How to determine the density of water. How is the density of a material measured? Density of various materials Density of a substance formula unit of measurement
Figure 1. Table of densities of some substances. Author24 - online exchange of student works
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 devices.
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 has a density in its normal liquid state of 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 under 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 the 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, special tables are formed 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 greatest 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 substance under study is in a liquid aggregate state, 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 obtained values must be substituted into the universal formula for the density of the substance and the indicator calculated.
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.
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 the appearance of the 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, at a density of 0.96 and a volume of 50 ml, the mass of the cream will be 48 g, and at 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 example given, 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, the specific gravity of bodies.
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 work, other instruments were invented or improved: a distiller, an astrolabe and a 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 liquid is equal to the weight of 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 the 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 problem, 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.
Density- a physical quantity characterizing the physical properties of a substance, which is equal to the ratio of the mass of a body to the volume occupied by this body.
Density (density of a homogeneous body or average density of a heterogeneous body) can be calculated using the formula:
[ρ] = kg/m³; [m] = kg; [V] = m³.
Where m- body mass, V- its volume; the formula is simply a mathematical notation for the definition of the term "density".
All substances consist of molecules, therefore the mass of any body consists of the masses of its molecules. This is similar to how the mass of a bag of candy is the sum of the masses of all the candies in the bag. If all the candies are the same, then the mass of a bag of candies could be determined by multiplying the mass of one candy by the number of candies in the bag.
The molecules of a pure substance are identical. Therefore, the mass of a drop of water is equal to the product of the mass of one water molecule and the number of molecules in the drop.
The density of a substance shows what the mass of 1 m³ of this substance is.
The density of water is 1000 kg/m³, which means that the mass of 1 m³ of water is 1000 kg. This number can be obtained by multiplying the mass of one water molecule by the number of molecules contained in 1 m³ of its volume.
The density of ice is 900 kg/m³, which means that the mass of 1 m³ of ice is 900 kg.
Sometimes the density unit g/cm³ is used, so we can also say that the mass of 1 cm³ of ice is 0.9 g.
Each substance occupies a certain volume. And it may turn out that the volumes of the two bodies are equal, and their masses are different. In this case, they say that the densities of these substances are different. 
Also when the masses of two bodies are equal their volumes will be different. For example, the volume of ice is almost 9 times greater than the volume of an iron bar.
The density of a substance depends on its temperature.
As temperature increases, density usually decreases. This is due to thermal expansion, when the volume increases while the mass remains unchanged.
As the temperature decreases, the density increases. Although there are substances whose density behaves differently in a certain temperature range. For example, water, bronze, cast iron. Thus, the density of water has a maximum value at 4 °C and decreases both with increasing and decreasing temperature relative to this value.
When the state of aggregation changes, the density of a substance changes abruptly: the density increases during the transition from a gaseous state to a liquid and when the liquid solidifies. Water, silicon, bismuth and some other substances are exceptions to this rule, since their density decreases when solidified.
Problem solving
Task No. 1.
A rectangular metal plate 5 cm long, 3 cm wide and 5 mm thick has a mass of 85 g. What material can it be made of?
Analysis of a physical problem. To answer the question posed, it is necessary to determine the density of the substance from which the plate is made. Then, using the density table, determine which substance the found density value corresponds to. This problem can be solved in these units (i.e. without conversion to SI). 
Task No. 2.
A copper ball with a volume of 200 cm 3 has a mass of 1.6 kg. Determine whether this ball is solid or empty. If the ball is empty, then determine the volume of the cavity.
Analysis of a physical problem. If the volume of copper is less than the volume of the sphere V copper 
Task No. 3.
A canister that holds 20 kg of water is filled with gasoline. Determine the mass of gasoline in the canister.
Analysis of a physical problem. To determine the mass of gasoline in a canister, we need to find the density of gasoline and the capacity of the canister, which is equal to the volume of water. The volume of water is determined by its mass and density. We find the density of water and gasoline in the table. It is better to solve the problem in SI units. 
Task No. 4.
An alloy was made from 800 cm 3 of tin and 100 cm 3 of lead. What is its density? What is the mass ratio of tin and lead in the alloy?
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 considered to be kg/m 3 , and in the GHS - g/cm 3 .
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 another gas, multiplied by the molar mass of the 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
| Exercise | Calculate the volume of water and the mass of sodium chloride NaCl that will be required to prepare 250 ml of a 0.7 M solution. Take the density of the solution equal to 1 g/cm. What is the mass fraction of sodium chloride in this solution? |
| Solution | A molar concentration of a solution equal to 0.7 M indicates that 1000 ml of solution contains 0.7 mol of salt. Then, you can find out the amount of salt substance in 250 ml of this solution: n(NaCl) = V solution (NaCl) × C M (NaCl); n(NaCl) = 250 × 0.7 / 1000 = 0.175 mol. Let's find the mass of 0.175 mol sodium chloride: M(NaCl) = Ar(Na) + Ar(Cl) = 23 + 35.5 = 58.5 g/mol. m(NaCl) = n(NaCl) × M(NaCl); m(NaCl) = 0.175 × 58.5 = 10.2375 g. Let's calculate the mass of water required to obtain 250 ml of 0.7 M sodium chloride solution: r = m solution / V; m solution = V ×r = 250 × 1 = 250 g. m(H 2 O) = 250 - 10.2375 = 239.7625 g. |
| Answer | The mass of water is 239.7625 g, the volume is the same value, since the density of water is 1 g/cm |
EXAMPLE 2
| Exercise | Calculate the volume of water and mass of potassium nitrate KNO 3 that will be required to prepare 150 ml of a 0.5 M solution. Take the density of the solution equal to 1 g/cm. What is the mass fraction of potassium nitrate in such a solution? |
| Solution | A molar concentration of a solution equal to 0.5 M indicates that 1000 ml of solution contains 0.7 mol of salt. Then, you can find out the amount of salt in 150 ml of this solution: n(KNO 3) = V solution (KNO 3) × C M (KNO 3); n(KNO 3) = 150 × 0.5 / 1000 = 0.075 mol. Let's find the mass of 0.075 mol of potassium nitrate: M(KNO 3) = Ar(K) + Ar(N) + 3×Ar(O) = 39 + 14 + 3×16 = 53 + 48 = 154 g/mol. m(KNO 3) = n(KNO 3) × M(KNO 3); m(KNO 3) = 0.075 × 154 = 11.55 g. Let's calculate the mass of water required to obtain 150 ml of a 0.5 M solution of potassium nitrate: r = m solution / V; m solution = V ×r = 150 ×1 = 150 g. m(H 2 O) = m solution - m(NaCl); m(H 2 O) = 150 - 11.55 = 138.45 g. |
| Answer | The mass of water is 138.45 g, the volume is the same value, since the density of water is 1 g/cm |
Figure 1. Table of densities of some substances. Author24 - online exchange of student works
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 devices.
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 has a density in its normal liquid state of 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 under 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 the 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, special tables are formed 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 greatest 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 substance under study is in a liquid aggregate state, 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 obtained values must be substituted into the universal formula for the density of the substance and the indicator calculated.
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.