According to their mechanical properties, gases have much in common with liquids. Like liquids, they do not have elasticity in relation to changes in shape. Separate parts of the gas can easily move relative to each other. Like liquids, they are elastic with respect to the deformation of all-round compression. As the external pressure increases, the volume of the gas decreases. When the external pressure is removed, the volume of the gas returns to its original value.

It is easy to verify the existence of elastic properties of a gas experimentally. Take a baby balloon. Inflate it not very much and tie it. After that, start squeezing it with your hands (Fig. 3.20). With the appearance of external pressures, the ball will shrink, its volume will decrease. If you stop squeezing, the ball will immediately straighten out, as if it had springs inside it.

Take an air pump for a car or a bicycle, close its outlet and push down on the piston handle. The air trapped inside the pump will begin to compress and you will immediately feel a rapid build-up of pressure. If you stop putting pressure on the piston, it will return to its place, and the air will take its original volume.

The elasticity of the gas in relation to all-round compression is used in car tires for shock absorption, in air brakes and other devices. Blaise Pascal was the first to notice the elastic properties of a gas, its ability to change its volume with a change in pressure.

As we have already noted, a gas differs from a liquid in that it cannot by itself keep the volume unchanged and does not have a free surface. It must necessarily be in a closed vessel and will always completely occupy the entire volume of this vessel.

Another important difference between a gas and a liquid is its greater compressibility (compliance). Already at very small changes in pressure, clearly visible large changes in the volume of the gas occur. In addition, the relationship between pressures and volume changes is more complex for a gas than for a liquid. Changes in volume will no longer be directly proportional to changes in pressure.

For the first time, the quantitative relationship between pressure and volume of gas was established by the English scientist Robert Boyle (1627-1691). In his experiments, Boyle observed changes in the volume of air contained in the sealed end of the tube (Fig. 3.21). He changed the pressure on this air by pouring mercury into the long elbow of the tube. The pressure was determined by the height of the mercury column

Boyle's experience in an approximate, rough form, you can repeat with an air pump. Take a good pump (it is important that the piston does not let air through), close the outlet and load the piston handle in turn with one, two, three identical weights. At the same time, mark the positions of the handle under different loads relative to the vertical ruler.

Even such rough experience will allow you to be convinced that the volume of a given mass of gas is inversely proportional to the pressure to which this gas is subjected. Regardless of Boyle, the same experiments were carried out by the French scientist Edmond Mariotte (1620-1684), who came to the same results as Boyle.

At the same time, Mariotte discovered that one very important precaution must be observed during the experiment: the temperature of the gas during the experiment must remain constant, otherwise the results of the experiment will be different. Therefore, Boyle's law - Mariotte is read like this; at constant temperature, the volume of a given mass of gas is inversely proportional to pressure.

If we denote through the initial volume and pressure of the gas, through the final volume and pressure of the same mass of gas, then

Boyle's law - Mariotte can be written as the following formula:

Let's present the Boyle-Mariotte law in a visual graphical form. For definiteness, let us assume that a certain mass of gas occupied the volume at pressure Let us graphically depict how the volume of this gas will change with increasing pressure at a constant temperature. To do this, we calculate the volumes of gas according to the Boyle-Mariotte law for pressures of 1, 2, 3, 4, etc. atmospheres and draw up a table:

Using this table, it is easy to plot the dependence of gas pressure on its volume (Fig. 3.22).

As can be seen from the graph, the dependence of pressure on gas volume is indeed complex. First, an increase in pressure from one to two units leads to a decrease in volume by half. Subsequently, with the same pressure increments, ever smaller changes in the initial volume occur. The more a gas is compressed, the more elastic it becomes. Therefore, for a gas, it is impossible to specify any constant modulus of compression (characterizing its elastic properties), as is done for solids. For gas, the compression modulus depends on the pressure under which the compression modulus is located increases with pressure.

Note that the Boyle-Mariotte law is observed only for not very high pressures and not very low temperatures. At high pressures and low temperatures, the relationship between gas volume and pressure becomes even more complex. For air, for example, at 0 ° C, the Boyle - Mariotte law gives the correct volume values ​​\u200b\u200bat a pressure not exceeding 100 atm.

At the beginning of the paragraph, it was already said that the elastic properties of a gas and its high compressibility are widely used by man in practical activities. Let's take a few more examples. The ability to highly compress a gas at high pressures makes it possible to store large masses of gas in small volumes. Cylinders with compressed air, hydrogen, oxygen are widely used in industry, for example, in gas welding (Fig. 3.23).

The good elastic properties of the gas served as the basis for the creation of river hovercraft (Fig. 3.24). These new types of ships are achieving speeds far beyond those previously achieved. Thanks to the use of the elastic properties of air, it was possible to get rid of large friction forces. True, in this case, the calculation of pressure is much more complicated, because it is necessary to calculate the pressure in fast air flows.

Many biological processes are also based on the use of the elastic properties of air. Have you thought, for example, about how you breathe? What happens when you inhale?

At the signal of the nervous system that the body lacks oxygen, a person, when inhaling, raises the ribs with the help of the muscles of the chest, and lowers the diaphragm with the help of other muscles. This increases the volume that the lungs (and the remaining air in them) can occupy. But this increase in volume leads to a large decrease in air pressure in the lungs. There is a pressure difference between the outside air and the air in the lungs. As a result, the outside air begins to enter the lungs itself due to its elastic properties.

We only give him the opportunity to enter by changing the volume of the lungs.

Not only this is the use of air elasticity during breathing. The lung tissue is very delicate, and it would not withstand repeated stretching and rather rough pressure on the pectoral muscles. Therefore, it is not attached to them (Fig. 3.25). In addition, the expansion of the lung by stretching its surface (with the help of the pectoral muscles) would cause uneven, unequal expansion of the lung in different parts. Therefore, the lung is surrounded by a special film - the pleura. The pleura is attached to the lung with one part, and the muscle tissue of the chest with the other. The pleura forms a kind of bag, the walls of which do not allow air to pass through.

The pleural cavity itself contains a very small amount of gas. The pressure of this gas becomes equal to the air pressure in the lungs only when the walls of the pleura are very close to each other. When inhaling, the volume of the cavity increases sharply. The pressure in it drops sharply. The lung, due to the remnants of the air contained in it, begins to expand itself evenly in all parts, like a rubber ball under the bell of an air pump.

Thus, nature has wisely used the elastic properties of air to create an ideal shock absorber for lung tissue and the most favorable conditions for its expansion and contraction.

When solving problems on the application of Newton's laws, we will use the Boyle-Mariotte law as an additional equation expressing the special elastic properties of gases.

The basic laws of ideal gases are used in technical thermodynamics to solve a number of engineering and technical problems in the process of developing design and technological documentation for aviation equipment, aircraft engines; their manufacture and operation.

These laws were originally obtained experimentally. Subsequently, they were derived from the molecular-kinetic theory of the structure of bodies.

Boyle's Law - Mariotte establishes the dependence of the volume of an ideal gas on pressure at a constant temperature. This dependence was deduced by the English chemist and physicist R. Boyle in 1662 long before the advent of the kinetic theory of gas. Regardless of Boyle in 1676, the same law was discovered by E. Mariotte. Law of Robert Boyle (1627 - 1691), English chemist and physicist who established this law in 1662, and Edme Mariotte (1620 - 1684), French physicist who established this law in 1676: the product of the volume of a given mass of an ideal gas and its pressure is constant at constant temperature or.

The law is called Boyle-Mariotte and states that at constant temperature, the pressure of a gas is inversely proportional to its volume.

Let at a constant temperature of a certain mass of gas we have:

V 1 - volume of gas at pressure R 1 ;

V 2 - volume of gas at pressure R 2 .

Then, according to the law, we can write

Substituting in this equation the value of the specific volume and taking the mass of this gas t= 1kg, we get

p 1 v 1 =p 2 v 2 or pv= const .(5)

The density of a gas is the reciprocal of its specific volume:

then equation (4) takes the form

i.e., the densities of gases are directly proportional to their absolute pressures. Equation (5) can be considered as a new expression of the Boyle-Mariotte law, which can be formulated as follows: the product of pressure and the specific volume of a certain mass of the same ideal gas for its various states, but at the same temperature, is a constant value.

This law can be easily obtained from the basic equation of the kinetic theory of gases. Replacing in equation (2) the number of molecules per unit volume by the ratio N/V (V is the volume of a given mass of gas, N is the number of molecules in the volume) we get

Since for a given mass of gas the quantities N and β constant, then at constant temperature T=const for an arbitrary amount of gas, the Boyle–Mariotte equation will have the form

pV = const, (7)

and for 1 kg of gas

pv = const.

Depict graphically in the coordinate system R – v change in the state of the gas.

For example, the pressure of a given mass of gas with a volume of 1 m 3 is 98 kPa, then, using equation (7), we determine the pressure of a gas with a volume of 2 m 3

Continuing the calculations, we get the following data: V(m 3) is equal to 1; 2; 3; 4; 5; 6; respectively R(kPa) equals 98; 49; 32.7; 24.5; 19.6; 16.3. Based on these data, we build a graph (Fig. 1).

Rice. 1. Dependence of the pressure of an ideal gas on the volume at

constant temperature

The resulting curve is a hyperbola, obtained at a constant temperature, is called an isotherm, and the process occurring at a constant temperature is called isothermal. The Boyle-Mariotte law is approximate and at very high pressures and low temperatures is unacceptable for thermal engineering calculations.

Gay–L u s s a ka law determines the dependence of the volume of an ideal gas on temperature at constant pressure. (The law of Joseph Louis Gay-Lussac (1778 - 1850), a French chemist and physicist who first established this law in 1802: the volume of a given mass of ideal gas at constant pressure increases linearly with increasing temperature, i.e , where is the specific volume at; β is the volume expansion coefficient equal to 1/273.16 per 1 o C.) The law was established experimentally in 1802 by the French physicist and chemist Joseph Louis Gay-Lussac, whose name is named. Investigating the thermal expansion of gases experimentally, Gay-Lussac discovered that at a constant pressure, the volumes of all gases increase almost equally when heated, i.e., with an increase in temperature by 1 ° C, the volume of a certain mass of gas increases by 1/273 of the volume that this mass gas occupied at 0°C.

The increase in volume during heating by 1 ° C by the same value is not accidental, but, as it were, is a consequence of the Boyle-Mariotte law. First, the gas is heated at a constant volume by 1 ° C, its pressure increases by 1/273 of the initial one. Then the gas expands at a constant temperature, and its pressure decreases to the initial one, and the volume increases by the same factor. Denoting the volume of a certain mass of gas at 0°C through V 0 , and at temperature t°C through V t Let's write the law as follows:

Gay-Lussac's law can also be represented graphically.

Rice. 2. Dependence of the volume of an ideal gas on temperature at a constant

pressure

Using equation (8) and assuming the temperature is 0°C, 273°C, 546°C, we calculate the volume of gas, respectively, V 0 , 2V 0 , 3V 0 . Let us plot the gas temperatures on the abscissa axis in some conditional scale (Fig. 2), and the gas volumes corresponding to these temperatures along the ordinate axis. Connecting the obtained points on the graph, we get a straight line, which is a graph of the dependence of the volume of an ideal gas on temperature at constant pressure. Such a line is called isobar, and the process proceeding at constant pressure - isobaric.

Let us turn once again to the graph of the change in the volume of gas from temperature. Let's continue the straight line to the intersection, with the x-axis. The point of intersection will correspond to absolute zero.

Let us assume that in equation (8) the value V t= 0, then we have:

but since V 0 ≠ 0, hence, whence t= – 273°C. But - 273°C=0K, which was required to be proved.

We represent the Gay-Lussac equation in the form:

Remembering that 273+ t=T, and 273 K \u003d 0 ° C, we get:

Substituting in equation (9) the value of the specific volume and taking t\u003d 1 kg, we get:

Relation (10) expresses the Gay-Lussac law, which can be formulated as follows: at constant pressure, the specific volumes of identical masses of the same ideal gas are directly proportional to its absolute temperatures. As can be seen from equation (10), the Gay-Lussac law states that that the quotient of dividing the specific volume of a given mass of gas by its absolute temperature is a constant value at a given constant pressure.

The equation expressing the Gay-Lussac law, in general, has the form

and can be obtained from the basic equation of the kinetic theory of gases. Equation (6) can be represented as

at p=const we obtain equation (11). Gay-Lussac's law is widely used in engineering. So, on the basis of the law of volumetric expansion of gases, an ideal gas thermometer was built to measure temperatures in the range from 1 to 1400 K.

Charles' Law establishes the dependence of the pressure of a given mass of gas on temperature at a constant volume. the pressure of an ideal gas of constant mass and volume increases linearly when heated, that is, where R o - pressure at t= 0°C.

Charles determined that when heated in a constant volume, the pressure of all gases increases almost equally, i.e. when the temperature rises by 1 ° C, the pressure of any gas increases exactly by 1/273 of the pressure that this mass of gas had at 0 ° C. Let us denote the pressure of a certain mass of gas in a vessel at 0°C through R 0 , and at temperature t° through p t . When the temperature rises by 1°C, the pressure increases by, and when the temperature increases by t°Cpressure increases by. pressure at temperature t°C equal to initial plus pressure increase or

Formula (12) allows you to calculate the pressure at any temperature if the pressure at 0°C is known. In engineering calculations, an equation (Charles' law) is often used, which is easily obtained from relation (12).

Because, and 273 + t = T or 273 K = 0°C = T 0

At constant specific volume, the absolute pressures of an ideal gas are directly proportional to the absolute temperatures. By interchanging the middle terms of the proportion, we get

Equation (14) is an expression of Charles's law in a general form. This equation can be easily derived from formula (6)

At V=const we obtain the general equation of Charles's law (14).

To construct a graph of the dependence of a given mass of gas on temperature at a constant volume, we use equation (13). Let, for example, at a temperature of 273 K=0°C, the pressure of a certain mass of gas is 98 kPa. According to the equation, the pressure at a temperature of 373, 473, 573 ° C, respectively, will be 137 kPa (1.4 kgf / cm 2), 172 kPa (1.76 kgf / cm 2), 207 kPa (2.12 kgf / cm 2). Based on these data, we build a graph (Fig. 3). The resulting straight line is called isochore, and the process proceeding at constant volume is called isochoric.

Rice. 3. Dependence of gas pressure on temperature at constant volume

Boyle's law - Mariotte

Boyle's Law - Mariotte- one of the fundamental gas laws, discovered in 1662 by Robert Boyle and independently rediscovered by Edme Mariotte in 1676. Describes the behavior of a gas in an isothermal process. The law is a consequence of the Clapeyron equation.

• 1 Wording
• 2 Consequences
• 3 See also
• 4 Notes
• 5 Literature

Wording

Boyle's law - Mariotte is as follows:

At constant temperature and mass of a gas, the product of the pressure of a gas and its volume is constant.

In mathematical form, this statement is written as a formula

where is the gas pressure; is the volume of gas, and is a constant value under the specified conditions. In general, the value is determined by the chemical nature, mass and temperature of the gas.

Obviously, if index 1 denotes the quantities related to the initial state of the gas, and index 2 - to the final state, then the above formula can be written as

. From what has been said and the above formulas, the form of the dependence of gas pressure on its volume in an isothermal process follows:

This dependence is another, equivalent to the first, expression of the content of the Boyle-Mariotte law. She means that

The pressure of a certain mass of gas at a constant temperature is inversely proportional to its volume.

Then the relationship between the initial and final states of the gas participating in the isothermal process can be expressed as:

It should be noted that the applicability of this and the above formula, which relates the initial and final pressures and volumes of gas to each other, is not limited to the case of isothermal processes. The formulas remain valid even in those cases when the temperature changes during the process, but as a result of the process, the final temperature is equal to the initial one.

It is important to clarify that this law is valid only in cases where the gas under consideration can be considered ideal. In particular, the Boyle-Mariotte law is fulfilled with high accuracy in relation to rarefied gases. If the gas is highly compressed, then significant deviations from this law are observed.

Boyle's law - Mariotte, Charles's law and Gay-Lussac's law, supplemented by Avogadro's law, are a sufficient basis for obtaining the ideal gas equation of state.

Consequences

The Boyle-Mariotte law states that the pressure of a gas in an isothermal process is inversely proportional to the volume occupied by the gas. If we take into account that the density of the gas is also inversely proportional to the volume it occupies, then we will come to the conclusion:

In an isothermal process, the pressure of a gas changes in direct proportion to its density.

It is known that compressibility, that is, the ability of a gas to change its volume under pressure, is characterized by a compressibility factor. In the case of an isothermal process, one speaks of an isothermal compressibility coefficient, which is determined by the formula

where the index T means that the partial derivative is taken at a constant temperature. Substituting in this formula the expression for the relationship between pressure and volume from the Boyle-Mariotte law, we get:

Thus, we come to the conclusion:

The isothermal compressibility coefficient of an ideal gas is equal to the reciprocal of its pressure.

see also

• Gay-Lussac's law
• Charles' law
• Avogadro's Law
• Ideal gas
• Ideal gas equation of state

Notes

1. Boyle - Mariotte's law // Physical Encyclopedia / Ch. ed. A. M. Prokhorov. - M.: Soviet Encyclopedia, 1988. - T. 1. - S. 221-222. - 704 p. - 100,000 copies.
2. Sivukhin DV General course of physics. - M.: Fizmatlit, 2005. - T. II. Thermodynamics and molecular physics. - S. 21-22. - 544 p. - ISBN 5-9221-0601-5.
3. 1 2 Elementary textbook of physics / Ed. G. S. Landsberg. - M.: Nauka, 1985. - T. I. Mechanics. Heat. Molecular physics. - S. 430. - 608 p.
4. 1 2 3 Kikoin A.K., Kikoin I.K. Molecular physics. - M.: Nauka, 1976. - S. 35-36.
5. At a constant mass.
6. Livshits L. D. Compressibility // Physical Encyclopedia / Ch. ed. A. M. Prokhorov. - M.: Great Russian Encyclopedia, 1994. - T. 4. - S. 492-493. - 704 p. - 40,000 copies.

   ISBN 5-85270-087-8.

Literature

• Petrushevsky F. F. Boyle-Mariotte law // Encyclopedic Dictionary of Brockhaus and Efron: in 86 volumes (82 volumes and 4 additional). - St. Petersburg, 1890-1907.

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Boyle-Mariotte law

The quantitative relationship between the volume and pressure of a gas was first established by Robert Boyle in 1662. * Boyle-Mariotte's law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure.

This law applies to any fixed amount of gas. As can be seen from fig. 3.2, its graphical representation may be different. The graph on the left shows that at low pressure, the volume of a fixed amount of gas is large.

The volume of a gas decreases as its pressure increases. Mathematically, this is written like this:

However, Boyle-Mariotte's law is usually written in the form

Such a record allows, for example, knowing the initial gas volume V1 and its pressure p to calculate the pressure p2 in the new volume V2.

Gay-Lussac's law (Charles' law)

In 1787, Charles showed that at constant pressure, the volume of a gas changes (in proportion to its temperature. This dependence is presented in graphical form in Fig. 3.3, from which it can be seen that the volume of a gas is linearly related to its temperature. In mathematical form, this dependence is expressed as follows :

Charles' law is often written in a different form:

V1IT1 = V2T1(2)

Charles' law was improved by J. Gay-Lussac, who in 1802 found that the volume of a gas, when its temperature changes by 1°C, changes by 1/273 of the volume that it occupied at 0°C.

It follows that if we take an arbitrary volume of any gas at 0°C and at constant pressure reduce its temperature by 273°C, then the final volume will be equal to zero. This corresponds to a temperature of -273°C, or 0 K. This temperature is called absolute zero. In fact, it cannot be achieved. On fig.

Figure 3.3 shows how the extrapolation of plots of gas volume versus temperature leads to zero volume at 0 K.

Absolute zero is, strictly speaking, unattainable. However, under laboratory conditions, it is possible to achieve temperatures that differ from absolute zero by only 0.001 K. At such temperatures, the random motions of molecules practically stop. This results in amazing properties.

For example, metals cooled to temperatures close to absolute zero lose their electrical resistance almost completely and become superconducting*. An example of substances with other unusual low-temperature properties is helium.

At temperatures close to absolute zero, helium loses its viscosity and becomes superfluid.

* In 1987, substances were discovered (ceramics sintered from oxides of lanthanide elements, barium and copper) that become superconducting at relatively high temperatures, on the order of 100 K (-173 °C). These "high-temperature" superconductors open up great prospects in technology.- Approx. transl.

Main laboratory equipment is the desktop on which all experimental work is carried out.

Every laboratory should have good ventilation. A fume hood is required, in which all work is carried out using foul-smelling or toxic compounds, as well as burning organic substances in crucibles.

In a special fume hood, in which work related to heating is not carried out, volatile, harmful or foul-smelling substances (liquid bromine, concentrated nitric and hydrochloric acids, etc.) are stored.

), as well as flammable substances (carbon disulfide, ether, benzene, etc.).

The laboratory needs water supply, sewerage, technical current, gas wiring and water heaters. It is also desirable to have a compressed air supply, vacuum line, hot water and steam supply.

If there is no special supply, water heaters of various systems are used to produce hot water.

By means of these apparatuses, heated by electricity or gas, a jet of hot water at a temperature of almost 100°C can be quickly obtained.

The laboratory must have installations for distillation (or demineralization) of water, since it is impossible to work in the laboratory without distilled or demineralized water. In cases where obtaining distilled water is difficult or impossible, commercial distilled water is used.

There must be clay jars with a capacity of 10-15 liters near work tables and water sinks for draining unnecessary solutions, reagents, etc., as well as baskets for broken glass, paper and other dry garbage.

In addition to working tables, the laboratory should have a desk where all notebooks and notes are stored, and, if necessary, a title table. There should be high stools or chairs near the work tables.

Analytical balances and instruments requiring a stationary installation (electrometric, optical, etc.) are placed in a separate room associated with the laboratory, and a special weighing room should be allocated for analytical balances. It is desirable that the weighing room be located with windows to the north. This is important because the balance must not be exposed to sunlight (“Scales and Weighing”).

In the laboratory, you must also have the most necessary reference books, manuals and textbooks, since often during work there is a need for tone or other information.

see also

Page 3

Chemical glassware used in laboratories can be divided into a number of groups. According to the purpose, the dishes can be divided into general-purpose, special-purpose and measured dishes. According to the material - for dishes made of plain glass, special glass, quartz.

To the group. general purpose items include those items that should always be in laboratories and without which most work cannot be carried out. These are: test tubes, simple and separating funnels, glasses, flat-bottomed flasks, crystallizers, conical flasks (Erlenmeyer), Bunsen flasks, refrigerators, retorts, flasks for distilled water, tees, taps.

The special purpose group includes those items that are used for any one purpose, for example: the Kipp apparatus, the Sok-rally apparatus, the Kjeldahl apparatus, reflux flasks, Wulff flasks, Tishchenko flasks, pycnometers, hydrometers, Drexel flasks, Kali apparatus , carbon dioxide tester, round bottom flasks, special refrigerators, molecular weight tester, melting and boiling point testers, etc.

Volumetric utensils include: graduated cylinders and beakers, pipettes, burettes and volumetric flasks.

To get started, we suggest watching the following video, where the main types of chemical glassware are briefly and easily considered.

see also:

General purpose cookware

Test tubes (Fig. 18) are narrow cylindrical vessels with a rounded bottom; they come in different sizes and diameters and from different glass. Ordinary" laboratory test tubes are made of fusible glass, but for special work, when heating to high temperatures is required, test tubes are made of refractory glass or quartz.

In addition to ordinary, simple test tubes, graduated and centrifuge conical test tubes are also used.

Test tubes in use are stored in special wooden, plastic or metal racks (Fig. 19).

Rice. 18. Plain and graduated tubes

Rice. 20. Adding powdered substances to the test tube.

Test tubes are used mainly for analytical or microchemical work. When carrying out reactions in a test tube, reagents should not be used in too large quantities. It is absolutely unacceptable that the test tube be filled to the brim.

The reaction is carried out with small amounts of substances; 1/4 or even 1/8 of the capacity of the test tube is sufficient. Sometimes it is necessary to introduce a solid substance (powders, crystals, etc.) into the test tube.

), for this, a strip of paper with a width slightly less than the diameter of the test tube is folded in half in length and the required amount of solid is poured into the resulting scoop. The tube is held in the left hand, tilted horizontally, and the scoop is inserted into it almost to the bottom (Fig. 20).

Then the test tube is placed vertically, but also lightly hit on it. When all the solid has poured out, the paper scoop is removed.

To mix the poured reagents, hold the test tube with the thumb and forefinger of the left hand at the upper end and support it with the middle finger, and with the index finger of the right hand, strike the bottom of the test tube with an oblique blow. This is enough for the contents to be well mixed.

It is absolutely unacceptable to close the test tube with your finger and shake it in this form; in this case, one can not only introduce something foreign into the liquid in the test tube, but sometimes damage the skin of the finger, get burned, etc.

If the tube is more than half full of liquid, the contents are mixed with a glass rod.

If the tube needs to be heated, it should be clamped in the holder.

When the test tube is ineptly and strongly heated, the liquid quickly boils and splashes out of it, so you need to heat it carefully. When bubbles begin to appear, the test tube should be set aside and, holding it not in the flame of the burner, but near it or above it, continue heating with hot air. When heated, the open end of the test tube should be turned away from the worker and from the neighbors on the table.

When strong heating is not required, it is better to lower the test tube with the heated liquid into hot water. If you work with small test tubes (for semi-microanalysis), then they are heated only in hot water poured into a glass beaker of the appropriate size (capacity not more than 100 ml).

Funnels are used for transfusion - liquids, for filtering, etc. Chemical funnels are produced in various sizes, their upper diameter is 35, 55, 70, 100, 150, 200, 250 and 300 mm.

Ordinary funnels have a smooth inner wall, but funnels with a ribbed inner surface are sometimes used for accelerated filtration.

Filter funnels always have a 60° angle and a cut long end.

During operation, the funnels are installed either in a special stand or in a ring on a conventional laboratory stand (Fig. 21).

For filtering into a glass, it is useful to make a simple holder for a funnel (Fig. 22). To do this, a strip of 70-80 lsh long and 20 mm wide is cut out of sheet aluminum with a thickness of about 2 mm.

A hole with a diameter of 12-13 mm is drilled at one of the ends of the strip and the strip is bent as shown in Fig. 22, a. How to fix the funnel on the glass is shown in fig. 22b.

When pouring liquid into a bottle or flask, do not fill the funnel to the brim.

If the funnel is tightly attached to the neck of the vessel into which the liquid is poured, then the transfusion is difficult, since increased pressure is created inside the vessel. Therefore, the funnel needs to be raised from time to time.

It is even better to make a gap between the funnel and the neck of the vessel by inserting, for example, a piece of paper between them. In this case, you need to make sure that the gasket does not get into the vessel. It is more expedient to use a wire triangle, which you can do yourself.

This triangle is placed on the neck of the vessel and then the funnel is inserted.

There are special rubber or plastic nozzles on the neck of the dishes, which provide communication between the inside of the flask and the outside atmosphere (Fig. 23).

Rice. 21. Strengthening the glass chemical funnel

Rice. 22. Device for mounting the funnel on a glass, in a tripod.

For analytical work when filtering, it is better to use analytical funnels (Fig. 24). The peculiarity of these funnels is that they have an elongated cut end, the inner diameter of which is smaller in the upper part than in the lower part; this design speeds up the filtering.

In addition, there are analytical funnels with a ribbed inner surface that supports the filter, and with a spherical expansion at the point where the funnel passes into the tube. Funnels of this design speed up the filtration process by almost three times compared to conventional funnels.

Rice. 23. Nozzles for bottle necks. Rice. 24. Analytical funnel.

Separating funnels(Fig. 25) is used to separate immiscible liquids (for example, water and oil). They are either cylindrical or pear-shaped and in most cases fitted with a ground glass stopper.

At the top of the outlet tube is a ground glass stopcock. The capacity of separating funnels is different (from 50 ml to several liters), depending on the capacity, the wall thickness also changes.

The smaller the capacity of the funnel, the thinner its walls, and vice versa.

During operation, separating funnels, depending on the capacity and shape, are strengthened in different ways. Cylindrical funnel of small capacity can be fixed simply in the foot. Large funnels are placed between two rings.

The lower part of the cylindrical funnel should rest on a ring, the diameter of which is slightly smaller than the diameter of the funnel, the upper ring has a slightly larger diameter.

If the funnel oscillates, a cork plate should be placed between the ring and the funnel.

The pear-shaped separating funnel is fixed on the ring, its neck is clamped with a foot. The funnel is always fixed first, and only then the liquids to be separated are poured into it.

Dropping funnels (Fig. 26) differ from separating funnels in that they are lighter, thin-walled and

Rice. 25. Separating funnels. rice. 26. Drip funnels.

In most cases with a long end. These funnels are used in many works, when a substance is added to the reaction mass in small portions or drop by drop. Therefore, they usually form part of the instrument. Funnels are fixed in the neck of the flask on a thin section or with a cork or rubber stopper.

Before working with a separating or dropping funnel, the glass tap section must be carefully lubricated with petroleum jelly or a special lubricant.

This makes it possible to open the faucet easily and effortlessly, which is very important, since if the faucet opens tightly, it can break it or damage the entire device when opening it.

The lubricant must be applied very thinly so that when the faucet is turned, it does not get into the funnel tube or inside the faucet opening.

For a more uniform flow of liquid drops from the dropping funnel and to monitor the rate of liquid supply, dropping funnels with a nozzle are used (Fig. 27). Such funnels immediately after the tap have an expanded part that passes into the tube. The liquid enters this expansion via a short tube through a stopcock and then into the funnel tube.

Rice. 27. Drip funnel with nozzle

Rice. 28. Chemical glasses.

Rice. 29. Flat funnel with nozzle

GLASSWARE 1 2 3

see also

Lesson 25

Lesson archive › Basic laws of chemistry

Lesson 25 " Boyle-Mariotte law» from the course « Chemistry for dummies» consider the law relating pressure and volume of gas, as well as graphs of pressure versus volume and volume versus pressure. Let me remind you that in the last lesson “Gas Pressure”, we examined the device and principle of operation of a mercury barometer, and also defined pressure and considered its units of measurement.

Robert Boyle(1627-1691), to whom we owe the first practically correct definition of a chemical element (we will learn in Chapter 6), was also interested in the phenomena occurring in vessels with rarefied air.

In inventing vacuum pumps for pumping air out of closed containers, he drew attention to a property familiar to anyone who had ever inflated a football chamber or carefully squeezed a balloon: the more air in a closed container is compressed, the more it resists compression.

Boyle called this property " springiness» air and measured it using a simple device shown in fig. 3.2, a and b.

Boyle sealed some air with mercury at the closed end of the curved tube (Fig. 3-2, a) and then compressed this air, gradually adding mercury to the open end of the tube (Fig. 3-2, b).

The pressure experienced by the air in the closed part of the tube is equal to the sum of atmospheric pressure and the pressure of a mercury column of height h (h is the height by which the level of mercury at the open end of the tube exceeds the level of mercury at the closed end). The pressure and volume measurement data obtained by Boyle are given in Table. 3-1.

Although Boyle did not take special measures to maintain a constant temperature of the gas, it seems that in his experiments it changed only slightly. However, Boyle noticed that the heat from the candle flame caused significant changes in the properties of the air.

Analysis of data on the pressure and volume of air during its compression

Table 3-1, which contains Boyle's experimental data on the relationship between pressure and volume for atmospheric air, is located under the spoiler.

After the researcher receives data similar to those given in Table. 3-1, he is trying to find a mathematical equation that relates two mutually dependent quantities that he measured.

One way to get such an equation is to graphically plot the various powers of one quantity against another, hoping to get a straight line graph.

The general equation of a straight line is:

where x and y are related variables, and a and b are constant numbers. If b is zero, a straight line passes through the origin.

On fig. 3-3 show various ways of graphical representation of data for pressure P and volume V, given in table. 3-1.

Graphs of P versus 1/K and V versus 1/P are straight lines passing through the origin.

The plot of log P versus log V is also a negatively sloped straight line whose angle tangent is -1. All three of these plots lead to the equivalent equations:

• P \u003d a / V (3-3a)
• V = a / P (3-3b)

• lg V \u003d lg a - lg P (3-3c)

Each of these equations is one of the variants Boyle-Mariotte law, which is usually formulated as follows: for a given number of moles of a gas, its pressure is proportional to its volume, provided that the temperature of the gas remains constant.

By the way, you probably wondered why the Boyle-Mariotte law is called a double name. This happened because this law, independently of Robert Boyle, who discovered it in 1662, was rediscovered by Edme Mariotte in 1676. That's it.

When the relationship between two measured quantities is as simple as in this case, it can also be established numerically.

If each value of pressure P is multiplied by the corresponding value of volume V, it is easy to verify that all products for a given gas sample at constant temperature are approximately the same (see Table 3-1). Thus, one can write that

Equation (3-3g) describes the hyperbolic relationship between the values ​​of P and V (see Fig. 3-3, a). To check that the graph of the dependence of P on V, built according to experimental data, really corresponds to a hyperbola, we will construct an additional graph of the dependence of the product P V on P and make sure that it is a horizontal straight line (see Fig. 3-3,e) .

Boyle found that for a given amount of any gas at a constant temperature, the relationship between pressure P and volume V is quite satisfactorily described by the relation

• P V = const (at constant T and n) (3-4)

Formula from the Boyle-Mariotte law

To compare the volumes and pressures of the same gas sample under different conditions (but at a constant temperature), it is convenient to represent boyle-mariotte law in the following formula:

where indices 1 and 2 correspond to two different conditions.

Example 4 Plastic food bags delivered to the Colorado Plateau (see Example 3) often burst because the air in them expands as it rises from sea level to a height of 2500 m, under conditions of reduced atmospheric pressure.

If we assume that there is 100 cm3 of air inside the bag at atmospheric pressure corresponding to sea level, what volume should this air occupy at the same temperature on the Colorado Plateau? (Assume that puckered bags are used to deliver products that do not restrict air expansion; the missing data should be taken from example 3.)

Decision
We will use Boyle's law in the form of equation (3-5), where index 1 will refer to conditions at sea level, and index 2 to conditions at an altitude of 2500 m above sea level. Then P1 = 1.000 atm, V1 = 100 cm3, P2 = 0.750 atm, and V2 should be calculated. So,

22. Boyle-Mariotte Law

One of the ideal gas laws is Boyle-Mariotte Law, which reads: product of pressure P per volume V gas at a constant mass of gas and temperature is constant. This equality is called isotherm equations. The isotherm is depicted on the PV-diagram of the gas state as a hyperbola and, depending on the temperature of the gas, occupies one or another position. The process taking place at T= const, called isothermal. Gas at T= const has a constant internal energy U. If the gas expands isothermally, then all the heat goes to do work. The work done by a gas expanding isothermally is equal to the amount of heat that must be imparted to the gas to perform it:

dA= dQ= PdV,

where d BUT- elementary work;

dv- elementary volume;

P- pressure. If V 1 > V 2 and P 1< P 2 , то газ сжимается, и работа принимает отрицательное значение. Для того чтобы условие T= const was satisfied, it is necessary to consider changes in pressure and volume as infinitely slow. There is also a requirement for the medium in which the gas is located: it must have a sufficiently large heat capacity. The formulas for the calculation are also suitable in the case of supplying thermal energy to the system. Compressibility gas is called its property to change in volume with a change in pressure. Each substance has compressibility factor, and it is equal to:

c = 1 / V O (dV / CP) T ,

here the derivative is taken at T= const.

The compressibility factor is introduced to characterize the change in volume with a change in pressure. For an ideal gas, it is equal to:

c = -1 / P.

In SI, the compressibility factor has the following dimensions: [c] = m 2 /N.

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The quantitative relationship between the volume and pressure of a gas was first established by Robert Boyle in 1662. * Boyle-Mariotte's law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure. This law applies to any fixed amount of gas. As can be seen from fig. 3.2, its graphical representation may be different. The graph on the left shows that at low pressure, the volume of a fixed amount of gas is large. The volume of a gas decreases as its pressure increases. Mathematically, this is written like this:

However, Boyle-Mariotte's law is usually written in the form

Such a record allows, for example, knowing the initial gas volume V1 and its pressure p to calculate the pressure p2 in the new volume V2.

Gay-Lussac's law (Charles' law)

In 1787, Charles showed that at constant pressure, the volume of a gas changes (in proportion to its temperature. This dependence is presented in graphical form in Fig. 3.3, from which it can be seen that the volume of a gas is linearly related to its temperature. In mathematical form, this dependence is expressed as follows :

Charles' law is often written in a different form:

V1IT1 = V2T1(2)

Charles' law was improved by J. Gay-Lussac, who in 1802 found that the volume of a gas, when its temperature changes by 1°C, changes by 1/273 of the volume that it occupied at 0°C. It follows that if we take an arbitrary volume of any gas at 0°C and at constant pressure reduce its temperature by 273°C, then the final volume will be equal to zero. This corresponds to a temperature of -273°C, or 0 K. This temperature is called absolute zero. In fact, it cannot be achieved. On fig. Figure 3.3 shows how the extrapolation of plots of gas volume versus temperature leads to zero volume at 0 K.

Absolute zero is, strictly speaking, unattainable. However, under laboratory conditions, it is possible to achieve temperatures that differ from absolute zero by only 0.001 K. At such temperatures, the random motions of molecules practically stop. This results in amazing properties. For example, metals cooled to temperatures close to absolute zero lose their electrical resistance almost completely and become superconducting*. An example of substances with other unusual low-temperature properties is helium. At temperatures close to absolute zero, helium loses its viscosity and becomes superfluid.

* In 1987, substances were discovered (ceramics sintered from oxides of lanthanide elements, barium and copper) that become superconducting at relatively high temperatures, on the order of 100 K (-173 °C). These "high-temperature" superconductors open up great prospects in technology.- Approx. transl.