One of the most important controlled indicators in the production of cosmetics and dietary supplements is density. Depending on the product being manufactured, the company’s specialists “ KorolevFarm» use several concepts and definitions of density.

A clearer definition of the concept of density requires clarification of the wording of this term:

With such a limiting transition, it is necessary to take into account that at the atomic level any body is inhomogeneous, and therefore it is necessary to focus on the volume that is used for the corresponding physical model used.

• Bulk density - the bulk density of various bulk materials (sugar, lactose, starch, etc.) is understood as the amount of this powder (bulk product) that is in a freely filled state in a certain unit of volume.
• Relative density is the ratio of two concepts, i.e. terms, and can be considered as the ratio of volumetric, that is, bulk density, to true density.

Product density is an important parameter in the manufacture of cosmetic products, as it affects appearance product, its organoleptic properties, weight and cost of the finished product. It is very important to take into account the density of the product when packaging manufactured products in bottles, tubes, jars, and so on.

For example, the density of creams is less than one. As a rule, the density of the cream is in the range of 0.96 - 0.98 g/cm3. In accordance with the tests, with a density of 0.96 and a volume of 50 ml, the mass of the cream will be 48 g, and with a density of 0.98 the mass increases to 49 g.

The density of shampoos, on the contrary, is greater than or equal to unity, it is in the range of 1.0 - 1.04 g/cm 3 . Research shows that with a density of 1.0 and a volume of 100 ml, the mass of shampoo in the package will be 100 g, and with a density of 1.04 it is already 104 g.

As already mentioned, density is defined as the ratio of body mass to occupied volume. Therefore, the numerical values ​​of the density of a substance show the mass of the accepted or specified unit volume of this substance. As can be seen from the above example, the density of the metal, in this case cast iron, is 7 kg/dm 3. It turns out that 1 dm 3 of cast iron has a mass of 7 kg. Let’s compare the density of tap water – 1 kg/l. From this example it follows that the mass of 1 liter of tap water is 1 kg. The same volume of different substances or substances have different weights.
It is known that as the temperature decreases, the density of bodies increases.

There are two main methods for determining the density of a substance: hydrometric and pycnometric. A hydrometer is used to measure the density of various liquids, and a pycnometer is used to measure the density of creams, balms, gels, and toothpastes.

Based on the measured density of cosmetic products according to the tables agreed upon at the enterprise “Limits of permissible deviations of the net contents from the nominal quantity” in accordance with GOST 8.579-2002 “Requirements for the quantity of packaged goods in packaging of any type during their production, packaging, sale and import” limits are determined permissible deviations of the net contents of the product from the nominal value.

A hydrometer is a device used to measure the density of various liquids and liquid substances. As a rule, it is a glass tube, the lower part of which is significantly expanded in diameter. In calibration, the expanded portion is filled with shot or mercury, which is used to achieve a specified mass. At the top of the hydrometer there is a graduated scale in certain corresponding density values. Since the density of liquids and liquid substances depends very significantly on temperature, the hydrometer is either equipped with a thermometer, or the temperature of the liquid is simultaneously measured with another thermometer.

To carry out the procedure for measuring the density of a liquid substance or liquid, a clean hydrometer is carefully placed in a sufficiently large measuring beaker with liquid, but in such a way that the hydrometer floats freely in it. Density values ​​are determined using the hydrometer scale of the liquid located at the lower edge of the meniscus.

In physics, a hydrometer is a device used to determine the density value and, therefore, determine specific gravity tel.

Historians of science believe that the hydrometer as a device for taking measurements was invented by Hypatia, a famous woman scientist, astronomer, mathematician and philosopher, head of the Alexandrian school of Neoplatonism. Thanks to her scientific activity Other devices were invented or improved: the distiller, the astrolabe and the planisphere.

The design of modern hydrometers, like hydrometers used in ancient times, is based on the well-known hydrostatic law - Archimedes' law. As is known from elementary school, Archimedes' law states that every body floats in a liquid and sinks so deeply into it that the weight of the body displaced by it liquids equal to weight the entire body floating in this liquid.

Interesting circumstances preceded the discovery of Archimedes' law, which glorified the scientist throughout time. “Eureka!” everyone exclaims, finding a solution to a difficult problem, but this is preceded by a whole story.

Archimedes served at the court of Hiero II, the tyrant of Syracuse, who reigned from 270-215 BC, and from 269 BC bore the title of king. Hieron was known as an insidious, greedy and suspicious ruler.

He suspected his jewelers that when making gold items, they mixed silver into gold, or worse, tin into a noble metal, which was the reason for the discovery of one of physical laws. He instructed Archimedes to expose the jewelers, since he was sure that when making the crown for him, the jewelers stole gold.

To solve this complex task it is necessary to know not only the mass, but also to determine the volume of the manufactured crown, and this was the most difficult thing in order to subsequently calculate the density of the metal. The crown has a complex and irregular geometric shape; determining its volume is a very difficult task, the solution of which Archimedes pondered for a long time.

The solution was found by Archimedes in an original way, when he immersed himself in a bath - the water level rose sharply after he immersed himself in the water. The scientist’s body displaced an equal volume of water. "Eureka!" - Archimedes exclaimed and ran to the palace, as legend says, without getting dressed. Then everything was simple. He immersed the crown in water, measured the volume of the displaced liquid, and thus determined the volume of the crown.

Thanks to this, Archimedes discovered the principle or, as it is also called, the law of buoyancy. A solid body immersed in a liquid will displace a volume of liquid equal to the volume of the body immersed in the liquid. Any body can float in water if its average density is less than the density of the liquid in which it was placed.

Archimedes' law states: any body that is immersed in a liquid or gas is acted upon by buoyant forces directed upward and equal to the weight of the liquid or gas displaced by it.
To this day, humanity has successfully applied the knowledge gained from distant ancestors in many areas of its activity, including in the production of cosmetics.

As already mentioned, a pycnometer is also used to measure density. Density measurements using a pycnometer are carried out as follows.

Before testing, it is necessary to rinse the pycnometer successively with a solvent to remove traces of the test substance, then with a chrome mixture, water, alcohol, ether, then dry to a constant weight and weigh (the weighing result is recorded in grams accurate to the fourth decimal place).

The pycnometer is filled with distilled water using a funnel or pipette slightly above the mark, closed with a stopper and placed for 20 minutes in a thermostat at a temperature of (20 ± 0.1) ° C.

When the temperature reaches (20 ± 0.1) ° C, it is necessary to bring the water level in the pycnometer to the mark, quickly removing excess water using a pipette or a strip of filter paper rolled into a tube, or, adding water to the mark, close the pycnometer with a stopper and place the pycnometer in thermostat with a temperature of (20 ±0.1) °C for 10 minutes.

Remove the pycnometer from the thermostat, weigh it, empty it of water, dry it, fill the pycnometer with the test liquid and thermostat it.

Calculate density () in g/cm3 using the formula:

Where : m 1 – mass of the pycnometer with the test liquid, g;
m 0 – mass of an empty pycnometer, g;
m 2 - mass of pycnometer with water, g;
A – correction for aerostatic forces, calculated by the formula:

A= 0.0012 x V.

Where : V – pycnometer volume, cm 3 ;
0.0012 – air density at 200C, g/cm3;
0.9982 – density of water at 200C, g/cm3;

At the KorolevPharm company, an express method is used to measure the density of cosmetic products with a thick consistency (emulsions, cream gels, gels, balms, etc.). Its essence lies in the fact that a calibrated syringe is used for testing.

To determine the density, weigh the empty syringe (the weighing result is recorded in grams to the second decimal place), fill the syringe with distilled water to the maximum mark, then thoroughly wipe the surface of the syringe and weigh again.

Determine the volume (V) of the syringe using the formula:

Where : m 1 – mass of a syringe with water (g), , 0.9982 - density of water at 200C, g/cm3;

Weigh the empty syringe again (the weighing result is recorded in grams accurate to the second decimal place), fill the syringe with cosmetic mass to the maximum mark, avoiding any air bubbles.

Carefully wipe the surface of the syringe and reweigh it.

Calculate density () in g/cm3 using the formula:

Where, m 1 – mass of a syringe with a cosmetic product (g), m 0 - mass of an empty syringe (g), V – syringe volume (cm 3)

The test result is taken as the arithmetic mean of the results of two parallel determinations, the discrepancy between which does not exceed 0.01 g/cm 3 .
This method allows you to quickly determine the density of the manufactured cosmetic product.

Everything around us consists of different substances. Ships and bathhouses are built from wood, irons and cots are made from iron, tires on wheels and erasers on pencils are made from rubber. AND various items have different weights - any of us can easily carry a juicy ripe melon from the market, but a weight of the same size will have to work hard.

Everyone remembers the famous joke: “Which is heavier? A kilogram of nails or a kilogram of fluff? We will no longer fall for this childish trick, we know that the weight of both will be the same, but the volume will be significantly different. So why is this happening? Why do different bodies and substances have different weights with the same size? Or vice versa, the same weight with different sizes? Obviously, there is some characteristic due to which substances are so different from each other. In physics, this characteristic is called the density of matter and is taught in the seventh grade.

Density of a substance: definition and formula

The definition of the density of a substance is as follows: density shows what the mass of a substance is in a unit of volume, for example, in one cubic meter. So, the density of water is 1000 kg/m3, and ice is 900 kg/m3, which is why ice is lighter and is on top of reservoirs in winter. That is, what does the density of matter show us in this case? An ice density of 900 kg/m3 means that an ice cube with sides of 1 meter weighs 900 kg. And the formula for determining the density of a substance is as follows: density = mass/volume. The quantities included in this expression are designated as follows: mass - m, volume of the body - V, and density is designated by the letter ρ (Greek letter “rho”). And the formula can be written as follows:

How to find the density of a substance

How to find or calculate the density of a substance? To do this you need to know body volume and body weight. That is, we measure the substance, weigh it, and then simply substitute the obtained data into the formula and find the value we need. And how the density of a substance is measured is clear from the formula. It is measured in kilograms per cubic meter. Sometimes they also use a value such as grams per cubic centimeter. Converting one value to another is very simple. 1 g = 0.001 kg, and 1 cm3 = 0.000001 m3. Accordingly, 1 g/(cm)^3 =1000kg/m^3. It should also be remembered that the density of a substance is different in different states of aggregation. That is, in solid, liquid or gaseous form. Density solids, most often, higher than the density of liquids and much higher than the density of gases. Perhaps a very useful exception for us is water, which, as we have already considered, weighs less in the solid state than in the liquid state. It is because of this strange feature of water that life is possible on Earth. Life on our planet, as we know, originated from the oceans. And if water behaved like all other substances, then the water in the seas and oceans would freeze through, the ice, being heavier than water, would sink to the bottom and lie there without melting. And only at the equator, in a small column of water, would life exist in the form of several species of bacteria. So we can say thank you to the water for our existence.

Let us place iron and aluminum cylinders of the same volume on the scales (Fig. 122). The balance of the scales has been disrupted. Why?

Rice. 122

Carrying out laboratory work, you measured your body weight by comparing the weight of the weights to your body weight. When the scales were in equilibrium, these masses were equal. Disequilibrium means that the masses of the bodies are not the same. The mass of the iron cylinder is greater than the mass of the aluminum one. But the volumes of the cylinders are equal. This means that a unit volume (1 cm3 or 1 m3) of iron has a greater mass than aluminum.

The mass of a substance contained in a unit volume is called the density of the substance. To find density, you need to divide the mass of a substance by its volume. Density is indicated Greek letterρ (rho). Then

density = mass/volume

ρ = m/V.

The SI unit of density is 1 kg/m3. Densities various substances determined experimentally and presented in table 1. Figure 123 shows the masses of substances known to you in a volume V = 1 m 3.

Rice. 123

Density of solids, liquids and gases
(at normal atmospheric pressure)

How do we understand that the density of water is ρ = 1000 kg/m3? The answer to this question follows from the formula. The mass of water in a volume V = 1 m 3 is equal to m = 1000 kg.

From the density formula, the mass of a substance

m = ρV.

Of two bodies of equal volume, the body with the greater density of matter has the greater mass.

Comparing the densities of iron ρ l = 7800 kg/m 3 and aluminum ρ al = 2700 kg/m 3, we understand why in the experiment (see Fig. 122) the mass of an iron cylinder turned out to be greater than the mass of an aluminum cylinder of the same volume.

If the volume of a body is measured in cm 3, then to determine the body mass it is convenient to use the density value ρ, expressed in g/cm 3.

The substance density formula ρ = m/V is used for homogeneous bodies, that is, for bodies consisting of one substance. These are bodies that do not have air cavities or do not contain impurities of other substances. The purity of the substance is judged by the measured density. Is there, for example, any cheap metal added inside a gold bar?

Think and answer

1. How would the balance of the scales change (see Fig. 122) if instead of an iron cylinder a wooden cylinder of the same volume were placed on a cup?
2. What is density?
3. Does the density of a substance depend on its volume? From the masses?
4. In what units is density measured?
5. How to move from the unit of density g/cm 3 to the unit of density kg/m 3?

Interesting to know!

As a rule, a substance in the solid state has a density greater than in the liquid state. The exception to this rule is ice and water, consisting of H 2 O molecules. The density of ice is ρ = 900 kg/m 3, the density of water? = 1000 kg/m3. The density of ice is less than the density of water, which indicates a less dense packing of molecules (i.e., greater distances between them) in the solid state of the substance (ice) than in the liquid state (water). In the future you will meet other very interesting anomalies(abnormalities) in the properties of water.

The average density of the Earth is approximately 5.5 g/cm 3 . This and others known to science facts allowed us to draw some conclusions about the structure of the Earth. The average thickness of the earth's crust is about 33 km. The earth's crust is composed primarily of soil and rocks. The average density of the earth's crust is 2.7 g/cm 3, and the density of the rocks lying directly under earth's crust, - 3.3 g/cm 3 . But both of these values ​​are less than 5.5 g/cm 3, i.e. less than the average density of the Earth. It follows that the density of the substance located in the depths globe, greater than the average density of the Earth. Scientists suggest that in the center of the Earth the density of the substance reaches 11.5 g/cm 3, that is, it approaches the density of lead.

The average density of human body tissue is 1036 kg/m3, the density of blood (at t = 20°C) is 1050 kg/m3.

Balsa wood has a low wood density (2 times less than cork). Rafts and life belts are made from it. In Cuba, the Eshinomena prickly hair tree grows, the wood of which has a density 25 times less than the density of water, i.e. ρ = 0.04 g/cm 3 . The snake tree has a very high wood density. A tree sinks in water like a stone.

Do it yourself at home

Measure the density of the soap. To do this, use a rectangular shaped bar of soap. Compare the density you measured with the values ​​obtained by your classmates. Are the resulting density values ​​equal? Why?

Interesting to know

Already during the life of the famous ancient Greek scientist Archimedes (Fig. 124), legends were formed about him, the reason for which was his inventions that amazed his contemporaries. One of the legends says that the Syracusan king Heron II asked the thinker to determine whether his crown was made of pure gold or whether the jeweler mixed a significant amount of silver into it. Of course, the crown had to remain intact. It was not difficult for Archimedes to determine the mass of the crown. Much more difficult was to accurately measure the volume of the crown in order to calculate the density of the metal from which it was cast and determine whether it was pure gold. The difficulty was that it was the wrong shape!

Rice. 124

One day, Archimedes, absorbed in thoughts about the crown, was taking a bath, where he came up with a brilliant idea. The volume of the crown can be determined by measuring the volume of water displaced by it (you are familiar with this method of measuring the volume of a body irregular shape). Having determined the volume of the crown and its mass, Archimedes calculated the density of the substance from which the jeweler made the crown.

As the legend goes, the density of the crown turned out to be less than the density of pure gold, and the dishonest jeweler was caught in deception.

Exercises

1. The density of copper is ρ m = 8.9 g/cm 3, and the density of aluminum is ρ al = 2700 kg/m 3. Which substance is more dense and by how many times?
2. Determine the mass of a concrete slab whose volume is V = 3.0 m 3.
3. What substance is a ball with volume V = 10 cm 3 made of if its mass m = 71 g?
4. Determine the mass of window glass whose length a = 1.5 m, height b = 80 cm and thickness c = 5.0 mm.
5. Total mass N = 7 identical sheets of roofing iron m = 490 kg. The size of each sheet is 1 x 1.5 m. Determine the thickness of the sheet.
6. Steel and aluminum cylinders have the same area cross section and masses. Which cylinder has the greater height and by how much?

Figure 1. Table of densities of some substances. Author24 - online exchange of student work

All bodies in the world around us have different sizes and volumes. But even with the same volumetric data, the mass of substances will differ significantly. In physics, this phenomenon is called the density of matter.

Density is a basic physical concept that gives an idea of ​​the characteristics of any known substance.

Definition 1

The density of a substance is a physical quantity that shows the mass of a certain substance per unit volume.

The units of volume in terms of the density of a substance are usually the cubic meter or cubic centimeter. Determination of the density of a substance is carried out using special equipment and instruments.

To determine the density of a substance, it is necessary to divide the mass of its body by its own volume. When calculating the density of a substance, the following values ​​are used:

body weight ($m$); body volume ($V$); body density ($ρ$)

Note 1

$ρ$ is a letter of the Greek alphabet "rho" and should not be confused with a similar designation for pressure - $p$ ("peh").

Substance density formula

The density of a substance is calculated using the SI measurement system. In it, density units are expressed in kilograms per cubic meter or grams per cubic centimeter. You can also use any measurement system.

A substance has different degrees of density if it is in different states of aggregation. In other words, the density of a substance in a solid state will be different than the density of the same substance in a liquid or gaseous state. For example, water is characterized by density in ordinary liquid state 1000 kilograms per cubic meter. In a frozen state, water (ice) will already have a density of 900 kilograms per cubic meter. Water vapor at normal atmospheric pressure and a temperature close to zero degrees will have a density of 590 kilograms per cubic meter.

The standard formula for the density of a substance is as follows:

In addition to the standard formula, which is used only for solids, there is a formula for gas in normal conditions:

$ρ = M / Vm$, where:

• $M$ is the molar mass of the gas,
• $Vm$ is the molar volume of the gas.

There are two types of solids:

• porous;
• bulk.

Note 2

Their physical characteristics directly affect the density of a substance.

Density of homogeneous bodies

Definition 2

The density of homogeneous bodies is the ratio of the mass of a body to its volume.

The concept of density of a substance includes the definition of the density of a homogeneous and uniformly distributed body with a heterogeneous structure, which consists of this substance. This is a constant value and for a better understanding of the information it is formed special tables, where all common substances are collected. The values ​​for each substance are divided into three components:

• density of a body in a solid state;
• density of a body in a liquid state;
• density of a body in a gaseous state.

Water is a fairly homogeneous substance. Some substances are not so homogeneous, so the average density of the body is determined for them. To derive this value, it is necessary to know the result ρ of the substance for each component separately. Loose and porous bodies have true density. It is determined without taking into account the voids in its structure. Specific gravity can be calculated by dividing the mass of a substance by the entire volume it occupies.

Similar values ​​are related to each other by the porosity coefficient. It represents the ratio of the volume of voids to the total volume of the body that is currently being examined.

The density of substances depends on many additional factors. A number of them simultaneously increase this value for some substances, and decrease them for others. At low temperatures, the density of the substance increases. Some substances are able to react to changes in temperature in different ways. In this case, it is customary to say that the density behaves anomalously at a certain temperature range. Such substances often include bronze, water, cast iron and some other alloys. The density of water is highest rate at 4 degrees Celsius. With further heating or cooling, this indicator can also change significantly.

Metamorphoses with the density of water occur during the transition from one state of aggregation to another. The indicator ρ changes its values ​​in these cases in an abrupt manner. It progressively increases during the transition to a liquid from a gaseous state, as well as at the moment of crystallization of the liquid.

There are many exceptional cases. For example, silicon has low density values ​​when solidified.

Measuring the density of matter

To effectively measure the density of a substance, special equipment is usually used. It consists of:

• scales;
• measuring instrument in the form of a ruler;
• volumetric flask.

If the substance under study is in a solid state, then a measure in the form of a centimeter is used as a measuring device. If the test substance is in a liquid state of aggregation, then a volumetric flask is used for measurements.

First, you need to measure your body volume using a centimeter or measuring flask. The researcher observes the measurement scale and records the resulting result. If a cube-shaped wooden beam is examined, then the density will be equal to the value of the side raised to the third power. When studying a liquid, it is necessary to additionally take into account the mass of the vessel with which the measurements are taken. The resulting values ​​must be substituted into universal formula based on the density of the substance and calculate the indicator.

For gases, calculating the indicator is very difficult, since it is necessary to use various measuring instruments.

Typically, a hydrometer is used to calculate the density of substances. It is designed to obtain results from liquids. True density is studied using a pycnometer. The soils are examined using Kaczynski and Seidelman drills.

DEFINITION

Density is a scalar physical quantity, which is defined as the ratio of the mass of a body to the volume it occupies.

This quantity is usually denoted by the Greek letter r or the Latin letters D and d. The unit of measurement for density in the SI system is usually considered to be kg/m3, and in the GHS - g/cm3.

Density can be calculated using the formula:

The ratio of the mass of a given gas to the mass of another gas taken in the same volume, at the same temperature and the same pressure is called the relative density of the first gas to the second.

For example, under normal conditions, the mass of carbon dioxide in a volume of 1 liter is 1.98 g, and the mass of hydrogen in the same volume and under the same conditions is 0.09 g, from which the density of carbon dioxide by hydrogen will be: 1.98 / 0. 09 = 22.

How to calculate the density of a substance

Let us denote the relative gas density m 1 / m 2 by the letter D. Then

Therefore, the molar mass of a gas is equal to its density relative to that of another gas, multiplied by molar mass second gas.

Often the densities of various gases are determined in relation to hydrogen, as the lightest of all gases. Since the molar mass of hydrogen is 2.0158 g/mol, in this case the equation for calculating molar masses takes the form:

or, if we round the molar mass of hydrogen to 2:

Calculating, for example, using this equation the molar mass of carbon dioxide, the density of which for hydrogen, as indicated above, is 22, we find:

M(CO 2) = 2 × 22 = 44 g/mol.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2