in one mole of a substance is called constant Avogadro.

\(~N_A = \frac(0.012)(m_(0C))= \frac(0.012)(1.995 \cdot 10^(-26))\) = 6.02 10 23 mol -1 . (3)

Thus, 1 mole of any substance contains the same number of particles - N A particles. Since the mass m 0 particles different substances different, then the mass N A particles in different substances is different.

The mass of a substance taken in an amount of 1 mol is called molar mass M:

\(~M = m_0 N_A . \qquad (4)\)

The SI unit of molar mass is the kilogram per mole (kg/mol).

between molar mass Μ and relative molecular weight M r there is the following relation:

\(~M = M_r \cdot 10^(-3) .\)

So the molecular weight carbon dioxide 44, molar 44 10 -3 kg/mol.

Knowing the mass of a substance and its molar mass M, you can find the number of moles (amount of substance) in the body\[~\nu = \frac(m)(M)\].

Then from formula (2) the number of particles in the body

\(~N = \nu N_A = \frac(m)(M) N_A .\)

Knowing the molar mass and Avogadro's constant, we can calculate the mass of one molecule:

\(~m_0 = \frac(M)(N_A) = \frac(m)(N) .\)

Literature

Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 124-125.

Mole, molar mass

The smallest particles - molecules, atoms, ions, electrons - participate in chemical processes. The number of such particles, even in a small portion of matter, is very large. Therefore, to avoid mathematical operations with big numbers, to characterize the amount of a substance participating in a chemical reaction, a special unit is used - mole.

mole- this is such an amount of a substance that contains a certain number of particles (molecules, atoms, ions) equal to the Avogadro constant

The Avogadro constant N A is defined as the number of atoms contained in 12 g of the 12 C isotope:

Thus, 1 mole of any substance contains 6.02 10 23 particles of this substance.

1 mole of oxygen contains 6.02 10 23 O 2 molecules.

1 mole of sulfuric acid contains 6.02 10 23 H 2 SO 4 molecules.

1 mole of iron contains 6.02 10 23 Fe atoms.

1 mole of sulfur contains 6.02 10 23 S atoms.

2 moles of sulfur contains 12.04 10 23 S atoms.

0.5 mol sulfur contains 3.01 10 23 S atoms.

Based on this, any amount of a substance can be expressed by a certain number of moles ν (nude). For example, a sample of a substance contains 12.04 10 23 molecules. Therefore, the amount of substance in this sample is:

In general:

where Nis the number of particles of a given substance;
N a- the number of particles that contains 1 mol of a substance (Avogadro's constant).

Molar mass of a substance (M) is the mass that 1 mole of a given substance has.
This value, equal to the ratio of the mass m substance to amount of substance ν , has dimension kg/mol or g/mol. The molar mass, expressed in g / mol, is numerically equal to the relative relative molecular mass M r (for substances atomic structure– relative atomic mass Ar).
For example, the molar mass of methane CH 4 is defined as follows:

M r (CH 4) \u003d A r (C) + 4 A r (H) \u003d 12 + 4 \u003d 16

M(CH 4) \u003d 16 g / mol, i.e. 16 g of CH 4 contains 6.02 10 23 molecules.

The molar mass of a substance can be calculated if its mass is known m and quantity (number of moles) ν , according to the formula:

Accordingly, knowing the mass and molar mass of a substance, we can calculate the number of its moles:

or find the mass of a substance by the number of moles and the molar mass:

m = ν M

It should be noted that the value of the molar mass of a substance is determined by its qualitative and quantitative composition, i.e. depends on M r and A r . Therefore, different substances with the same number of moles have different masses. m.

Example
Calculate the masses of methane CH 4 and ethane C 2 H 6 taken in the amount ν = 2 moles each.

Decision
The molar mass of methane M(CH 4) is 16 g/mol;
molar mass of ethane M (C 2 H 6) \u003d 2 12 + 6 \u003d 30 g / mol.
From here:

m(CH 4) \u003d 2 mol 16 g / mol \u003d 32 g;
m(C 2 H 6) \u003d 2 mol 30 g / mol \u003d 60 g.

Thus, a mole is a portion of a substance containing the same number of particles, but having a different mass for different substances, since particles of matter (atoms and molecules) are not the same in mass.

n(CH 4) = n(C 2 H 6), but m(CH 4) < m (C 2 H 6)

calculation ν used in almost every computational problem.

Relationship:

Problem Solving Samples

Task number 1. Calculate the mass (g) of iron taken by the amount of substance

0.5 mol?

Given: ν (Fe) \u003d 0.5 mol

To find: m(Fe) - ?

Decision:

m = M ν

M (Fe) \u003d Ar (Fe) \u003d 56 g / mol (From the periodic system)

m (Fe) \u003d 56 g / mol 0.5 mol \u003d 28 g

Answer: m (Fe) \u003d 28 g

Task number 2. Calculate mass (g) 12.04 10 23 oxide moleculescalciumCaO?

Given: N (CaO) \u003d 12.04 * 10 23 molecules

To find: m (CaO) - ?

Decision:

m \u003d M ν, ν \u003d N /N a,

therefore, the formula for calculating

m = M (N/N a)

M(CaO) = Ar(Ca) + Ar(O) = 40 + 16 = 56 g/mol

m \u003d 56 g / mol (12.04 * 10 23 / 6.02 10 23 1 / mol) \u003d 112 g

Lesson Objectives:

Introduce the concept of the amount of a substance and its units of measurement: mol, mmol, kmol.
Give an idea of the Avogadro constant.
Show the relationship between mass, amount of matter and number of particles.

Lesson objectives:

1. Contribute to the formation of students' worldview ideas about the relationship of different properties of the phenomena of the surrounding world.
2. To develop the ability of students to establish causal relationships, as well as to observe, generalize and draw conclusions.

Basic terms:

non-metals - chemical elements that form in a free form simple substances that do not have physical properties metals.
mole is the amount of any substance that contains as many structural elements as atoms contained in 12g. carbon-12 nuclide
DURING THE CLASSES

Amount of substance

In chemistry (as well as in physics and other natural sciences) have to deal with large quantities of tiny particles - with the so-called structural elements of matter (molecules, atoms, ions, electrons, etc.).
In order to express the number of such particles, the unit of quantity, the mole, was introduced. 1 mole is such an amount of any substance that contains as many structural elements as there are atoms in 12g. carbon-12 nuclide. It was experimentally found that the number of structural elements corresponding to 1 mol is 6.02∙1023 (the constant 6.02∙1023 mol-1 is called the Avogadro constant. Cylinders with substances in 1 mol).

Rice. 1. Avogadro's constant
Illustration of the corollary of Avogadro's law

Rice. 2. - unit of the amount of substance

Mole is a unit of quantity of a substance

Rice. 3. Amount of substance
This portion of the substance has a mass, which is called the molar mass. It is denoted by M, which is found by the formula M \u003d m / n. What units will the molar mass be measured in?
The molar mass coincides in value with the relative atomic or molecular mass, but differ in units of measurement (M - g / mol; Mr, Ar - dimensionless quantities).

Rice. 4. Amount of substance in moles

Rice. 5. Molar mass

Control block

№1.
The mass of 3 mol H2O is ____ g
The mass of 20 mol H2O is ____ g
№2.
36 g of H2O are ______ mol
180 g of H2O are _______ mol

Homework

How many molecules are there in 180 g of water?
Find the mass of 24x1023 ozone molecules?

Oxygen is the most common chemical element in the earth's crust. Oxygen is part of almost all the substances around us. For example, water, sand, many rocks and minerals that make up the earth's crust contain oxygen. Oxygen is also an important part of many organic compounds, for example, proteins, fats and carbohydrates, which are of exceptional importance in the life of plants, animals and humans.
In 1772, the Swedish chemist K.V. Scheele found that air is made up of oxygen and nitrogen. In 1774, D. Priestley obtained oxygen by decomposition of mercury oxide (2). Oxygen is a colorless gas, tasteless and odorless, relatively slightly soluble in water, slightly heavier than air: 1 liter of oxygen under normal conditions weighs 1.43 g, and 1 liter of air weighs 1.29 g. (Normal conditions - abbreviated: n. u . – temperature 0 °C and pressure 760 mm Hg, or 1 atm). At a pressure of 760 mm Hg. Art. and a temperature of -183 °C, oxygen liquefies, and when the temperature drops to -218.8 °C, it solidifies.
The chemical element oxygen O, in addition to ordinary oxygen O2, exists in the form of another a simple substance– O3 ozone. Oxygen O2 is converted to ozone in a device called an ozonator.
It is a gas with a sharp characteristic odor (the name “ozone” in Greek means “smelling”). You have probably smelled ozone more than once during a thunderstorm. Ozone is made up of three atoms of the element oxygen. Pure ozone is a gas of blue color, one and a half times heavier than oxygen, it dissolves better in water.
There is an ozone layer in the air atmosphere above the Earth at an altitude of 25 km. There, ozone is formed from oxygen under the influence of ultraviolet radiation from the sun. In turn, the ozone layer delays this radiation, which is dangerous for all living beings, which ensures normal life on Earth.
Ozone is used for disinfection drinking water, since ozone oxidizes harmful impurities in natural water. In medicine, ozone is used as a disinfectant.

Bibliography

1. Lesson on the topic “Amount of substance”, teacher of biology and chemistry Yakovleva Larisa Alexandrovna, Kurgan region, Petukhovsky district, municipal educational institution "Novogeorgievskaya secondary school"
2. F. A. Derkach "Chemistry", - scientific and methodological manual. - Kyiv, 2008.
3. L. B. Tsvetkova " Inorganic chemistry» - 2nd edition, corrected and enlarged. – Lvov, 2006.
4. V. V. Malinovsky, P. G. Nagorny "Inorganic Chemistry" - Kyiv, 2009.
4. Glinka N.L. general chemistry. - 27 ed. / Under. ed. V.A. Rabinovich. - L .: Chemistry, 2008. - 704 pages.

Edited and sent by Borisenko I.N.