Shows atomic mass. How to Calculate Atomic Mass

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 the atomic theory Dalton did, who compiled a table of atomic masses, taking the mass of a hydrogen atom as a unit.

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

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

1 amu \u003d 1/12 m (12 C) \u003d 1.66057 × 10-27 kg \u003d 1.66057 × 10-24 g.

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

Ar(Cl) = (0.755xm(35Cl) + 0.245xm(37Cl)) / (1/12xm(12C) = 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 times the 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 units of atomic mass. 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 mass of the electrons is ignored as 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 a substance;
• Number of neutrons How many neutrons are in the nucleus of matter.

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

Table of chemical elements and their atomic mass hydrogen H 1,0079 nickel There is no 58,70 helium is he 4,0026 baker Cu 63,546 lithium Li 6941 zinc Zn 65,38 beryllium be 9,01218 Gaul Georgia 69,72 Bor AT 10,81 Germany G.E. 72,59 carbon With 12,011 arsenic as 74,9216 nitrogen N 14,0067 selenium are 78,96 oxygen about 15,9994 Bromine bromine 79904 fluoride F 18,99840 krypton Cr 83,80 neon not 20,179 rubidium Rb 85,4678 sodium on the 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 do not 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 in 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 the oxygen molecule. task number. 4.1.2 from the "Collection of problems of preparation for the upcoming exams in physics of USPTU" information: Decision: Consider a molecular oxygen molecule \(\nu\) (arbitrary number). Recall that the oxygen formula is O2. To find the mass (\m) of a given amount of oxygen, the molecular weight 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 mole, 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 \), the total mass \ (m \) 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 If you don't understand the solution, and if you have any questions or find 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 this will be a number for which the comma 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. 1/12 of the mass of a carbon atom is chosen as the unit for measuring the mass of an 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 quantity, since the two masses are separated. Ar = math. / (1/12) mug. However, absolute atomic mass is equal to the relative value and has the measurement unit amu. This means that the relative atomic mass indicates 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 of the mass of a carbon atom, or, in other words, 12 atomic mass units. It 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 1/12 of 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. Usually, for each chemical element, its value is the absolute mass of atoms, expressed as a. For example. The value of atomic mass units is recorded 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 of 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 weight is equal to their relative atomic weight. Chemistry is called a significant amount mass fraction of a chemical element in a molecule or substance. It shows how much relative molecular weight belongs to this 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 weight, they react without leaving any 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, the accuracy of which measures mass from one to several hundred micrograms; a special high-precision instrument that allows you to measure the mass of objects up to 0.1 ng (nanovesy). description One of the first references to the microglobuk is from 1910, when William Ramsay was informed of how much it had evolved, allowing weights in the 0.1mm3 body range to 10-9g (1ng) to be determined. Nowadays, the term "microbial" is more commonly used to refer to devices that measure and determine changes in mass in the microgram (10-6 grams) range. Microbiologists have entered the practice of modern research and industrial laboratories and have been produced in different versions with different sensitivities and corresponding costs. At the same time, a measurement technique is being developed in the area of ​​nanograms. 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 the measurement of mass using this method implies the need to convert weighing objects into ions, which is sometimes very undesirable. This is not necessary when using another practically important and widely used device for accurate measurement of bulk 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).

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 the atomic theory Dalton did, who compiled a table of atomic masses, taking the mass of a hydrogen atom as a unit.

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

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

1 amu \u003d 1/12 m (12 C) \u003d 1.66057 × 10 -27 kg \u003d 1.66057 × 10 -24 g.

DEFINITION

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

When calculating the 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) \u003d (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 times the amu:

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

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

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 assumed to be 12 amu and is1,66 10 24 G.

Comparing the masses of atoms of elements with one amu, find the numerical values ​​of the relative atomic mass (Ar).

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

!MOLE (v) - a unit of measurement of the amount of a substance containing as many structural units (molecules, atoms, ions) as there are atoms 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 value is called constant Avogadro(notation NBUT, dimension 1/mol).

The Italian scientist Amadeo Avogadro put forward a hypothesis in 1811, which was later confirmed by experimental data and later received the name Avogadro's law. He drew attention to the fact that all gases are equally compressed (Boyle-Mariotte law) and have the same coefficients of thermal expansion (Gay-Lussac 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 (they usually talk about normal conditions: absolute pressure is 1013 millibars and temperature is 0 ° C), the distance between molecules is the same for all gases, and the volume of molecules is negligible. Given all of the above, we can make an 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 liters. 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\u003d + 20 ° C and a pressure of 1013 mbar, 1 mol occupies a volume of about 24.2 liters.

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

Therefore, 1 mole of any substance has such a mass in grams, which is numerically equal to the molecular weight of this substance, expressed in atomic mass units.

For example, M(O2) = 16 a. e.m. 2 \u003d 32 a.m. e. m., thus, 1 mol of oxygen corresponds to 32 g. The densities of gases measured under the same conditions are related as their molar masses. Since molecular substances (liquids, vapors, gases) are the main object of practical problems during the transportation of liquefied gases on gas carriers, the main sought quantities will be the 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, it is possible to solve some practical problems that arise during the transportation of liquefied gases.

Example 1. There are 22 tons of liquefied ethylene in the deck tank (WITH2 H4 ). It is necessary to determine whether there is enough cargo on board to purge three cargo tanks of 5000 m 3 each, if, after purge, the temperature of the tanks is 0 ° C and the pressure is 1013 millibars.

1. Determine the molecular weight of ethylene:

M \u003d 2 12.011 + 4 1.0079 \u003d 28.054 g / mol.

2. We calculate the density of ethylene vapor under normal conditions:

ρ \u003d M / V \u003d 28.054: 22.4 \u003d 1.232 g / l.

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

22∙10 6: 1.252= 27544 m 3 .

The total volume of cargo tanks is 15,000 m 3 . 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 H8 ) will be required to purge cargo tanks with a total capacity of 8000 m 3 if the temperature of the tanks is +15 ° C, and the propane vapor pressure in the tank after the end of the purge will not exceed 1013 millibars.

1. Determine the molar mass of propane With3 H8

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

2. Determine the density of propane vapor after purging the tanks:

ρ \u003d M: v \u003d 44.1: 23.641 \u003d 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 \u003d ρ v \u003d 1.865 8000 \u003d 14920 kg ≈ 15 tons.

One of the fundamental properties of atoms is their mass. Absolute (true) mass of an atom- is extremely small. It is impossible to weigh atoms on a scale, because such exact scales do not exist. Their masses were determined by calculations.

For example, the mass of one hydrogen atom is 0.000,000,000,000,000,000,000,001,663 grams! The mass of an atom of uranium, one of the heaviest atoms, is approximately 0.000,000,000,000,000,000,000 4 grams.

The exact value of the 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 make calculations with small numbers. Therefore, instead of the absolute masses of atoms, their relative masses are used.

Relative atomic mass

The mass of any atom can be judged by comparing it with the mass of another atom (to find the ratio of their masses). Since the determination of the relative atomic masses of the elements, different atoms have been used as a comparison. At one time, hydrogen and oxygen atoms were original standards for comparison.

A unified scale of relative atomic masses and a new unit of atomic mass, adopted International Congress of Physicists (1960) and unified by the International Congress of Chemists (1961).

To date, the benchmark for comparison is 1/12 of the mass of a carbon atom. This value is called the atomic mass unit, abbreviated a.u.m.

Atomic mass unit (a.m.u.) - the mass of 1/12 of a carbon atom

Let's compare how many times the absolute mass of a hydrogen atom and uranium differs from 1 amu, for this we divide these numbers one by one:

The values ​​obtained in the calculations and are the relative atomic masses of the elements - relatively 1/12 of the mass of a carbon atom.

So, the relative atomic mass of hydrogen is approximately equal to 1, and uranium - 238. Note that relative atomic mass does not have units, as absolute mass units (grams) are canceled when divided.

The relative atomic masses of all elements are indicated in the Periodic Table of chemical elements by D.I. Mendeleev. The symbol used to represent relative atomic mass is Ar (the letter r is an abbreviation for the word relative, which means relative).

Values ​​for the relative atomic masses of elements are used in many calculations. As a general rule, values ​​given in the Periodic System are rounded to whole numbers. Note that the elements in the Periodic Table are listed in order of increasing relative atomic masses.

For example, using the Periodic System, we determine the relative atomic masses of a number of elements:

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 the 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 integers, with the exception of chlorine, for which Ar = 35.5
• Relative atomic mass has no units

atomic mass, relative atomic mass(obsolete name - atomic weight) - the value of the mass of an atom, expressed in atomic mass units. Currently, the atomic mass unit is assumed to be 1/12 of the mass of a neutral atom of the most common isotope of carbon 12C, so the atomic mass of this isotope is by definition exactly 12. For any other isotope, the atomic mass is not an integer, although it is close to the mass number of this isotope (i.e., the total number of nucleons - protons and neutrons - in its nucleus). The difference between the atomic mass of an isotope and its mass number is called the mass excess (usually expressed in MeV). It can be both positive and negative; the reason for its occurrence is the nonlinear dependence of the binding energy of nuclei on the number of protons and neutrons, as well as the difference in the masses of the proton and neutron.

The dependence of the atomic mass on the mass number is as follows: the excess mass is positive for hydrogen-1, with increasing mass number it decreases and becomes negative until a minimum is reached for iron-56, then it begins to grow and increases to positive values ​​for heavy nuclides. This corresponds to the fact that the fission of nuclei heavier than iron releases energy, while the fission of light nuclei requires energy. On the contrary, the fusion of nuclei lighter than iron releases energy, while the fusion of elements heavier than iron requires additional energy.

The atomic mass of a chemical element (also "average atomic mass", "standard atomic mass") is the weighted average atomic mass of all stable isotopes of a given chemical element, taking into account their natural abundance in the earth's crust and atmosphere. It is this atomic mass that is presented in the periodic table, it is used in stoichiometric calculations. The atomic mass of an element with a disturbed isotope ratio (for example, enriched in some isotope) differs from the standard one.

The molecular weight mo of a chemical compound is the sum of the atomic masses of the elements that make it up, multiplied by the stoichiometric coefficients of the elements according to the chemical formula of the compound. Strictly speaking, the mass of a molecule is less than the mass of its constituent atoms by a value equal to the binding energy of the molecule. However, this mass defect is 9–10 orders of magnitude smaller than the mass of the molecule and can be neglected.

The definition of a mole (and Avogadro's number) is chosen so that the mass of one mole of a substance (molar mass), expressed in grams, is numerically equal to the atomic (or molecular) mass of that substance. For example, the atomic mass of iron is 55.847. Therefore, one mole of iron atoms (that is, their number equal to Avogadro's number, 6.022 1023) contains 55.847 grams.

Direct comparison and measurement of the masses of atoms and molecules is performed using mass spectrometric methods.
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Until the 1960s, atomic mass was determined so that the oxygen-16 isotope had an atomic mass of 16 (oxygen scale). However, the ratio of oxygen-17 to oxygen-18 in natural oxygen, which was also used in atomic mass calculations, resulted in two different tables of atomic masses. Chemists used a scale based on the fact that a natural mixture of oxygen isotopes should have an atomic mass of 16, while physicists assigned the same number of 16 to the atomic mass of the most abundant oxygen isotope (having eight protons and eight neutrons).
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