Amount of substance formula - examples of calculations for different substances

What is a mole

Before we talk about how to find the molar mass of a substance, let's define the concept of “mole”.
It was introduced as an artificial quantity to simplify calculations. This is the amount of substance that contains the same number of tiny particles as 12 g of one of the carbon isotopes - C12. For all chemicals this amount is the same and is Avogadro's number 6.02 1023. Avogadro's constant is denoted NA and is measured in mol-1.

Avogadro's number is the number of molecules, ions or other small particles in 1 mole of a substance.

NA = 6.02 1023 mol-1.

Historical reference

In 1811, chemist Amedeo Avogadro suggested that if you take two equal volumes of gases under equal significant conditions (at the same temperature and pressure), then the number of molecules in these volumes will also be the same. Based on his hypothesis, he determined the atomic and molecular masses of many substances, and also calculated the number of atoms in molecules of water, nitrogen oxides, etc. However, Avogadro’s hypothesis was not understood for a long time in scientific circles. It became generally accepted only in 1860.

Mechanical lever, moment of force

Archimedes spoke about a mechanical lever when he promised to turn the Earth upside down if only a suitable fulcrum could be found. It is a simple mechanism that helps lift weights attached to one end by applying force to the other end. In this case, the weight of the load greatly exceeds the applied force. In grade 7, physical formulas describing this process are studied in the same section of dynamics.

A lever is in equilibrium if the product of the force on the arm on one side is equal to the product of the force on the arm on the other side.

What is molar mass

Molar mass is the mass of one mole of a substance and is measured in grams divided by mole (g/mol). This value is the ratio of the mass of a substance to its quantity, which is measured in moles.

How is molar mass indicated: M.

, where is the mass of the substance, and is the amount of the substance.

Unit of molar mass: g/mol.

Let's remember!

It is correct to say molar mass, not molar mass.

Despite the fact that 1 mole of any chemical substance contains the same number of molecules (and it is equal to Avogadro's number), the molar masses of different substances differ. This is because the atoms that make up these molecules are different. In particular, the difference between them is the relative atomic mass (Ar) - for example, Ar(Mg) = 24, and Ar(Hg) = 200. Now it will become clear why this matters.

Measurement of physical quantities

In the 7th grade physics course, they study the rules of measurement using instruments with a scale. If the scale division value is unknown, you can find it out using the following formula:

CD = (max − min) / n, where CD is the division price, max is the maximum scale value, min is the minimum scale value, n is the number of divisions between them.

Instead of the maximum and minimum, we can take any other scale values ​​whose numerical expression is known to us.

There are direct and indirect measurements:

• with direct measurement, the result can be seen directly on the instrument scale;
• with indirect measurement, the value of a quantity is calculated through another quantity (for example, the average speed is determined based on several speed measurements).

For convenience and standardization of measurements, the International System of Units SI was adopted in 1963. It regulates which units of measurement are considered basic and used for formulas. The designations of these units are also taught in the 7th grade physics curriculum.

How to determine molar mass

This quantity is closely related to concepts such as relative atomic and molecular masses. Precisely relative, because the absolute mass of a molecule or atom of a substance in chemistry is not used to solve problems - these are too small values.

The relative atomic mass of a substance (Ar) shows how many times its atom is larger than 1/12 of a carbon atom. This value for each chemical element can be seen in the periodic table.

The relative molecular mass (Mr) is the sum of the Ar of each atom in the molecule of a substance, taking into account the indices. It shows how much the mass of a molecule is greater than 1/12 of a carbon atom.

, where is the number of atoms.

Let's look at examples.

In a molecule of sodium chloride NaCl there is 1 sodium atom and 1 chlorine atom, with Ar(Na) = 23, Ar (Cl) = 35.5.

Mr(NaCl) = 23 + 35.5 = 58.5.

A NaNO2 molecule contains 1 sodium atom, 1 nitrogen atom and 2 oxygen atoms.

Ar(Na) = 23, Ar(N) = 14, Ar(O) = 16.

Mr(NaNO2) = 23 + 14 + 16 2 = 69.

Actually, nothing else is required to calculate the molar mass.

Important

The molar mass of a substance is numerically equal to the relative molecular mass. But these two concepts should not be confused - they have different physical meanings. Molar mass characterizes 1 mole, and relative molecular mass characterizes 1 molecule.

News

from 01/01/2017

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Quantity of substance

From the previous formulas it is clear that the molar mass and the amount of a substance are closely related. Let's look at this connection in more detail. Let's start with the fact that the amount of a substance can be denoted by either a Latin letter or a Greek letter (nu). The international designation is , but do not be surprised when you encounter any of these letters in formulas.

In the formula for finding the molar mass, we denoted the amount of substance through:

, hence .

Using this, we can find the amount of a substance (in moles) if we know its absolute and molar mass.

Example 1

How to determine what amount of substance is included in 350 g of barium sulfate BaSO4?

Let's use the formula.

We remember that M = Mr (the value of the molar mass is equal to the value of the relative molecular mass).

Mr(BaSO4) = Ar(Ba) + Ar(S) + Ar(O) 4 = 137 + 32 + 16 4 = 233.

M(BaSO4) = Mr(BaSO4) = 233 g/mol.

Let's substitute the molar mass value into the formula:

mole.

There is another formula for the amount of a substance that allows you to find it if the number of molecules or other structural units is known.

, where is the number of structural units, is Avogadro’s number.

Example 2

Let's say a certain volume of CaCO3 contains 3.01 · 1023 molecules. How to find the amount of a substance corresponding to a given volume?

Let's use the formula mole.

Mechanical movement: formulas for grade 7

In order to describe motion, a reference body, a coordinate system, and an instrument for measuring time are required. These are the components of the reference system.

The study of mechanical motion in the 7th grade physics course includes the following terms:

• The displacement of a body is a vector drawn from the starting point to the ending point.
• The trajectory of movement is a mental line along which the body moves.
• Path is the length of the body’s trajectory from the start to the end point.
• Speed ​​is the speed at which a body moves or the ratio of the distance it travels to the time it travels.
• Acceleration is the rate of change in speed at which a body moves.

Formula for the speed of uniform rectilinear motion:

V = S / t, where S is the path of the body, t is the time during which this path is covered.

Formula for the speed of uniform curvilinear motion:

where S1 and S2 are sections of the path, and t1 and t2 are the time during which each of them was covered.

The SI unit of speed is meters per second (m/s).

Formula for speed of uniformly accelerated motion:

V = V0 + at, where V0 is the initial velocity and is the acceleration.

The SI unit of acceleration is m/s2.

Molar volume

Above we found the amount of a substance through molar mass, but for gases this can also be done through molar volume. According to Avogadro's law, an amount of any gas equal to 1 mole will occupy the same volume if the gases are considered at the same temperature and pressure.

Under standard physical conditions - temperature 0°C and pressure 1 atm or 760 mmHg, 1 mole of gas occupies a volume of 22.4 liters.

Molar volume is the volume of gas taken in the amount of 1 mole. It is designated Vm.

Under normal conditions, Vm = 22.4 l/mol.

The values ​​of the molar and actual volume of a gas help to find the amount of a substance.

, where is the actual volume of gas, and is the molar volume.

Example 1

How many moles are contained in 120 liters of gas under normal conditions?

Let's calculate using the formula mole.

Answer: 120 liters of any gas under standard conditions contain 5.36 moles.

But you can find out the exact weight of such products much easier on our website.

We bring to your attention a universal interactive mass calculator for independently calculating the mass of products of various shapes from cylindrical or sheet materials. Its peculiarity is that it allows you to find out the weight of a part or product not only made of rolled metal and alloys, but also any other materials: wood and MDF, plastics and polymers, paper, cardboard, rubber, concrete, brick. This can be done simply by entering the overall dimensions of the part, minus the sizes of holes and slots, as well as the density coefficient of the material from which the part is made. The exact data can be found in the adjacent table.

Relative density of one gas to another

Sometimes, to solve a problem, you need to know how to find the molar mass of a gas, for which only its density in air or another gas is reported. This is possible if you know the relative density formula, which is denoted by the letter D.

, where and are some gases.

Example 1

How to determine how many times carbon monoxide is denser than hydrogen?

First, let's find the molar mass of CO and H2:

M(CO) = Mr(CO) = Ar(C) + Ar(O) = 12 + 16 = 28.

M(H) = Mr(H2) = 2 Ar(H) = 2 1 = 2.

.

Answer: Carbon monoxide is 14 times denser than hydrogen.

Example 2

How to calculate the molar mass of a gas x, which is known to be 10 times denser than carbon dioxide CO2?

First, let's calculate the molar mass of carbon dioxide:

M(CO2) = Mr(CO2) = 12 + 2 16 = 44.

Based on the relative density formula, we will calculate the molar mass of the desired gas x.

M(x) = D(x/CO2) M(CO2) = 10 44 = 440 g/mol.

Answer: This gas has a molar mass of 440 g/mol.

Physics cheat sheets for 7th grade

It is difficult to cover the entire physics course in one article, but we covered the main topics for grade 7 and this is enough to refresh your memory. Download and print both cheat sheets - one of them (detailed) will be useful for thoughtful preparation for the Unified State Exam and Unified State Exam, and the second (short) will be used for solving problems.

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For those who are homeschooled or are forced to study the material on their own due to absences due to illness, we also recommend a textbook on physics by A. V. Peryshkin with formulas for grade 7 and easy, accessible explanations on all topics. It was written several decades ago, but is still very popular and in demand.