XII. States of matter Iron vapor and solid air Isn't it a strange combination of words? However, this is not nonsense at all: both iron vapor and solid air exist in nature, but not under ordinary conditions. What conditions are we talking about? The state of matter is determined

Gas pressure arises as a result of collisions of molecules with the walls of a vessel (and on a body placed in a gas), in which there are randomly moving gas molecules. The more frequent the blows, the stronger they are - the higher the pressure. If the mass and volume of a gas are constant, then its pressure in a closed vessel depends entirely on temperature. Pressure also depends on the speed of forward moving gas molecules. The unit of pressure is pascal p(Pa) . Gas pressure is measured with a pressure gauge (liquid, metal and electric).

Ideal gas is a model of real gas. A gas in a vessel is taken to be an ideal gas when a molecule flying from wall to wall of the vessel does not experience collisions with other molecules. More precisely, an ideal gas is a gas in which the interaction between its molecules is negligible ⇒ E to >> E r.

Basic MKT equation relates macroscopic parameters (pressure p , volume V , temperature T , weight m ) gas system with microscopic parameters (mass of molecules, average speed of their movement):

Where n - concentration, 1/m 3; m — molecular mass, kg; - root mean square speed of molecules, m/s.

Ideal gas equation of state- a formula establishing the relationship between pressure, volume and absolute temperature ideal gas, characterizing the state of a given gas system. —Mendeleev-Clapeyron equation (for an arbitrary mass of gas). R = 8.31 J/mol K — universal gas constant. pV = RT – (for 1 mole).

It is often necessary to investigate a situation when the state of a gas changes while its quantity remains unchanged ( m=const ) and in the absence of chemical reactions ( M=const ). This means that the amount of substance ν=const . Then:

For a constant mass of an ideal gas, the ratio of the product of pressure and volume to the absolute temperature in a given state is a constant value: — Clapeyron's equation.

Thermodynamic process (or simply process) is a change in the state of a gas over time. During the thermodynamic process, the values ​​of macroscopic parameters change - pressure, volume and temperature. Of particular interest are isoprocesses - thermodynamic processes in which the value of one of the macroscopic parameters remains unchanged. Fixing each of the three parameters in turn, we get t Three types of isoprocesses.

The last equation is called the unified gas law. It makes laws of Boyle - Mariotte, Charles and Gay-Lussac. These laws are called laws for isoprocesses:

Isoprocesses - these are processes that occur at the same parameter or T-temperature, or V-volume, or p-pressure.

Isothermal process— - Boyle's law - Mariotte (at a constant temperature and a given mass of gas, the product of pressure and volume is a constant value)

Isobaric process — - law

The Mendeleev-Clapeyron equation is an equation of state for an ideal gas, referred to 1 mole of gas. In 1874, D.I. Mendeleev, based on the Clapeyron equation, combining it with Avogadro’s law, using the molar volume V m and relating it to 1 mole, derived the equation of state for 1 mole of an ideal gas:

pV = RT, Where R- universal gas constant,

R = 8.31 J/(mol. K)

The Clapeyron-Mendeleev equation shows that for a given mass of gas it is possible to simultaneously change three parameters characterizing the state of an ideal gas. For an arbitrary mass of gas M, the molar mass of which is m: pV = (M/m) . RT. or pV = N A kT,

where N A is Avogadro's number, k is Boltzmann's constant.

Derivation of the equation:

Using the equation of state of an ideal gas, one can study processes in which the mass of the gas and one of the parameters - pressure, volume or temperature - remain constant, and only the other two change, and theoretically obtain gas laws for these conditions of change in the state of the gas.

Isobaric process- the process of changing the state of a system at constant pressure. For a gas of a given mass, the ratio of gas volume to its temperature remains constant if the gas pressure does not change. This Gay-Lussac's law. According to Gay-Lussac's law, the volume of a gas is directly proportional to its temperature: V/T=const. Graphically, this dependence in V-T coordinates is depicted as a straight line extending from the point T=0. This straight line is called an isobar. Different pressures correspond to different isobars. Gay-Lussac's law is not observed in the region of low temperatures close to the temperature of liquefaction (condensation) of gases.

Isochoric process- the process of changing the state of the system at a constant volume. For a given mass of gas, the ratio of gas pressure to its temperature remains constant if the volume of the gas does not change. This is Charles' gas law. According to Charles's law, gas pressure is directly proportional to its temperature: P/T=const. Graphically, this dependence in P-T coordinates is depicted as a straight line extending from the point T=0. This straight line is called an isochore. Different isochores correspond to different volumes. Charles's law is not observed in the region of low temperatures close to the temperature of liquefaction (condensation) of gases.

So, from the law pV = (M/m). RT derives the following laws:

T = const=> PV = const- Boyle's law - Mariotta.

p = const => V/T = const- Gay-Lussac's law.

If an ideal gas is a mixture of several gases, then according to Dalton’s law, the pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the gases entering it. Partial pressure is the pressure that a gas would produce if it alone occupied the entire volume equal to the volume of the mixture.

Some may be interested in the question of how it was possible to determine Avogadro’s constant N A = 6.02·10 23? The value of Avogadro's number was experimentally established only at the end of the 19th and beginning of the 20th centuries. Let us describe one of these experiments.

A sample of the radium element weighing 0.5 g was placed in a vessel with a volume V = 30 ml, evacuated to a deep vacuum and kept there for one year. It was known that 1 g of radium emits 3.7 10 10 alpha particles per second. These particles are helium nuclei, which immediately accept electrons from the walls of the vessel and turn into helium atoms. Over the course of a year, the pressure in the vessel increased to 7.95·10 -4 atm (at a temperature of 27 o C). The change in the mass of radium over a year can be neglected. So, what is N A equal to?

First, let's find how many alpha particles (that is, helium atoms) were formed in one year. Let's denote this number as N atoms:

N = 3.7 10 10 0.5 g 60 sec 60 min 24 hours 365 days = 5.83 10 17 atoms.

Let us write the Clapeyron-Mendeleev equation PV = n RT and note that the number of moles of helium n= N/N A . From here:

N A = NRT = 5,83 . 10 17 . 0,0821 . 300 = 6,02 . 10 23

PV 7.95. 10 -4. 3. 10 -2

At the beginning of the 20th century, this method of determining Avogadro's constant was the most accurate. But why did the experiment last so long (a year)? The fact is that radium is very difficult to obtain. With its small amount (0.5 g), the radioactive decay of this element produces very little helium. And the less gas in a closed vessel, the less pressure it will create and the greater the measurement error will be. It is clear that a noticeable amount of helium can be formed from radium only over a sufficiently long time.

Gas is one of four states of aggregation in which a substance can exist.

The particles that make up the gas are very mobile. They move almost freely and chaotically, periodically colliding with each other like billiard balls. Such a collision is called elastic collision . During a collision, they dramatically change the nature of their movement.

Since in gaseous substances the distance between molecules, atoms and ions is much greater than their sizes, these particles interact very weakly with each other, and their potential interaction energy is very small compared to the kinetic energy.

The connections between molecules in a real gas are complex. Therefore, it is also quite difficult to describe the dependence of its temperature, pressure, volume on the properties of the molecules themselves, their quantity, and the speed of their movement. But the task is greatly simplified if, instead of real gas, we consider its mathematical model - ideal gas .

It is assumed that in the ideal gas model there are no attractive or repulsive forces between molecules. They all move independently of each other. And the laws of classical Newtonian mechanics can be applied to each of them. And they interact with each other only during elastic collisions. The time of the collision itself is very short compared to the time between collisions.

Classical ideal gas

Let's try to imagine the molecules of an ideal gas as small balls located in a huge cube at a great distance from each other. Because of this distance, they cannot interact with each other. Therefore, their potential energy is zero. But these balls move at great speed. This means they have kinetic energy. When they collide with each other and with the walls of the cube, they behave like balls, that is, they bounce elastically. At the same time, they change the direction of their movement, but do not change their speed. This is roughly what the motion of molecules in an ideal gas looks like.

1. The potential energy of interaction between molecules of an ideal gas is so small that it is neglected compared to kinetic energy.
2. Molecules in an ideal gas are also so small that they can be considered material points. And this means that they total volume is also negligible compared to the volume of the vessel in which the gas is located. And this volume is also neglected.
3. The average time between collisions of molecules is much greater than the time of their interaction during a collision. Therefore, the interaction time is also neglected.

Gas always takes the shape of the container in which it is located. Moving particles collide with each other and with the walls of the container. During an impact, each molecule exerts some force on the wall for a very short period of time. This is how it arises pressure . The total pressure of a gas is the sum of the pressures of all molecules.

Ideal gas equation of state

The state of an ideal gas is characterized by three parameters: pressure, volume And temperature. The relationship between them is described by the equation:

Where R - pressure,

V M - molar volume,

R - universal gas constant,

T - absolute temperature (degrees Kelvin).

Because V M = V / n , Where V - volume, n - the amount of substance, and n= m/M , That

Where m - gas mass, M - molar mass. This equation is called Mendeleev-Clayperon equation .

At constant mass the equation becomes:

This equation is called united gas law .

Using the Mendeleev-Cliperon law, one of the gas parameters can be determined if the other two are known.

Isoprocesses

Using the equation of the unified gas law, it is possible to study processes in which the mass of a gas and one of the most important parameters - pressure, temperature or volume - remain constant. In physics such processes are called isoprocesses .

From The unified gas law leads to other important gas laws: Boyle-Mariotte law, Gay-Lussac's law, Charles's law, or Gay-Lussac's second law.

Isothermal process

A process in which pressure or volume changes but temperature remains constant is called isothermal process .

In an isothermal process T = const, m = const .

The behavior of a gas in an isothermal process is described by Boyle-Mariotte law . This law was discovered experimentally English physicist Robert Boyle in 1662 and French physicist Edme Mariotte in 1679. Moreover, they did this independently of each other. The Boyle-Mariotte law is formulated as follows: In an ideal gas at a constant temperature, the product of the gas pressure and its volume is also constant.

The Boyle-Marriott equation can be derived from the unified gas law. Substituting into the formula T = const , we get

p · V = const

That's what it is Boyle-Mariotte law . From the formula it is clear that the pressure of a gas at constant temperature is inversely proportional to its volume. The higher the pressure, the lower the volume, and vice versa.

How to explain this phenomenon? Why does the pressure of a gas decrease as the volume of a gas increases?

Since the temperature of the gas does not change, the frequency of collisions of molecules with the walls of the vessel does not change. If the volume increases, the concentration of molecules becomes less. Consequently, per unit area there will be fewer molecules that collide with the walls per unit time. The pressure drops. As the volume decreases, the number of collisions, on the contrary, increases. The pressure increases accordingly.

Graphically, an isothermal process is displayed on a curve plane, which is called isotherm . She has a shape hyperboles.

Each temperature value has its own isotherm. The higher the temperature, the higher the corresponding isotherm is located.

Isobaric process

The processes of changing the temperature and volume of a gas at constant pressure are called isobaric . For this process m = const, P = const.

The dependence of the volume of a gas on its temperature at constant pressure was also established experimentally French chemist and physicist Joseph Louis Gay-Lussac, who published it in 1802. That is why it is called Gay-Lussac's law : " Etc and constant pressure, the ratio of the volume of a constant mass of gas to its absolute temperature is a constant value."

At P = const the equation of the unified gas law turns into Gay-Lussac equation .

An example of an isobaric process is a gas located inside a cylinder in which a piston moves. As the temperature rises, the frequency of molecules hitting the walls increases. The pressure increases and the piston rises. As a result, the volume occupied by the gas in the cylinder increases.

Graphically, an isobaric process is represented by a straight line, which is called isobar .

The higher the pressure in the gas, the lower the corresponding isobar is located on the graph.

Isochoric process

Isochoric, or isochoric, is the process of changing the pressure and temperature of an ideal gas at constant volume.

For an isochoric process m = const, V = const.

It is very simple to imagine such a process. It occurs in a vessel of a fixed volume. For example, in a cylinder, the piston in which does not move, but is rigidly fixed.

The isochoric process is described Charles's law : « For a given mass of gas at constant volume, its pressure is proportional to temperature" The French inventor and scientist Jacques Alexandre César Charles established this relationship through experiments in 1787. In 1802, it was clarified by Gay-Lussac. Therefore this law is sometimes called Gay-Lussac's second law.

At V = const from the equation of the unified gas law we get the equation Charles's law or Gay-Lussac's second law .

At constant volume, the pressure of a gas increases if its temperature increases. .

On graphs, an isochoric process is represented by a line called isochore .

The larger the volume occupied by the gas, the lower the isochore corresponding to this volume is located.

In reality, no gas parameter can be maintained unchanged. This can only be done in laboratory conditions.

Of course, an ideal gas does not exist in nature. But in real rarefied gases at very low temperatures and pressures no higher than 200 atmospheres, the distance between the molecules is much greater than their sizes. Therefore, their properties approach those of an ideal gas.