Density units. Mass and density The density of a substance is the ratio of mass
Among all other substances on planet Earth, gases have the lowest density. Liquids, as a rule, are characterized by a higher density compared to them, and the maximum value of this indicator can be found in solids. For example, osmium is considered to be the densest metal.
Density measurement
To measure density, as well as other subject areas, this concept, a special complex unit of measurement has been adopted, based on the relationship of density with the mass and volume of a substance. Thus, in the international system of measurement units SI, the unit used to describe the density of a substance is kilogram per cubic meter, which is usually denoted as kg/m³.However, in the case of very small volumes of a substance for which it is necessary to measure density, the use of a derivative of this generally accepted unit, expressed as the number of grams per cubic centimeter, is used. In abbreviated form, this unit is usually denoted g/cm³.
Moreover, the density of various substances tends to change depending on temperature: in most cases, a decrease in temperature entails an increase in the density of the substance. So, for example, ordinary air at a temperature of +20°C has a density equal to 1.20 kg/m³, while when the temperature drops to 0°C its density will increase to 1.29 kg/m³, and with a further decrease to -50°C the air density will reach 1.58 kg/m³. At the same time, some substances are an exception to this rule, since the change in their density does not obey the specified pattern: this includes, for example, water.
Various physical instruments are used to measure the density of substances. For example, you can measure the density of a liquid using a hydrometer, and in order to determine the density of a solid or gaseous substance, you can use a pycnometer.
In chemical laboratories it is very often necessary to determine density. In the literature of previous years and in reference books of old publications, tables of the specific gravities of solutions and solids are given. This quantity was used instead of density, which is one of the most important physical quantities that characterize the properties of a substance.
The density of a substance is the ratio of the mass of a body to its volume:
Therefore, the density of a substance is expressed * in g/cm3. Specific gravity y is the ratio of the weight (gravity) of a substance to its volume:
The density and specific gravity of a substance are in the same relationship with each other as mass and weight, i.e.
where g is the local value of the acceleration due to gravity during free fall. Thus, the dimensions of specific gravity "(g/cm2 sec2) and density (g/cm3), as well as their numerical values expressed in the same system of units, differ from each other *.
The density of a body does not depend on its location on Earth, while its specific gravity varies depending on where on Earth it is measured.
In some cases, they prefer to use the so-called relative density, which is the ratio of the density of a given substance to the density of another substance under certain conditions. Relative density is expressed as an abstract number.
The relative density d of liquid and solid substances is usually determined in relation to the density of distilled water:
It goes without saying that p and pb must be expressed in the same units.
Relative density d can also be expressed as the ratio of the mass of a substance taken to the mass of distilled water taken in the same volume as the substance, under certain, constant conditions.
Since the numerical values of both relative density and relative specific gravity under the specified constant conditions are the same, you can use tables of relative specific gravity in reference books in the same way as if they were density tables.
Relative density is a constant value for each chemically homogeneous substance and for solutions at a given temperature. Therefore, according to
* In some cases, density is expressed in g/ml. The difference between the numerical density values expressed in g/cm3 and g/ml is very small. It should be taken into account only when working with extreme precision.
Therefore, in many cases, the relative density can be used to judge the concentration of a substance in a solution.
* In the technical system of units (MKXCC). in which the basic unit is not a unit of mass, but a unit of force - kilogram-force (kg or kgf), specific gravity is expressed in kg / m3 or G / cm3. It should be noted that the numerical values of specific gravity, measured in G/cm3, and density, measured in g/cm3, are the same, which often causes confusion in the concepts of “density” and “specific gravity”.
Typically, the density of a solution increases with increasing concentration of the solute (if the solute itself has a density greater than the solvent). But there are substances for which the increase in density with increasing concentration goes only up to a certain limit, after which the density decreases with increasing concentration.
For example, sulfuric acid has the highest density of 1.8415 at a concentration of 97.35%. A further increase in concentration is accompanied by a decrease in density to 1.8315, which corresponds to 99.31%.
Acetic acid has a maximum density at a concentration of 77-79%, and 100% acetic acid has the same density as 41%.
Relative density depends on the temperature at which it is determined. Therefore, they always indicate the temperature at which the determination was made and the temperature of the water (volume taken as a unit). In reference books this is shown using appropriate indexes, for example eft; the given designation indicates that the relative density was determined at a temperature of 2O0C and the density of water at a temperature of 4°C was taken as a unit for comparison. There are also other indices indicating the conditions under which the relative density was determined, for example R4 Ul, etc.
The change in relative density of 90% sulfuric acid depending on the ambient temperature is given below:
The relative density decreases with increasing temperature, and increases with decreasing temperature.
When determining the relative density, it is necessary to note the temperature at which it was carried out, and compare the obtained values with tabular data determined at the same temperature.
If the measurement was not carried out at the temperature indicated in the reference book, then. a correction is introduced, calculated as the average change in relative density per degree. For example, if in the interval between 15 and 20 0C the relative density of 90% sulfuric acid decreases by 1.8198-1.8144 = 0.0054, then on average we can assume that with a temperature change of 1 0C (above 15 0C) relative density decreases by 0.0054: 5 = 0.0011.
Thus, if the determination is carried out at 18 0C, then the relative density of the specified solution should be equal to:
However, to introduce a temperature correction to the relative density, it is more convenient to use the nomogram below (Fig. 488). This nomogram, in addition, makes it possible for the known relative density, calculated at a standard temperature of 20 ° C, to approximately determine the relative density at other temperatures, which may sometimes be necessary. The relative density of liquids can be determined using hydrometers, pycnometers, special balances and etc.
Determination of relative density using hydrometers.
To quickly determine the relative density of a liquid, so-called hydrometers are used (Fig. 489). This is a glass tube (Fig. 489, a), expanding at the bottom and having at the end a glass reservoir filled with shot or a special mass (less often - mercury). In the upper narrow part of the hydrometer there is a scale with divisions. The lower the relative density of the liquid, the deeper the hydrometer sinks into it. Therefore, on its scale, the smallest relative density value that can be determined by this hydrometer is indicated at the top, and the largest at the bottom. For example, for hydrometers for liquids with a relative density less than one, the value below is 1.000, above 0.990, even above 0.980, etc.
The spaces between the numbers are divided into smaller divisions, allowing the relative density to be determined with an accuracy of the third decimal place. For the most accurate hydrometers, the scale covers relative density values in the range of 0.2-0.4 units (for example, to determine density from 1,000 to 1,200, from 1,200 to 1,400, etc.). Such hydrometers are usually sold in the form of kits, which make it possible to determine relative density over a wide range.
Nomogram for introducing temperature correction
Sometimes hydrometers are equipped with thermometers (Fig. 489.6), which makes it possible to simultaneously measure the temperature at which the determination is carried out. To determine the relative density using a hydrometer, the liquid is poured into a glass cylinder (Fig. 490) with a capacity of at least 0.5 liters, similar in shape to the measuring cylinder, but without a spout or divisions. The size of the cylinder must match the size of the hydrometer. You should not pour liquid into the cylinder to the brim, since when the hydrometer is immersed, the liquid may overflow. This can even be dangerous when measuring the density of concentrated acids or concentrated alkalis, etc. Therefore, the liquid level in the cylinder should be several centimeters below the edge of the cylinder.
Sometimes the cylinder for determining density has a groove at the top, located concentrically, so that if the liquid overflows when the hydrometer is immersed, it will not spill out onto the table.
To determine the relative density, there are special instruments that maintain a constant level of liquid in the cylinder. A diagram of one of these devices is shown in Fig. 491. This is a cylinder 2, which has an outlet tube 3 at a certain height for draining the liquid displaced by the hydrometer when it is immersed in the liquid. The displaced liquid enters tube 4, which has a tap 5, through which the liquid can be drained. The cylinder can be filled with the test liquid through an equalizing tube /, which has a cylindrical extension in the upper part.
Density is usually called a physical quantity that determines the ratio of the mass of an object, substance or liquid to the volume it occupies in space. Let's talk about what density is, how the density of a body and a substance differs, and how (using what formula) to find density in physics.
Types of density
It should be clarified that density can be divided into several types.
Depending on the object being studied:
- The density of a body - for homogeneous bodies - is the direct ratio of the mass of a body to its volume occupied in space.
- The density of a substance is the density of bodies consisting of this substance. The density of substances is constant. There are special tables that indicate the density of different substances. For example, the density of aluminum is 2.7 * 103 kg/m3. Knowing the density of aluminum and the mass of the body that is made of it, we can calculate the volume of this body. Or, knowing that the body consists of aluminum and knowing the volume of this body, we can easily calculate its mass. We will look at how to find these quantities a little later, when we derive a formula for calculating density.
- If a body consists of several substances, then to determine its density it is necessary to calculate the density of its parts for each substance separately. This density is called the average density of the body.
Depending on the porosity of the substance of which the body is composed:
- True density is the density that is calculated without taking into account voids in the body.
- Specific gravity - or apparent density - is that which is calculated taking into account the voids of a body consisting of a porous or crumbly substance.
So how do you find density?
Formula for calculating density
The formula to help find the density of a body is as follows:
- p = m / V, where p is the density of the substance, m is the mass of the body, V is the volume of the body in space.
If we calculate the density of a particular gas, the formula will look like this:
- p = M / V m p - gas density, M - molar mass of gas, V m - molar volume, which under normal conditions is 22.4 l/mol.
Example: the mass of a substance is 15 kg, it occupies 5 liters. What is the density of the substance?
Solution: substitute the values into the formula
- p = 15 / 5 = 3 (kg/l)
Answer: density of the substance is 3 kg/l
Density units
In addition to knowing how to find the density of a body and substance, you also need to know the units of measurement of density.
- For solids - kg/m 3, g/cm 3
- For liquids - 1 g/l or 10 3 kg/m 3
- For gases - 1 g/l or 10 3 kg/m 3
You can read more about density units in our article.
How to find density at home
In order to find the density of a body or substance at home, you will need:
- Scales;
- Centimeter if the body is solid;
- A vessel if you want to measure the density of a liquid.
To find the density of a body at home, you need to measure its volume using a centimeter or vessel, and then put the body on the scale. If you are measuring the density of a liquid, be sure to subtract the mass of the container into which you poured the liquid before making your calculations. It is much more difficult to calculate the density of gases at home; we recommend using ready-made tables that already indicate the densities of various gases.
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 different objects have different weights - any of us can easily carry a juicy ripe melon from the market, but we will have to sweat over a weight of the same size.
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. The density of solids is 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
In lab work, you measured body weight by comparing the weight of 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 cylinder. 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 denoted by the Greek letter ρ (rho). Then
density = mass/volume
ρ = m/V.
The SI unit of density is 1 kg/m3. The densities of various substances are determined experimentally and are 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
- 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?
- What is density?
- Does the density of a substance depend on its volume? From the masses?
- In what units is density measured?
- 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 encounter 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 other facts known to science 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 the earth's crust is 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 matter located in the depths of the globe is 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 lifebelts 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 an irregularly shaped body). 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’s substance turned out to be less than the density of pure gold, and the dishonest jeweler was caught in deception.
Exercises
- 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?
- Determine the mass of a concrete slab whose volume is V = 3.0 m 3.
- What substance is a ball with volume V = 10 cm 3 made of if its mass m = 71 g?
- Determine the mass of window glass whose length a = 1.5 m, height b = 80 cm and thickness c = 5.0 mm.
- 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.
- Steel and aluminum cylinders have the same cross-sectional area and mass. Which cylinder has the greater height and by how much?