Finding molar volume. Volume of one mole of gas under normal conditions

Molar volume of gas equal to the ratio volume of gas to the amount of substance of this gas, i.e.

V m = V(X) / n(X),

where V m is the molar volume of gas - constant for any gas under given conditions;

V(X) – volume of gas X;

n(X) – amount of gas substance X.

Molar volume of gases at normal conditions(normal pressure p n = 101,325 Pa ≈ 101.3 kPa and temperature T n = 273.15 K ≈ 273 K) is V m = 22.4 l/mol.

Ideal gas laws

In calculations involving gases, it is often necessary to switch from these conditions to normal ones or vice versa. In this case, it is convenient to use the formula following from the combined gas law of Boyle-Mariotte and Gay-Lussac:

pV / T = p n V n / T n

Where p is pressure; V - volume; T - temperature on the Kelvin scale; the index “n” indicates normal conditions.

Volume fraction

The composition of gas mixtures is often expressed using the volume fraction - the ratio of the volume of a given component to the total volume of the system, i.e.

φ(X) = V(X) / V

where φ(X) - volume fraction component X;

V(X) - volume of component X;

V is the volume of the system.

Volume fraction is a dimensionless quantity; it is expressed in fractions of a unit or as a percentage.

Example 1. What volume will ammonia weighing 51 g occupy at a temperature of 20°C and a pressure of 250 kPa?

Example 2. Determine the volume that a gas mixture containing hydrogen, weighing 1.4 g, and nitrogen, weighing 5.6 g, will occupy under normal conditions.

Law of volumetric relations

How to solve a problem using the “Law of Volumetric Relations”?

Law of Volume Ratios: The volumes of gases involved in a reaction are related to each other as small integers equal to the coefficients in the reaction equation.

The coefficients in the reaction equations show the numbers of volumes of reacting and formed gaseous substances.

Example. Calculate the volume of air required to burn 112 liters of acetylene.

1. We compose the reaction equation:

2. Based on the law of volumetric relations, we calculate the volume of oxygen:

112 / 2 = X / 5, from where X = 112 5 / 2 = 280l

3. Determine the volume of air:

V(air) = V(O 2) / φ(O 2)

V(air) = 280 / 0.2 = 1400 l.

P1V1=P2V2, or, which is the same, PV=const (Boyle-Mariotte law). At constant pressure The ratio of volume to temperature remains constant: V/T=const (Gay-Lussac's law). If we fix the volume, then P/T=const (Charles’ law). Combining these three laws gives a universal law which states that PV/T=const. This equation was established French physicist B. Clapeyron in 1834.

The value of the constant is determined only by the amount of substance gas. DI. Mendeleev derived an equation for one mole in 1874. So it is the value of the universal constant: R=8.314 J/(mol∙K). So PV=RT. In the case of an arbitrary quantity gasνPV=νRT. The amount of a substance itself can be found from mass to molar mass: ν=m/M.

Molar mass is numerically equal to relative molecular mass. The latter can be found from the periodic table; it is indicated in the cell of the element, as a rule, . The molecular weight is equal to the sum molecular weights elements included in it. In the case of atoms of different valences, an index is required. On at mer, M(N2O)=14∙2+16=28+16=44 g/mol.

Normal conditions for gases at It is commonly assumed that P0 = 1 atm = 101.325 kPa, temperature T0 = 273.15 K = 0°C. Now you can find the volume of one mole gas at normal conditions: Vm=RT/P0=8.314∙273.15/101.325=22.413 l/mol. This tabular value is the molar volume.

Under normal conditions conditions quantity relative to volume gas to molar volume: ν=V/Vm. For arbitrary conditions you need to use the Mendeleev-Clapeyron equation directly: ν=PV/RT.

Thus, to find the volume gas at normal conditions, you need the amount of substance (number of moles) of this gas multiply by the molar volume equal to 22.4 l/mol. Reverse operation you can find the amount of a substance from a given volume.

To find the volume of one mole of a substance in a solid or liquid state, find its molar mass and divide by its density. One mole of any gas under normal conditions has a volume of 22.4 liters. If conditions change, calculate the volume of one mole using the Clapeyron-Mendeleev equation.

You will need

• Periodic table of Mendeleev, table of density of substances, pressure gauge and thermometer.

Instructions

Determining the volume of one mole or solid
Define chemical formula solid or liquid that is being studied. Then, using periodic table Find Mendeleev atomic masses elements that are included in the formula. If one is included in the formula more than once, multiply its atomic mass by that number. Add up the atomic masses and get the molecular mass of which it is composed solid or liquid. It will be numerically equal to the molar mass measured in grams per mole.

Using the table of substance densities, find this value for the material of the body or liquid being studied. After this, divide the molar mass by the density of the substance, measured in g/cm³ V=M/ρ. The result is the volume of one mole in cm³. If the substance remains unknown, it will be impossible to determine the volume of one mole of it.

: V = n*Vm, where V is the volume of gas (l), n is the amount of substance (mol), Vm is the molar volume of gas (l/mol), at normal (norm) is a standard value and is equal to 22, 4 l/mol. It happens that in a condition there is no quantity of a substance, but there is mass a certain substance, then we do this: n = m/M, where m is the mass of the substance (g), M is molar mass substances (g/mol). We find the molar mass using the table D.I. Mendeleev: under each element is its atomic mass, add up all the masses and get what we need. But such tasks are quite rare, usually present in the tasks. The solution to such problems changes slightly. 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 excess hydrochloric acid.

If we are dealing with a gas system, then the following formula holds: 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).

Please note

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

Sources:

• "Chemistry Manual", G.P. Khomchenko, 2005.
• how to find the amount of work
• Find the volume of hydrogen during the electrolysis of a ZnSO4 solution

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

Instructions

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

This position forms the mathematical dependence 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. Pressure is expressed in . It can be expressed by and , with 1 atm = 101.325 kPa.

The dependence considered 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 the total amount of substance ν, or the number of moles. The Mendeleev-Clapeyron equation is valid for all gases that can be considered. This is the physical gas law.

Gases are the most simple object for research, therefore their properties and reactions between gaseous substances have been studied most fully. To make it easier for us to understand the decision rules calculation tasks,based on equations 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 laid down the law volumetric relations:

For example, 1 liter of chlorine connects with 1 liter of hydrogen , producing 2 liters of hydrogen chloride ; 2 l sulfur oxide (IV) connect with 1 liter of oxygen, forming 1 liter of sulfur oxide (VI).

This law allowed the Italian scientist assume that 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 hydrogen chloride molecules. 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 original gases.
Thus, volumetric relations are easily explained if we proceed from the idea of ​​​​the diatomic nature of 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 put forward a hypothesis, which was subsequently confirmed by experimental data, and therefore became known as Avogadro’s law:

An important consequence follows from Avogadro's law 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 conditions, (n.s.) i.e. temperature 273К (О°С) 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.

Hence:

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 system substance;n - the amount of substance in the system. Example entry:V m gas (Well.)=22.4 l/mol.

Based on Avogadro's law, the molar masses of gaseous substances are determined. How more mass gas molecules, the greater the mass of the same volume of gas. Equal volumes of gases under the same conditions contain same number molecules, and therefore moles of gases. Mass ratio equal volumes gases is equal to the ratio of their molar masses:

Where m 1 - mass of a certain volume of the first gas; m 2 — mass of the same volume of the second gas; M 1 And M 2 - molar masses of the first and second gases.

Typically, gas density is determined in relation to the lightest gas - hydrogen (denoted D H2 ). The molar mass of hydrogen is 2g/mol . Therefore we get.

Molecular mass of a substance in gaseous state equal to its double hydrogen density.

Often the density of a gas is 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 29 g/mol. In this case, the molar mass is determined by the expression M = 29D B .

Determination of molecular masses showed that molecules of simple gases consist of two atoms (H2, F2,Cl2, O2 N2) , and molecules of inert gases are made from one atom (He, Ne, Ar, Kr, Xe, Rn). For noble gases, “molecule” and “atom” are equivalent.

Boyle-Mariotte Law: at constant temperature volume given quantity gas is inversely proportional to the pressure it is under.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 scale TO (kelvin)

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 under other conditions is known. 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 =22.4 l/mol) .

If the mass and quantity of a gas are known, but it is necessary to calculate its volume, or vice versa, use Mendeleev-Clayperon equation:

Where n - amount of gas substance, mol; m — mass, g; M - molar mass of gas, g/iol ; R — universal gas constant. R = 8.31 J/(mol*K)

In order to find out the composition of any gaseous substances, you must be able to operate with concepts such as molar volume, molar mass and density of the substance. In this article, we will look at what molar volume is and how to calculate it?

Quantity of substance

Quantitative calculations are carried out in order to actually carry out a particular process or to find out the composition and structure of a certain substance. These calculations are inconvenient to perform with absolute values the mass of atoms or molecules because they are very small. Relative atomic masses also cannot be used in most cases, since they are not related to generally accepted measures of mass or volume of a substance. Therefore, the concept of quantity of a substance was introduced, which is denoted Greek letter v (nude) or n. The amount of a substance is proportional to the number of substances contained in the substance structural units(molecules, atomic particles).

The unit of quantity of a substance is the mole.

A mole is an amount of substance that contains the same number of structural units as there are atoms in 12 g of carbon isotope.

The mass of 1 atom is 12 a. e.m., therefore the number of atoms in 12 g of carbon isotope is equal to:

Na= 12g/12*1.66057*10 to the power-24g=6.0221*10 to the power of 23

The physical quantity Na is called Avogadro's 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 using 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 international system Measurement of the molar volume of gaseous substances is carried out in cubic meters per mole (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 mole always occupies the same volume (if the same parameters are met).

The volume of gas depends on temperature and pressure, so when calculating, you 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 mole of gas under normal conditions is always the same and equal to 22.41 dm 3 /mol. This volume is called molar volume 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: