^ Molar mass and molar volume of a substance. Molar mass is the mole mass of a substance. It is calculated through the mass and amount of a substance according to the formula:

Мв = К · Мr (1)

Where: K - coefficient of proportionality, equal to 1 g / mol.

Indeed, for the carbon isotope 12 6 С Ar = 12, and the molar mass of atoms (by the definition of the concept "mol") is 12 g / mol. Consequently, the numerical values ​​of the two masses coincide, which means that K = 1. It follows that the molar mass of a substance, expressed in grams per mole, has the same numerical value as its relative molecular(atomic) weight. So, the molar mass of atomic hydrogen is 1.008 g / mol, molecular hydrogen - 2.016 g / mol, molecular oxygen - 31.999 g / mol.

According to Avogadro's law, the same number of molecules of any gas occupies the same volume under the same conditions. On the other hand, 1 mole of any substance contains (by definition) the same number of particles. Hence it follows that at a certain temperature and pressure, 1 mol of any substance in a gaseous state occupies the same volume.

The ratio of the volume occupied by a substance to its amount is called the molar volume of the substance. Under normal conditions (101.325 kPa; 273 K), the molar volume of any gas is 22,4l / mol(more precisely, Vn = 22.4 l / mol). This statement is true for a gas when other types of interaction of its molecules with each other, except for their elastic collision, can be neglected. These gases are called ideal gases. For imperfect gases, called real gases, the molar volumes are different and differ somewhat from exact value... However, in most cases, the difference affects only the fourth and subsequent significant figures.

Gas volume measurements are usually made under abnormal conditions. To bring the volume of gas to normal conditions, you can use the equation that combines the gas laws of Boyle - Mariotte and Gay - Lussac:

pV / T = p 0 V 0 / T 0

Where: V - gas volume at pressure p and temperature T;

V 0 - gas volume at normal pressure p 0 (101.325 kPa) and temperature T 0 (273.15 K).

The molar masses of gases can also be calculated using the equation of state for an ideal gas - the Clapeyron - Mendeleev equation:

pV = m B RT / M B,

Where: p - gas pressure, Pa;

V is its volume, m 3;

M B is the mass of the substance, g;

M B - its molar mass, g / mol;

T - absolute temperature, TO;

R is a universal gas constant equal to 8.314 J / (mol · K).

If the volume and pressure of the gas are expressed in other units of measurement, then the value of the gas constant in the Clapeyron - Mendeleev equation will take on a different value. It can be calculated by the formula arising from the combined law of the gas state for a mole of a substance under normal conditions for one mole of gas:

R = (p 0 V 0 / T 0)

Example 1. Express in moles: a) 6.0210 21 CO2 molecules; b) 1.2010 24 oxygen atoms; c) 2.0010 23 water molecules. What is the molar mass of these substances?

Solution. A mole is the amount of a substance that contains the number of particles of any given kind, equal to Avogadro's constant. Hence, a) 6.0210 21 i.e. 0.01 mol; b) 1.2010 24, i.e. 2 mol; c) 2.0010 23, i.e. 1/3 mol. The mole mass of a substance is expressed in kg / mol or g / mol. The molar mass of a substance in grams is numerically equal to its relative molecular (atomic) mass, expressed in atomic mass units (amu)

Since the molecular weights of CO 2 and H 2 O and atomic mass oxygen are respectively equal to 44; 18 and 16 amu, then their molar masses are equal: a) 44 g / mol; b) 18 g / mol; c) 16g / mol.

Example 2. Calculate the absolute mass of the sulfuric acid molecule in grams.

Solution. A mole of any substance (see example 1) contains Avogadro's constant N A of structural units (in our example, molecules). The molar mass of H 2 SO 4 is 98.0 g / mol. Therefore, the mass of one molecule is 98 / (6.02 10 23) = 1.63 10 -22 g.

Molar volume- the volume of one mole of a substance, the value obtained from dividing the molar mass by density. It characterizes the packing density of molecules.

Meaning N A = 6.022 ... × 10 23 called Avogadro's number after the Italian chemist Amedeo Avogadro. This is a universal constant for the smallest particles of any substance.

It is this number of molecules that contains 1 mole of oxygen O 2, the same number of atoms in 1 mole of iron (Fe), molecules in 1 mole of water H 2 O, etc.

According to Avogadro's law, 1 mole of ideal gas at normal conditions has the same volume V m= 22.413 996 (39) l... Under normal conditions, most gases are close to ideal, so all reference Information about molar volume chemical elements refers to their condensed phases, unless otherwise stated

Where m-mass, M-molar mass, V - volume.

4. Avogadro's law. Installed 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, we can formulate the concept of the amount of a substance: 1 mole of a substance contains a number of particles equal to 6.02 * 10 23 (called Avogadro's constant)

The consequence of this law is that 1 mole of any gas occupies under normal conditions (P 0 = 101.3 kPa and T 0 = 298K) a volume equal to 22.4 liters.

5. Boyle-Mariotte's law

At a constant temperature, the volume of a given amount of gas is inversely proportional to the pressure under which it is located:

6. Gay-Lussac's law

At constant pressure, the change in gas volume is directly proportional to 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 conditions to another:

P 0, V 0, T 0 - pressure of volume and temperature under normal conditions: P 0 = 760 mm Hg. Art. or 101.3 kPa; T 0 = 273 K (0 0 C)

8. Independent assessment of the value of molecular masses M can be done using the so-called ideal gas equations of state or the Clapeyron-Mendeleev equation :

pV = (m / M) * RT = vRT.(1.1)

where R - gas pressure in a closed system, V- the volume of the system, T - gas mass, 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 normal conditions into equation (1.1):

r = (p V) / (T) = (101.325 kPa 22.4 L) / (1 mol 273K) = 8.31J / mol.K)

Examples of problem solving

Example 1. Bringing the gas volume to normal conditions.



What volume (n.u.) will take up 0.4 × 10 -3 m 3 of gas at 50 0 С and a pressure of 0.954 × 10 5 Pa?

Solution. To bring the gas volume to normal conditions, use general formula combining the laws of Boyle-Mariotte and Gay-Lussac:

pV / T = p 0 V 0 / T 0.

The gas volume (n.a.) is equal to, where T 0 = 273 K; p 0 = 1.013 × 10 5 Pa; T = 273 + 50 = 323 K;

M 3 = 0.32 × 10 -3 m 3.

At (n.o.), the gas occupies a volume equal to 0.32 × 10 -3 m 3.

Example 2. Calculation of the relative density of a gas by its molecular weight.

Calculate the density of ethane C 2 H 6 in terms of hydrogen and air.

Solution. It follows from Avogadro's law that the relative density of one gas in another is equal to the ratio of molecular masses ( M h) of these gases, i.e. D = M 1 / M 2... If M 1 C2H6 = 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 gas mixture by relative density.

Calculate the average molecular weight of a gas mixture of 80% methane and 20% oxygen (by volume) using the relative hydrogen densities of these gases.

Solution. Calculations are often 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. She will be more density methane but less density oxygen:

80D H2 - 640 = 320 - 20 D H2; D H2 = 9.6.

The hydrogen density of this gas mixture is 9.6. average molecular weight of a 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- gas mass; M- molar mass of gas; R- molar (universal) gas constant, the value of which is determined adopted units measurements.

If the pressure is measured in Pa, and the volume in m 3, then R= 8.3144 × 10 3 J / (kmol × K).

: V = n * Vm, where V is the volume of the gas (l), n is the amount of substance (mol), Vm is the molar volume of the gas (l / mol), at normal (n.o.) it is a standard value and is equal to 22, 4 l / mol. It so happens that in the condition there is no amount of substance, but there is a mass of a certain substance, then we do this: n = m / M, where m is the mass of the substance (g), M is the molar mass of the substance (g / mol). We find the molar mass according to the table of D.I. Mendeleev: under each element is its atomic mass, we add all the masses and we get what we need. But such tasks are quite rare, usually they are present in the tasks. The solution to such problems is slightly changed in this regard. Let's look at an example.

What volume of hydrogen will be released under normal conditions if aluminum weighing 10.8 g is dissolved in an excess of hydrochloric acid.

If we are dealing with a gas system, then the following formula takes place: q (x) = V (x) / V, where q (x) (phi) is the fraction of the component, V (x) is the volume of the component (l), V - system volume (l). To find the volume of a component, we obtain the formula: V (x) = q (x) * V. And if you need to find the volume of the system, then: V = V (x) / q (x).

note

There are other formulas for finding the volume, but if you need to find the volume of gas, only the formulas given in this article will do.

Sources:

  • "A manual on chemistry", G.P. Khomchenko, 2005.
  • how to find the scope of work
  • Find the volume of hydrogen in the electrolysis of a ZnSO4 solution

A gas in which the interaction between molecules is negligible is considered ideal. In addition to pressure, the state of a gas is characterized by temperature and volume. The relationships between these parameters are displayed in gas laws.

Instructions

The gas pressure is directly proportional to its temperature, the amount of substance, and inversely proportional to the volume of the vessel occupied by the gas. The proportional factor is the universal gas constant R, approximately equal to 8.314. It is measured in joules divided by mole and by.

This position forms the mathematical relationship P = νRT / V, where ν is the amount of substance (mol), R = 8.314 is the universal gas constant (J / mol K), T is the gas temperature, V is the volume. The pressure is expressed in. It can be expressed and, while 1 atm = 101.325 kPa.

The considered dependence is a consequence of the Mendeleev-Clapeyron equation PV = (m / M) RT. Here m is the mass of the gas (g), M is its molar mass (g / mol), and the fraction m / M gives as a result the amount of substance ν, or the number of moles. The Mendeleev-Clapeyron equation is valid for all gases that can be considered. This is a physical-gas law.

One of the basic units in the International System of Units (SI) is the unit of the amount of substance is the mole.

Moth – 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 in 0.012 kg (12 g) of the carbon isotope 12 WITH .

Considering that the value of the absolute atomic mass for carbon is m(C) = 1.99 10  26 kg, you can calculate the number of carbon atoms 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 in the amount of one mole is 6.02 10 23 and 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 mol.

The molar mass is designated by the letter M and has the dimension [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:

Мr (Н 2 О) = 2Аr (Н) + Аr (O) = 2 ∙ 1 + 16 = 18 amu

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. In water, the amount of substance is 1 mol, contains 2 mol of hydrogen atoms and one mol of oxygen atoms.

1.3.4. The relationship between the mass of a substance and its amount

Knowing the mass of a substance and its chemical formula, and hence the value of its molar mass, it is possible to determine the amount of a substance and, conversely, knowing the amount of a substance, it is possible to determine its mass. For such calculations, you should use the formulas:

where ν is the amount of substance, [mol]; m- mass of 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:

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

2) the 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 amount

Under normal conditions (n.o.), i.e. at pressure R equal to 101325 Pa (760 mm Hg), and a 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 normal conditions is called molar volumegas and has a 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 is the volume of the gaseous substance [l]; V mol = 22.4 l / mol.

And, conversely, knowing the volume ( V) of a gaseous substance under normal conditions, you can calculate its amount (ν) :