Atomic mass of a substance. Relative atomic mass of chemical elements

The masses of atoms and molecules are very small, so it is convenient to choose the mass of one of the atoms as a unit of measurement and express the masses of the remaining atoms relative to it. This is exactly what the founder of atomic theory, Dalton, did, who compiled a table of atomic masses, taking the mass of the hydrogen atom as one.

Until 1961, in physics, 1/16 of the mass of the oxygen atom 16 O was taken as an atomic mass unit (amu), and in chemistry - 1/16 of the average atomic mass of natural oxygen, which is a mixture of three isotopes. The chemical unit of mass was 0.03% larger than the physical one.

Currently accepted for physics and chemistry one system measurements. The standard unit of atomic mass is 1/12 of the mass of a 12 C carbon atom.

1 amu = 1/12 m(12 C) = 1.66057×10 -27 kg = 1.66057×10 -24 g.

DEFINITION

Relative atomic mass of an element (A r) is a dimensionless quantity equal to the ratio of the average mass of an atom of an element to 1/12 of the mass of an atom of 12 C.

When calculating relative atomic mass, the abundance of isotopes of elements in the earth's crust is taken into account. For example, chlorine has two isotopes 35 Cl (75.5%) and 37 Cl (24.5%). The relative atomic mass of chlorine is:

A r (Cl) = (0.755×m(35 Cl) + 0.245×m(37 Cl)) / (1/12×m(12 C) = 35.5.

From the definition of relative atomic mass it follows that the average absolute mass of an atom is equal to the relative atomic mass multiplied by amu:

m(Cl) = 35.5 × 1.66057 × 10 -24 = 5.89 × 10 -23 g.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

To measure the mass of an atom, relative atomic mass is used, which is expressed in atomic mass units (amu). Relative molecular weight is made up of the relative atomic masses of substances.

Concepts

To understand what relative atomic mass is in chemistry, you should understand that the absolute mass of an atom is too small to be expressed in grams, much less in kilograms. Therefore in modern chemistry 1/12 of the mass of carbon is taken as an atomic mass unit (amu). Relative atomic mass is equal to the ratio of the absolute mass to 1/12 of the absolute mass of carbon. In other words, relative mass reflects how many times the mass of an atom of a particular substance exceeds 1/12 the mass of a carbon atom. For example, the relative mass of nitrogen is 14, i.e. The nitrogen atom contains 14 a. e.m. or 14 times more than 1/12 of a carbon atom.

Rice. 1. Atoms and molecules.

Among all the elements, hydrogen is the lightest, its mass is 1 unit. The heaviest atoms have a mass of 300 a. eat.

Molecular mass is a value indicating how many times the mass of a molecule exceeds 1/12 of the mass of carbon. Also expressed in a. e.m. The mass of a molecule is made up of the mass of atoms, therefore, to calculate the relative molecular mass it is necessary to add up the masses of the atoms of the substance. For example, the relative molecular weight of water is 18. This value is the sum of the relative atomic masses of two hydrogen atoms (2) and one oxygen atom (16).

Rice. 2. Carbon in the periodic table.

As you can see, these two concepts have several common characteristics:

• the relative atomic and molecular masses of a substance are dimensionless quantities;
• relative atomic mass is designated Ar, molecular mass - Mr;
• The unit of measurement is the same in both cases - a. eat.

Molar and molecular masses are the same numerically, but differ in dimension. Molar mass is the ratio of the mass of a substance to the number of moles. It reflects the mass of one mole, which is equal to Avogadro’s number, i.e. 6.02 ⋅ 10 23 . For example, 1 mole of water weighs 18 g/mol, and M r (H 2 O) = 18 a. e.m. (18 times heavier than one atomic mass unit).

How to calculate

To express relative atomic mass mathematically, one should determine that 1/2 part of carbon or one atomic mass unit is equal to 1.66⋅10 −24 g. Therefore, the formula for relative atomic mass is as follows:

A r (X) = m a (X) / 1.66⋅10 −24,

where m a is the absolute atomic mass of the substance.

Relative atomic mass chemical elements is indicated in the periodic table of Mendeleev, so it does not need to be calculated independently when solving problems. Relative atomic masses are usually rounded to whole numbers. The exception is chlorine. The mass of its atoms is 35.5.

It should be noted that when calculating the relative atomic mass of elements that have isotopes, their average value is taken into account. Atomic mass in this case is calculated as follows:

A r = ΣA r,i n i ,

where A r,i is the relative atomic mass of isotopes, n i is the content of isotopes in natural mixtures.

For example, oxygen has three isotopes - 16 O, 17 O, 18 O. Their relative mass is 15.995, 16.999, 17.999, and their content in natural mixtures is 99.759%, 0.037%, 0.204%, respectively. Dividing the percentages by 100 and substituting the values, we get:

A r = 15.995 ∙ 0.99759 + 16.999 ∙ 0.00037 + 17.999 ∙ 0.00204 = 15.999 amu

Referring to the periodic table, it is easy to find this value in the oxygen cell.

Rice. 3. Periodic table.

Relative molecular mass is the sum of the masses of the atoms of a substance:

When determining the relative molecular weight value, symbol indices are taken into account. For example, calculating the mass of H 2 CO 3 is as follows:

M r = 1 ∙ 2 + 12 + 16 ∙ 3 = 62 a. eat.

Knowing the relative molecular weight, you can calculate the relative density of one gas from the second, i.e. determine how many times one gaseous substance is heavier than the second. To do this, use the equation D (y) x = M r (x) / M r (y).

What have we learned?

From the 8th grade lesson we learned about relative atomic and molecular mass. The unit of relative atomic mass is taken to be 1/12 of the mass of carbon, equal to 1.66⋅10 −24 g. To calculate the mass, it is necessary to divide the absolute atomic mass of the substance by the atomic mass unit (amu). The value of the relative atomic mass is indicated in the periodic table of Mendeleev in each cell of the element. The molecular mass of a substance is the sum of the relative atomic masses of the elements.

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One of the main characteristics of any chemical element is its relative atomic mass.

(An atomic mass unit is 1/12 of the mass of a carbon atom, the mass of which is taken to be 12 amu and is1,66 10 24 G.

By comparing the masses of atoms of elements per amu, the numerical values ​​of the relative atomic mass (Ar) are found.

The relative atomic mass of an element shows how many times the mass of its atom is greater than 1/12 the mass of a carbon atom.

For example, for oxygen Ar (O) = 15.9994, and for hydrogen Ar (H) = 1.0079.

For molecules of simple and complex substances, determine relative molecular weight, which is numerically equal to the sum of the atomic masses of all atoms that make up the molecule. For example, the molecular weight of water is H2O

Mg (H2O) = 2 1.0079 + 1 15.9994 = 18.0153.

Avogadro's law

In chemistry, along with units of mass and volume, a unit of quantity of a substance is used, called the mole.

!MOL (v) - a unit of measurement of the amount of a substance containing as many structural units (molecules, atoms, ions) as there are atoms contained in 0.012 kg (12 g) of the carbon isotope “C’’.

This means that 1 mole of any substance contains the same number of structural units, equal to 6,02 10 23 . This quantity is called Avogadro's constant(designation NA, dimension 1/mol).

The Italian scientist Amadeo Avogadro put forward a hypothesis in 1811, which was later confirmed by experimental data and was subsequently called Avogadro's law. He drew attention to the fact that all gases are equally compressed (Boyle-Marriott's law) and have the same coefficients of thermal expansion (Gay-Lussac's law). In this regard, he suggested that:

equal volumes of different gases under the same conditions contain the same number of molecules.

Under the same conditions (usually we talk about normal conditions: the absolute pressure is 1013 millibars and the temperature is 0 ° C) the distance between the molecules of all gases is the same, and the volume of the molecules is negligible. Considering all of the above, we can make the following assumption:

!if equal volumes of gases under the same conditions contain the same number of molecules, then the masses containing the same number of molecules must have the same volumes.

In other words,

Under the same conditions, 1 mole of any gas occupies the same volume. Under normal conditions, 1 mole of any gas occupies a volume v, equal to 22.4 l. This volume is calledmolar volume of gas (dimension l/mol or m³ /mol).

The exact value of the molar volume of gas under normal conditions (pressure 1013 millibars and temperature 0 ° C) is 22.4135 ± 0.0006 l/mol. Under standard conditions (t=+15° C, pressure = 1013 mbar) 1 mole of gas occupies a volume of 23.6451 liters, and att=+20° C and a pressure of 1013 mbar, 1 mole occupies a volume of about 24.2 liters.

In numerical terms, molar mass coincides with the masses of atoms and molecules (in amu) and with relative atomic and molecular masses.

Consequently, 1 mole of any substance has a mass in grams that is numerically equal to the molecular mass of this substance, expressed in atomic mass units.

For example, M(O2) = 16 a. e.m. 2 = 32 a. e.m., thus, 1 mole of oxygen corresponds to 32 g. The densities of gases measured under the same conditions are referred to as their molar masses. Since when transporting liquefied gases on gas carriers the main object of practical problems are molecular substances (liquids, vapors, gases), the main sought-for quantities will be molar mass M(g/mol), amount of substance v in moles and mass T substances in grams or kilograms.

Knowing the chemical formula of a particular gas, you can solve some practical problems that arise when transporting liquefied gases.

Example 1. A deck tank contains 22 tons of liquefied ethylene (WITH2 N4 ). It is necessary to determine whether there is enough cargo on board to blow through three cargo tanks with a volume of 5000 m 3 each, if after blowing the temperature of the tanks is 0 ° C and the pressure is 1013 millibars.

1. Determine the molecular weight of ethylene:

M = 2 12.011 + 4 1.0079 = 28.054 g/mol.

2. Calculate the density of ethylene vapor under normal conditions:

ρ = M/V = 28.054: 22.4 = 1.232 g/l.

3. Find the volume of cargo vapor under normal conditions:

22∙10 6: 1.252= 27544 m3.

The total volume of cargo tanks is 15,000 m3. Consequently, there is enough cargo on board to purge all cargo tanks with ethylene vapor.

Example 2. It is necessary to determine how much propane (WITH3 N8 ) will be required for purging cargo tanks with a total capacity of 8000 m 3, if the temperature of the tanks is +15 ° C, and the pressure of propane vapor in the tank after the end of purging will not exceed 1013 millibars.

1. Determine the molar mass of propane WITH3 N8

M = 3 12,011 + 8 1,0079 = 44.1 g/mol.

2. Let’s determine the propane vapor density after purging the tanks:

ρ = M: v = 44.1: 23.641 = 1.865 kg/m 3.

3. Knowing the vapor density and volume, we determine the total amount of propane required to purge the tank:

m = ρ v = 1.865 8000 = 14920 kg ≈ 15 t.

The masses of atoms and molecules are very small, so it is convenient to choose the mass of one of the atoms as a unit of measurement and express the masses of the remaining atoms relative to it. This is exactly what the founder of atomic theory, Dalton, did, who compiled a table of atomic masses, taking the mass of the hydrogen atom as one.

Until 1961, in physics, 1/16 of the mass of the 16O oxygen atom was taken as an atomic mass unit (amu), and in chemistry – 1/16 of the average atomic mass of natural oxygen, which is a mixture of three isotopes. The chemical unit of mass was 0.03% larger than the physical one.

Currently, a unified measurement system has been adopted in physics and chemistry. 1/12 of the mass of a 12C carbon atom was chosen as the standard unit of atomic mass.

1 amu = 1/12 m(12С) = 1.66057×10-27 kg = 1.66057×10-24 g.

When calculating relative atomic mass, the abundance of isotopes of elements in the earth's crust is taken into account. For example, chlorine has two isotopes 35Сl (75.5%) and 37Сl (24.5%). The relative atomic mass of chlorine is:

Ar(Cl) = (0.755×m(35Сl) + 0.245×m(37Сl)) / (1/12×m(12С) = 35.5.

From the definition of relative atomic mass it follows that the average absolute mass of an atom is equal to the relative atomic mass multiplied by amu:

m(Cl) = 35.5 × 1.66057 × 10-24 = 5.89 × 10-23 g.

Examples of problem solving

Relative atomic and molecular masses

This calculator is designed to calculate the atomic mass of elements.

Atomic mass(also called relative atomic mass) Is the value of the mass of one atom of a substance. Relative atomic mass is expressed in atomic mass units. Relative atomic mass distinctive(True) weight atom. At the same time, the actual mass of an atom is too small and therefore unsuitable for practical use.

The atomic mass of a substance affects the amount protons And neutrons in the nucleus of an atom.

The electron mass is ignored since it is very small.

To determine the atomic mass of a substance, you must enter the following information:

• Number of protons- how many protons are in the nucleus of the substance;
• Number of neutrons— how many neutrons are in the nucleus of a substance.

Based on this data, the calculator will calculate the atomic mass of the substance, expressed in atomic mass units.

Table of chemical elements and their atomic mass hydrogen H 1,0079 nickel There is no 58,70 helium He 4,0026 baker Cu 63,546 lithium Li 6941 zinc Zn 65,38 beryllium be 9,01218 Gaul Georgia 69,72 Bor IN 10,81 Germany G.E. 72,59 carbon WITH 12,011 arsenic How 74,9216 nitrogen N 14,0067 selenium are 78,96 oxygen O 15,9994 Bromine bromine 79904 fluoride F 18,99840 krypton Cr 83,80 neon Not 20,179 rubidium Rb 85,4678 sodium on 22,98977 strontium erased 87,62 magnesium mg 24,305 yttrium Y 88,9059 aluminum Al 26,98154 zirconium Zr 91,22 niobium Nb 92,9064 Nobel Not 255 molybdenum Mo 95,94 Lawrence Lr 256 technetium Ts 98,9062 Kurchatovy ka 261 ruthenium Ru 101,07 * * * rhodium rhesus 102.9055 * * * palladium Pd 106,4 * * * silver Ag 107 868 * * * silicone You 28,086 cadmium CD 112,40 phosphorus P 30,97376 India 114,82 sulfur 32,06 tin Sn 118,69 chlorine Cl 35,453 antimony Sb 121,75 argon Arkansas 39,948 tellurium these 127,60 potassium TO 39,098 iodine I 126,904 calcium California 40,08 xenon Xe 131,30 scandium South Carolina 44,9559 cesium Cs 132.9054 Titanium these 47,90 barium ba 137,34 vanadium 50,9414 lanthanum la 138.9055 chromium Cr 51,996 cerium Ce 140,12 manganese Minnesota 54,9380 Praseodim Pr 140.9077 iron Fe 55,847 I don't Nd 144,24 cobalt Co. 58,9332 promethium evenings Samaria Sm 150,4 bismuth would 208.9804 europium European Union 151,96 Polonium after 209 gadolinium G-d 157,25 ASTAT V 210 terbium Tb 158.9254 radon Rn 222 dysprosium du $ 16,50 France fr 223 Holmium Hey 164.9304 radius R 226.0254 erbium Er 167,26 actinium alternating current 227 thulium Tm 168.9342 thorium th 232.0381 ytterbium Yb 173,04 protactinium Pennsylvania 231.0359 Lutetia Lu 174,97 Uranus U 238,029 hafnium high frequency 178,49 neptunium Np 237.0482 tantalum This 180.9479 plutonium Pu 244 tungsten W 183,85 America Am 243 rhenium re 186,207 curie cm 247 osmium OS 190,2 Berkeley B.K. 247 iridium infrared 192,22 California compare 251 platinum Pt 195,09 Einstein es 254 gold Au 196.9665 Fermi Fm 257 mercury mercury 200,59 Mendelevy Maryland 258 thallium Tl 204,37 * * * Lead Pb 207,2 * * *

Relative atomic mass of an element Task status: Determine the mass of an oxygen molecule. Task no. 4.1.2 from the “Collection of problems in preparing upcoming exams in physics at USPTU” information: Solution: Consider a molecular oxygen molecule \(\nu\) (arbitrary number). Let us remember that the oxygen formula is O2. To find the mass (\m) of a given amount of oxygen, the molecular mass of oxygen\(M\) is multiplied by the number of moles\(\nu\). Using the periodic table, it is easy to establish that the molar mass of oxygen is \(M\) 32 g/mol or 0.032 kg/mol. In one mol, the number of avogadro molecules \(N_A\) and v\(\nu\) mol - v\(\nu\) is sometimes greater, i.e. To find the mass of one molecule \(m_0\), total weight\(t\) must be divided by the number of molecules \(N\). \ [(m_0) = \frac (m) (N)\] \ [(m_0) = \frac ((\nu \cdot M)) ((\nu \cdot (N_A)))\] \ ((M_0) = \frac (M) (((N_A))) \] Avogadro's number (N_A1) is a tabular value equal to 6.022 1023 mol-1. We perform calculations: \[(M_0) = \frac ((0.032)) ((6.022\cdot ((10) * (23)))) = 5.3\cdot (10^(-26))\; = 5.3 kg\cdot(10^(-23))\; r\] Answer: 5.3 · 10-23 g. If you don't understand the solution and if you have any questions or found a bug, you can leave a comment below. Atoms are very small and very small. If we express the mass of an atom of a chemical element in grams, then it will be a number for which the decimal point is more than twenty zeros. Therefore, measuring the mass of atoms in grams is inappropriate. However, if we take a very small mass per unit, all other small masses can be expressed as a ratio between that unit. The unit of measurement for atomic mass is 1/12 of the mass of a carbon atom. It is called 1/12 of the mass of a carbon atom atomic mass(Ae. Atomic mass formula Relative atomic mass the value is equal to the ratio of the actual mass of an atom of a particular chemical element to 1/12 of the actual mass of a carbon atom. This is an infinite value, since the two masses are separated. Ar = mathematics. / (1/12) mug. Nevertheless, absolute atomic mass equal to a relative value and has a measurement unit amu. This means that relative atomic mass shows how many times the mass of a given atom is greater than 1/12 of a carbon atom. If an Ar atom = 12, then its mass is 12 times greater than 1/12 the mass of a carbon atom or, in other words, 12 atomic mass units. This can only be for carbon (C). On the hydrogen atom (H) Ar = 1. This means that its mass is equal to the mass of 1/12 parts of the mass of the carbon atom. For oxygen (O), the relative atomic mass is 16 amu. This means that an oxygen atom is 16 times larger than a carbon atom, it has 16 atomic mass units. The lightest element is hydrogen. Its mass is about 1 amu. On the heaviest atoms the mass approaches 300 amu. Typically, for each chemical element, its value is the absolute mass of the atoms, expressed as a. For example. The meaning of atomic mass units is written in the periodic table. Concept used for molecules relative molecular weight (g). Relative molecular weight indicates how many times the mass of a molecule is greater than 1/12 the mass of a carbon atom. However, since the mass of a molecule is equal to the sum of the masses of its atomic atoms, the relative molecular mass can be found simply by adding the relative masses of those atoms. For example, a water molecule (H2O) contains two hydrogen atoms with Ar = 1 and one oxygen atom with Ar = 16. Therefore, gentleman (H2O) = 18. Many substances have a non-molecular structure, such as metals. In this case, their relative molecular mass is equal to their relative atomic mass. Chemistry is called a significant amount mass fraction of a chemical element in a molecule or substance. It shows the relative molecular weight of that element. For example, in water, hydrogen has 2 parts (as both atoms) and oxygen 16. This means that when hydrogen is mixed with 1 kg and 8 kg of oxygen, they react without a residue. The mass fraction of hydrogen is 2/18 = 1/9, and the oxygen content is 16/18 = 8/9. Microbalance otherwise support, atomic equilibrium(English microbial or English nanotubes) is a term referring to: a large group of analytical instruments whose accuracy measures mass from one to several hundred micrograms; a special high-precision instrument that allows you to measure the mass of objects down to 0.1 ng (nanovesy). description One of the first references to the microglob is in 1910, when William Ramsay was informed of the extent to which it had developed, allowing the weight range of 0.1 mm3 of body to be determined to be 10-9 g (1 ng). The term microbial is now more commonly used to refer to devices that can measure and detect mass changes in the microgram range (10-6 grams). Microbiologists have become common practice in modern research and industrial laboratories and are available in different versions with varying sensitivities and associated costs. At the same time, measurement techniques are being developed in the nanogram field. chemistry. how to find relative atomic mass? When we talk about measuring mass at the nanogram level, which is important for measuring the mass of atoms, molecules or clusters, we first consider mass spectrometry. In this case, it should be borne in mind that measuring mass using this method implies the need to convert the weighed objects into ions, which is sometimes very undesirable. This is not necessary when using another practically important and widely used instrument for the accurate measurement of mass quartz microbes, the mechanism of action of which is described in the corresponding article. links Jensen K., Kwanpyo Kim, Zettl A. Nanomechan atomic resolution atomic detector // arXiv: 0809.2126 (September 12, 2008).

Absolute masses of atoms One of the fundamental properties of atoms is their mass. Absolute (true) mass of an atom– the value is extremely small. It is impossible to weigh atoms on a balance because such precise scales do not exist. Their masses were determined using calculations. For example, the mass of one hydrogen atom is 0.000 000 000 000 000 000 000 001 663 grams! The mass of a uranium atom, one of the heaviest atoms, is approximately 0.000 000 000 000 000 000 000 4 grams. Writing and reading these numbers is not easy; You can make a mistake by missing a zero or adding an extra one. There is another way to write it - in the form of a product: 4 ∙ 10−22 (22 is the number of zeros in the previous number). The exact mass of the uranium atom is 3.952 ∙ 10−22 g, and the hydrogen atom, the lightest among all atoms, is 1.673 ∙ 10−24 g. It is inconvenient to carry out calculations with small numbers. Therefore, instead of the absolute masses of atoms, their relative masses are used.

Relative atomic mass

Ar(O) = 16; Ar(Na) = 23; Ar(P) = 31. The relative atomic mass of chlorine is usually written as 35.5! Ar(Cl) = 35.5

• Relative atomic masses are proportional to the absolute masses of atoms
• The standard for determining relative atomic mass is 1/12 of the mass of a carbon atom
• 1 amu = 1.662 ∙ 10−24 g
• Relative atomic mass is denoted by Ar
• For calculations, the values ​​of relative atomic masses are rounded to whole numbers, with the exception of chlorine, for which Ar = 35.5
• Relative atomic mass has no units of measurement