Gases are the simplest object for research, therefore their properties and reactions between gaseous substances have been studied most fully. In order to make it easier for us to parse the decision rules calculation tasks,based on the equations of chemical reactions,it is advisable to consider these laws at the very beginning of the systematic study of general chemistry
French scientist J.L. Gay-Lussac made the law bulk relations:
For example, 1 l chlorine connects with 1 l of hydrogen , forming 2 liters of hydrogen chloride ; 2 liters of sulfur oxide (IV) connect with 1 liter of oxygen, forming 1 liter of sulfur oxide (VI).
This law allowed the Italian scientist assume that the molecules of simple gases ( hydrogen, oxygen, nitrogen, chlorine, etc.
) consist of two identical atoms
. When hydrogen combines with chlorine, their molecules break down into atoms, and the latter form molecules of hydrogen chloride. But since two molecules of hydrogen chloride are formed from one molecule of hydrogen and one molecule of chlorine, the volume of the latter must be equal to the sum of the volumes of the initial gases.
Thus, the volume ratios are easily explained if we proceed from the concept of the diatomic nature of the molecules of simple gases ( H2, Cl2, O2, N2, etc.
)- This, in turn, serves as proof of the diatomic nature of the molecules of these substances.
The study of the properties of gases allowed A. Avogadro to express a hypothesis, which was later confirmed by experimental data, and therefore became known as Avogadro's law:
From the law of Avogadro follows an important consequence: under the same conditions, 1 mole of any gas occupies the same volume.
This volume can be calculated if the mass is known 1 l gas. Under normal conditions, (n.o.) i.e. temperature 273K (O°C) and pressure 101 325 Pa (760 mmHg) , the mass of 1 liter of hydrogen is 0.09 g, its molar mass is 1.008 2 = 2.016 g / mol. Then the volume occupied by 1 mole of hydrogen under normal conditions is equal to 22.4 l
Under the same conditions, the mass 1l oxygen 1.492g ; molar 32g/mol . Then the volume of oxygen at (n.s.) is also equal to 22.4 mol.
Consequently:
The molar volume of a gas is the ratio of the volume of a substance to the amount of that substance:
where V m - molar volume of gas (dimensionl/mol ); V is the volume of the substance of the system;n is the amount of matter in the system. Recording example:V m gas (well.)\u003d 22.4 l / mol.
Based on Avogadro's law, the molar masses of gaseous substances are determined. The greater the mass of gas molecules, the greater the mass of the same volume of gas. Equal volumes of gases under the same conditions contain the same number of molecules, and hence the moles of gases. The ratio of the masses of equal volumes of gases is equal to the ratio of their molar masses:
where m 1 - mass of a certain volume of the first gas; m 2 is the mass of the same volume of the second gas; M 1 and M 2 - molar masses of the first and second gases.
Usually, the density of a gas is determined in relation to the lightest gas - hydrogen (denoted D H2 ). The molar mass of hydrogen is 2g/mol . Therefore, we get.
The molecular weight of a substance in the gaseous state is equal to twice its hydrogen density.
The density of a gas is often determined relative to air. (D B ) . Although air is a mixture of gases, they still talk about its average molar mass. It is equal to 29g/mol. In this case, the molar mass is given by M = 29D B .
The determination of molecular weights showed that the molecules of simple gases consist of two atoms (H2, F2, Cl2, O2 N2) , and the molecules of inert gases - from one atom (He, Ne, Ar, Kr, Xe, Rn). For noble gases, "molecule" and "atom" are equivalent.
Boyle's Law - Mariotte:
at constant temperature, the volume of a given amount of gas is inversely proportional to the pressure under which it is located.From here
pV = const
,
where
R
- pressure, V
- volume of gas.
Gay-Lussac's law:
at constant pressure and the change in gas volume is directly proportional to temperature, i.e.
V/T = const
where
T
- temperature on a scale To
(kelvin)
The combined gas law of Boyle - Mariotte and Gay-Lussac:
pV/T = const.
This formula is usually used to calculate the volume of a gas under given conditions, if its volume is known under other conditions. If a transition is made from normal conditions (or to normal conditions), then this formula is written as follows:
pV/T = p
0
V
0
/T
0
,
where R
0
,V
0
,T
0
-pressure, gas volume and temperature under normal conditions ( R
0
= 101 325 Pa
, T
0
= 273 K
V
0
\u003d 22.4 l / mol)
.
If the mass and amount of gas are known, but it is necessary to calculate its volume, or vice versa, use Mendeleev-Claiperon equation:
where n - amount of gas substance, mol; m — mass, g; M is the molar mass of the gas, g/yol ; R is the universal gas constant. R \u003d 8.31 J / (mol * K)
Where m is mass, M is molar mass, V is volume.
4. Avogadro's law. Established by the Italian physicist Avogadro in 1811. The same volumes of any gases, taken at the same temperature and the same pressure, contain the same number of molecules.
Thus, the concept of the amount of a substance can be formulated: 1 mole of a substance contains a number of particles equal to 6.02 * 10 23 (called the Avogadro constant)
The consequence of this law is that 1 mole of any gas occupies under normal conditions (P 0 \u003d 101.3 kPa and T 0 \u003d 298 K) a volume equal to 22.4 liters.
5. Boyle-Mariotte Law
At constant temperature, the volume of a given amount of gas is inversely proportional to the pressure under which it is:
6. Gay-Lussac's Law
At constant pressure, the change in the volume of a gas is directly proportional to the temperature:
V/T = const.
7. The relationship between gas volume, pressure and temperature can be expressed the combined law of Boyle-Mariotte and Gay-Lussac, which is used to bring gas volumes from one condition to another:
P 0 , V 0 ,T 0 - volume pressure and temperature under normal conditions: P 0 =760 mm Hg. Art. or 101.3 kPa; T 0 \u003d 273 K (0 0 C)
8. Independent assessment of the value of molecular masses M can be done using the so-called equations of state for an ideal gas or the Clapeyron-Mendeleev equations :
pV=(m/M)*RT=vRT.(1.1)
where R - gas pressure in a closed system, V- volume of the system, t - mass of gas T - absolute temperature, R- universal gas constant.
Note that the value of the constant R can be obtained by substituting the values characterizing one mole of gas at N.C. into equation (1.1):
r = (p V) / (T) \u003d (101.325 kPa 22.4 l) / (1 mol 273K) \u003d 8.31J / mol.K)
Examples of problem solving
Example 1 Bringing the volume of gas to normal conditions.
What volume (n.o.) will occupy 0.4×10 -3 m 3 of gas at 50 0 C and a pressure of 0.954×10 5 Pa?
Solution. To bring the volume of gas to normal conditions, use the general formula that combines the laws of Boyle-Mariotte and Gay-Lussac:
pV/T = p 0 V 0 /T 0 .
The volume of gas (n.o.) is , where T 0 = 273 K; p 0 \u003d 1.013 × 10 5 Pa; T = 273 + 50 = 323 K;
M 3 \u003d 0.32 × 10 -3 m 3.
When (n.o.) gas occupies a volume equal to 0.32×10 -3 m 3 .
Example 2 Calculation of the relative density of a gas from its molecular weight.
Calculate the density of ethane C 2 H 6 from hydrogen and air.
Solution. It follows from Avogadro's law that the relative density of one gas over another is equal to the ratio of molecular masses ( M h) of these gases, i.e. D=M 1 /M 2. If a M 1С2Н6 = 30, M 2 H2 = 2, the average molecular weight of air is 29, then the relative density of ethane with respect to hydrogen is D H2 = 30/2 =15.
Relative density of ethane in air: D air= 30/29 = 1.03, i.e. ethane is 15 times heavier than hydrogen and 1.03 times heavier than air.
Example 3 Determination of the average molecular weight of a mixture of gases by relative density.
Calculate the average molecular weight of a mixture of gases consisting of 80% methane and 20% oxygen (by volume) using the values of the relative density of these gases with respect to hydrogen.
Solution. Often calculations are made according to the mixing rule, which is that the ratio of the volumes of gases in a two-component gas mixture is inversely proportional to the differences between the density of the mixture and the densities of the gases that make up this mixture. Let us denote the relative density of the gas mixture with respect to hydrogen through D H2. it will be greater than the density of methane, but less than the density of oxygen:
80D H2 - 640 = 320 - 20 D H2; D H2 = 9.6.
The hydrogen density of this mixture of gases is 9.6. average molecular weight of the gas mixture M H2 = 2 D H2 = 9.6×2 = 19.2.
Example 4 Calculation of the molar mass of a gas.
The mass of 0.327 × 10 -3 m 3 of gas at 13 0 C and a pressure of 1.040 × 10 5 Pa is 0.828 × 10 -3 kg. Calculate the molar mass of the gas.
Solution. You can calculate the molar mass of a gas using the Mendeleev-Clapeyron equation:
where m is the mass of gas; M is the molar mass of the gas; R- molar (universal) gas constant, the value of which is determined by the accepted units of measurement.
If the pressure is measured in Pa, and the volume in m 3, then R\u003d 8.3144 × 10 3 J / (kmol × K).
In order to know the composition of any gaseous substances, it is necessary to be able to operate with such concepts as molar volume, molar mass and density of a substance. In this article, we will consider what is molar volume, and how to calculate it?
Amount of substance
Quantitative calculations are carried out in order to actually carry out a particular process or find out the composition and structure of a certain substance. These calculations are inconvenient to make with the absolute values of the masses of atoms or molecules due to the fact that they are very small. Relative atomic masses are also in most cases impossible to use, since they are not related to generally accepted measures of the mass or volume of a substance. Therefore, the concept of the amount of 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 the amount of a substance that contains as many structural units as there are atoms in 12 g of a carbon isotope.
The mass of 1 atom is 12 a. e. m., so the number of atoms in 12 g of the carbon isotope is:
Na \u003d 12g / 12 * 1.66057 * 10 to the power of -24g \u003d 6.0221 * 10 to the power of 23
The physical quantity Na is called the Avogadro 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 according to 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 measurement of the molar volume of gaseous substances is carried out in cubic meters per mol (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 mol always occupies the same volume (if the same parameters are observed).
The volume of gas depends on temperature and pressure, so the calculation 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 mol 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 |
| H2 | 22,432 |
| O2 | 22,391 |
| Cl2 | 22,022 |
| CO2 | 22,263 |
| NH3 | 22,065 |
| SO2 | 21,888 |
| Ideal | 22,41383 |
Lesson 1.
Topic: Amount of substance. mole
Chemistry is the science of substances. How do you measure substances? In what units? In the molecules that make up substances, but this is very difficult to do. In grams, kilograms or milligrams, but this is how mass is measured. But what if we combine the mass that is measured on the scales and the number of molecules of a substance, is this possible?
a) H-hydrogen
A n = 1a.u.m.
1a.u.m = 1.66 * 10 -24 g
Let's take 1 g of hydrogen and calculate the number of hydrogen atoms in this mass (offer students to do this using a calculator).
N n \u003d 1g / (1.66 * 10 -24) g \u003d 6.02 * 10 23
b) O-oxygen
A o \u003d 16a.u.m \u003d 16 * 1.67 * 10 -24 g
N o \u003d 16g / (16 * 1.66 * 10 -24) g \u003d 6.02 * 10 23
c) C-carbon
A c \u003d 12a.u.m \u003d 12 * 1.67 * 10 -24 g
N c \u003d 12g / (12 * 1.66 * 10 -24) g \u003d 6.02 * 10 23
Let's conclude: if we take such a mass of a substance that is equal to the atomic mass in magnitude, but taken in grams, then there will always be (for any substance) 6.02 * 10 23 atoms of this substance.
H 2 O - water
18g / (18 * 1.66 * 10 -24) g \u003d 6.02 * 10 23 water molecules, etc.
N a \u003d 6.02 * 10 23 - Avogadro's number or constant.
Mole - the amount of a substance that contains 6.02 * 10 23 molecules, atoms or ions, i.e. structural units.
There is a mole of molecules, a mole of atoms, a mole of ions.
n is the number of moles, (the number of moles is often referred to as nu),
N is the number of atoms or molecules,
N a = Avogadro's constant.
Kmol \u003d 10 3 mol, mmol \u003d 10 -3 mol.
Show a portrait of Amedeo Avogadro on a multimedia installation and briefly talk about it, or instruct the student to prepare a short report on the life of a scientist.
Lesson 2
Topic "Molar mass of matter"
What is the mass of 1 mole of a substance? (Students can often draw the conclusion themselves.)
The mass of one mole of a substance is equal to its molecular weight, but expressed in grams. The mass of one mole of a substance is called the molar mass and is denoted - M.
Formulas:
M - molar mass,
n is the number of moles,
m is the mass of the substance.
The mass of a mole is measured in g/mol, the mass of a kmol is measured in kg/kmol, and the mass of a mmol is measured in mg/mol.
Fill in the table (tables are distributed).
Substance |
Number of molecules |
Molar mass |
Number of moles |
Mass of matter |
5mol |
||||
H 2 SO 4 |
||||
12 ,0 4*10 26 |
Lesson 3
Topic: Molar volume of gases
Let's solve the problem. Determine the volume of water, the mass of which under normal conditions is 180 g.
Given:
Those. the volume of liquid and solid bodies is calculated through density.
But, when calculating the volume of gases, it is not necessary to know the density. Why?
The Italian scientist Avogadro determined that equal volumes of different gases under the same conditions (pressure, temperature) contain the same number of molecules - this statement is called Avogadro's law.
Those. if under equal conditions V (H 2) \u003d V (O 2), then n (H 2) \u003d n (O 2), and vice versa, if under equal conditions n (H 2) \u003d n (O 2) then the volumes of these gases will be the same. And a mole of a substance always contains the same number of molecules 6.02 * 10 23 .
We conclude - under the same conditions, moles of gases should occupy the same volume.
Under normal conditions (t=0, P=101.3 kPa or 760 mm Hg), moles of any gases occupy the same volume. This volume is called molar.
V m \u003d 22.4 l / mol
1 kmol occupies a volume of -22.4 m 3 / kmol, 1 mmol occupies a volume of -22.4 ml / mmol.
Example 1(Decided on the board):
Example 2(You can ask students to solve):
| Given: | Solution: |
m(H 2) \u003d 20g |
Ask students to complete the table.
Substance |
Number of molecules |
Mass of matter |
Number of moles |
Molar mass |
Volume |
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 FROM .
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) :
