Mixtures of ideal gases Dalton's law. gas mixtures. Dalton's Law. See what "Dalton's Laws" are in other dictionaries

The partial pressure of each gas that is part of the mixture is the pressure that would be created by the same mass of this gas if it occupied the entire volume of the mixture at the same temperature.

In nature and technology, we very often deal not only with one pure gas, but with a mixture of several gases. For example, air is a mixture of nitrogen, oxygen, argon, carbon dioxide and other gases. What does the pressure of a mixture of gases depend on?

In 1801, John Dalton established that the pressure of a mixture of several gases is equal to the sum of the partial pressures of all the gases that make up the mixture.

This law is called the law of partial pressures of gases

Dalton's Law The partial pressure of each gas in a mixture is the pressure that would be created by the same mass of that gas if it occupied the entire volume of the mixture at the same temperature.

Dalton's law states that the pressure of a mixture of (ideal) gases is the sum of the partial pressures of the components of the mixture (the partial pressure of a component is the pressure that a component would exert if it alone occupied the entire space occupied by the mixture). This law indicates that each component is not affected by the presence of other components and the properties of the component in the mixture do not change.

Two laws of Dalton

Law 1 The pressure of a mixture of gases is equal to the sum of their partial pressures. It follows from this that the partial pressure of a component of a gas mixture is equal to the product of the pressure of the mixture and the molar fraction of this component.

Law 2 The solubility of a component of a gas mixture in a given liquid at a constant temperature is proportional to the partial pressure of this component and does not depend on the pressure of the mixture and the nature of other components.

The laws are formulated by J. Dalton resp. in 1801 and 1803.

Dalton's law equation

As already noted, the individual components of the gas mixture are considered independent. Therefore, each component creates pressure:

\[ p = p_i k T \quad \left(1\right), \]

and the total pressure is equal to the sum of the pressures of the components:

\[ p = p_(01) k T + p_(02) k T + \cdots + p_(i) k T = p_(01) + p_(02) + \cdots + p_(i) \quad \left( 2\right),\]

where \(p_i\) is the partial pressure i of the gas component. This equation is Dalton's law.

At high concentrations, high pressures, Dalton's law is not fulfilled exactly. Since the interaction between the components of the mixture is manifested. Components are no longer independent. Dalton explained his law using the atomistic hypothesis.

Let there be i component in the mixture of gases, then the Mendeleev-Claiperon equation will look like:

\[ ((p)_1+p_2+\dots +p_i)V=(\frac(m_1)((\mu )_1)+\frac(m_2)((\mu )_2)+\dots +\frac(m_i )((\mu )_i))RT\ \quad \left(3\right), \]

where \(m_i \) are the masses of the gas mixture components, \((\mu )_i \) - molar masses component of the gas mixture.

If you enter \(\left\langle \mu \right\rangle \) such that:

\[ \frac(1)(\left\langle \mu \right\rangle )=\frac(1)(m)\left[\frac(m_1)((\mu )_1)+\frac(m_2)( (\mu )_2)+\dots +\frac(m_i)((\mu )_i)\right] \quad \left(4\right), \]

then equation (3) can be written as:

\[ pV=\frac(m)(\left\langle \mu \right\rangle )RT \quad \left(5\right). \]

Dalton's law can be written as:

\[ p=\sum\limits^N_(i=1)(p_i)=\frac(RT)(V)\sum\limits^N_(i=1)((\nu )_i)\ \quad \left (6\right). \]

\[ p_i=x_ip\ \quad \left(7\right), \]

where \(x_i-molar\ concentration\ i-th \) gas in the mixture, while:

\[ x_i=\frac((\nu )_i)(\sum\limits^N_(i=1)(n_i))\ \quad \left(8\right), \]

where \((\nu )_i \) is the number of moles \(i-th\) gas in the mixture.

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Law Formulation

The law of the total pressure of a mixture of gases

Law on the solubility of the components of a gas mixture

At a constant temperature, the solubility in a given liquid of each of the components of the gas mixture above the liquid is proportional to their partial pressure.

Limits of applicability

Both Dalton's laws are strictly fulfilled for ideal gases. For real gases, these laws are applicable provided that their solubility is low and their behavior is close to that of an ideal gas.

Discovery history

The law of addition of partial pressures was formulated in 1801. At the same time, the correct theoretical justification, based on the molecular kinetic theory, was made much later.

Notes

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See what "Dalton's Laws" are in other dictionaries:

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Dalton's laws- discovered by the English physicist and chemist J. Dalton (1766 1844) in 1801 and 1803. 1) the pressure of a mixture of chemically non-interacting ideal gases is equal to the sum of the partial pressures. Applicable to real gases at temperatures and pressures, ... ... Concepts modern natural science. Glossary of basic terms

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gas mixtures. Dalton's law

Partial pressure is that part of the total pressure of a gas mixture, which is due to a given gas or vapor. The partial gas in the mixture is equal to the pressure of the gas in the mixture, which it would have alone, occupying the same volume as the mixture occupies at the same temperature.

Dalton's Law.With absence chemical reactions the total pressure of the gas mixture Ptot is equal to the sum of the partial pressures of all gases included in it p 1, p 2, p 3 ..., p n ˸

P total \u003d p 1 + p 2 + ... + p n. (62)

The partial pressure of a given gas is proportional to the fraction of ᴇᴦο molecules of the total number of molecules in the mixture (mole fraction)˸

p i = P total X i = P total · . (63)

Mole fraction X i - is the ratio of the number of moles of a given substance - n i (or a certain type of particles) to the total number of moles of a substance (or particles) in the system n i .

The mole fraction can be attributed either to the entire system or to some phase. In the latter case, the ratio of the number of moles of a given substance in this phase to the total number of moles of a substance forming this phase is taken. The sum of the mole fractions of all substances forming a system (or phase) is equal to one.

The composition of gas mixtures can also be expressed using weight, volume parts. The weight fraction of a given gas in a mixture is the ratio of the mass of this gas to the mass of the gas mixture. If we denote the weight fractions of gases through G 1 , G 2 , G 3 , …, G i ; and the masses of gases in the mixture - through m 1, m 2, m 3, ..., m i and the total mass of the gas mixture - through m, then we get ˸

G 1 \u003d G 2 \u003d G 3 \u003d ... G n \u003d (64)

G 1 + G 2 + G 3 + ... + G n \u003d 1

m 1 + m 2 + m 3 + ... + m n \u003d m.

To express the composition of a gas mixture in volume units, it is necessary to reduce the volumes of the gases that make up the mixture to one pressure and one temperature. The volume of an individual gas that is part of a mixture, reduced to the pressure of the mixture, is called the reduced volume. In order to find the reduced volume of gas at the pressure of the gas mixture Ptotal and temperature T, it is necessary to use the Boyle-Mariotte law

p 1 V total = v 1 P total; p 2 V total = v 2 P total; p 3 V total = v 3 P total; … ; p n V total = v n P total,

where v 1, v 2, v 3, ..., v n are the reduced volumes of individual gases that make up the mixture; р 1 , р 2 , р 3 , …, р n – partial pressures of individual gases;

v 1 = v 2 = v 3 = ...; v n = (65)

The sum of the reduced volumes of the individual gases is equal to the total volume of the mixture˸

v 1 + v 2 + v 3 + ... + v n = V total.

The ratio of the reduced volumes of individual gases to the total volume of the mixture is called the volume fraction and is expressed in terms of r˸

r 1 \u003d r 2 \u003d r 3 \u003d ...; r n = (66)

For gas mixtures, the composition expressed by volume and mole fractions is the same, i.e. ˸

gas mixtures. Dalton's law - concept and types. Classification and features of the category "Gas mixtures. Dalton's law" 2015, 2017-2018.

Formulation: the total pressure of the mixture and gases is equal to the sum of the partial pressures of the gases that make up this mixture.

The partial pressure of a gas is the pressure that a gas would exert if it were alone in the system and occupied the entire volume that the system occupies.

• 44 g - 6.02*
• 4 g - x
• 4= 66,22*

A task. The combustion of 2 g of metal consumes 400 ml of oxygen. Find the metal equivalent.

A task. The relative density for hydrogen is 14. Calculate the molar mass.

М=28 g/mol

Chemical thermodynamics

Chemical thermodynamics is a section of the course physical chemistry, which studies the processes of heat transfer between the system and the environment, as well as the properties of the system in equilibrium.

Basic concepts.

A system is a material part of the Universe, which is subjected to theoretical and experimental study.

The interface between the system and the environment can be both real and fictitious (imaginary).

If the system exchanges matter and energy with the environment, then such a system is called open.

If the system does not exchange matter and energy with the environment, then such a system is called isolated.

If it exchanges energy and does not exchange matter, then it is called closed.

exothermic reaction - reaction passing with the absorption of heat.

An endothermic reaction is a reaction that releases heat.

The state function F (p, V, T…) is called the state function if its value does not depend on the path of the system transition from one state to another, but depends only on the value of the parameters in the initial and final states.

• 1. Potential energy (since its value depends only on the height difference and does not depend on the transition path)
• 2.PV
• 3. Internal energy of the system.

The system is in a state thermodynamic equilibrium, if the equilibrium mechanism is simultaneously carried out (the pressure at all points of the system is the same), thermodynamic and chemical equilibrium (this is the composition of the starting materials and reaction products at all points is the same).

A reversible process is one in which the system passes from one state to another through a continuous series of equilibrium processes. In this case, the parameters of the system and the environment differ from each other by an infinitesimal value. Otherwise, the process is called irreversible.

A homogeneous system is one in which the components are in the same phase. A heterogeneous system is a system in which the components are in different phases. Consider whether heat and work are state functions. Both work and heat are forms of energy transfer. Work in the form of an ordered movement of particles, heat - in a chaotic.

Consider the process of expansion of an ideal gas at t=const

1. The process is reversible

d is the infinitesimal of the state function

p inside = p outside

2. The process is irreversible

Thus, the amount of mechanical work is not a state function. It depends on the path of the process transition from one state to another and therefore its small change in heat will denote.

I law of thermodynamics.

Formulation: the internal energy of the system is a function of state, which means that it does not matter which way the process goes.

Let's consider special cases.

1. When p=const

Enthalpy

The physical meaning of enthalpies is the thermal effect of the reaction at p=const.

2. When V=const

Physical meaning - the thermal effect of the reaction at V=const

Thermochemistry. Hess' law.

The thermal effect of the reaction is due to the fact that the energy of the products differs from the energy of the reactants.

Heat release (exothermic reaction)

Heat absorption (endothermic reaction)

If the reaction passes through a series of intermediate states, then the thermal effect of the reaction does not depend on the path of the system's transition from one state to another, but depends only on the value of the system parameters in the final and initial states.

I corollary of Hess's law: the thermal effect of the reaction is equal to the difference the sums of the heats of formation of products and reactants, taking into account the stoichiometric coefficients in the reaction equation.

nj, ni - stoichiometric coefficients - heat of formation

The thermal effect of the reaction is the formation of 1 mol of a complex substance from simple ones.

o - standard state

All heats of formation are measured for the standard state (298K, Pa, for liquids with a concentration of 1 mol in 1 liter, for solids, the most stable crystallographic modification is selected)

In thermochemistry, heats of formation simple substances conditionally we take equal to zero.

I consequence of the Hess law: the heat effect of the reaction is equal to the difference between the sums of the heats of combustion of the reactants and products, taking into account the stoichiometric coefficients in the reaction equation.

The heat of combustion is the thermal effect of the reaction of complete combustion of one mole of a substance in a calorimeter current at atmospheric pressure.

A task. Determine the heat of combustion

(kJ/mol) : -873.79 -1966.91 2254.21 0

\u003d (-873.79-1566.97) - (-2254.81) \u003d 13.51 - exothermic reaction, i.e. 13.51 heat is released per 1 mole of acetic acid.

The dependence of the thermal effect of the reaction on temperature. Kirchhoff equation.

Heat capacities

the heat that needs to be imparted to 1 mole of a substance in order to heat it up.

In order to calculate the thermal effect of a reaction at a temperature, it is necessary to calculate the thermal effect at 298K of a change in the heat capacity of a given reaction (the difference between the sums of thermal effects of products and reactants, taking into account stoichiometric coefficients)

Despite the fact that the heat capacity depends on temperature, for calculations we will assume that the heat capacity does not depend on temperature and the temperature will be taken as 298 K.

II law of thermodynamics. There is a state function S called entropy. dS-total differential, which in reversible processes is equal to

dS = , in irreversible - dS . =

For isolated systems, heat exchange with the environment does not occur, therefore, for reversible processes, for irreversible ones.

For isolated systems, spontaneous processes (irreversible processes) occur with increasing entropy.

If the system is in thermodynamic state 1, which corresponds to the number of microstates, then the system goes into thermodynamic state 2 if it corresponds to a larger number of microstates

The physical meaning of entropy is a measure of molecular disorder.

The more random, the more S.

To calculate the change in entropy during a reaction, you need to know all those involved in the reaction.

The standard entropy values ​​of all substances at 298 K are given in the Handbook of Thermodynamic Quantities.

III law of thermodynamics.

The entropy of an ideal crystal at a temperature of absolute 0 Kelvin is S=0.

An ideal crystal is a crystal in which atoms occupy all nodes of the crystal lattice in strict accordance with geometric laws. At 0 K, such a crystal completely lacks vibrational, rotational, translational motion of particles, i.e., one single microstate is described by one single macrostate.

Calculation of entropy change during heating.

Processes phase transitions are isobaric-isothermal and reversible, so the change in entropy for a reversible process is equal to the ratio of the heat of formation of the product to the temperature.

Gibbs energy.

Gibbs energy change as a criterion for the spontaneous flow of a process in closed systems.

Reversible process Irreversible process

DG - isothermal potential

• ?S=?U/T
• ?H-T?S=0 P,T=const
• ?S_ >?H/T

DG=DH-TDS< 0

(Gibbs energy)

• ?S>?U/T
• ?H-T?S

Isochoric-isothermal potential

Balance state

The physical meaning of the change in the Gibbs energy: the maximum useful work that the system does.

If there is a phase transition

Physical meaning: if enthalpy characterizes the tendency of the system to order (i.e., to reduce the energy reserve), then entropy characterizes the tendency of the system to chaos, and the Gibbs energy is the resulting value of these oppositely directed processes.

chemical balance.

Thermodynamics makes it possible to determine not only the direction of the process (by the sign of the Gibbs energy), but also the quantitative calculation of the system in equilibrium.

Consider a homogeneous gaseous reaction

equilibrium constant

The equilibrium constant is equal to the ratio of the partial pressures of the products to the partial pressures of the starting materials in powers equal to their stoichiometric coefficients.

Offset Conditions chemical equilibrium(Le Chatelier's principle)

Statement: if an external force acts on a system in equilibrium, then the equilibrium shifts in the direction that weakens the applied force.

I. Influence of temperature on the equilibrium shift (van't Hoff isobar)

An increase in temperature contributes to the flow of the reaction, which reduces the heat input, shifts the equilibrium towards an isothermal reaction.

The more, the more the temperature affects the equilibrium shift.

II. Influence of pressure on the displacement of equilibrium.

equilibrium

The pressure of gaseous systems is determined by the number of impacts of molecules on the walls of the vessel.

With increasing pressure, the equilibrium shifts towards those substances that occupy a smaller volume (toward a decrease in the number of molecules).

III. Influence of composition.

An increase in the concentration of one of the reactants contributes to a shift in the equilibrium towards the formation of reaction products.

The basic equation for calculating chemical equilibrium according to the table of thermodynamic quantities is

(all substances are gases) at T = 600K.

(kJ) (J/mol)

7.22 J/mol K

When substituting, we get:

Answer: - 84%

The greater the negative Gibbs energy, the greater the value of the equilibrium constant, therefore, the equilibrium system will be dominated by the reaction products.

If the equilibrium constant is less than 1, then the Gibbs energy is greater than 0.

Chemical kinetics.

Chemical kinetics is a branch of physical chemistry that studies the course of processes over time.

Average rate - change in the concentration of reactants or products over a certain period of time.

True (instantaneous) speed

The reaction rate is always a positive value, and the sign depends on what concentration it takes, the starting substances or products (“-” - starting substances, “+” - products). The tangent of the slope of the tangent to the curve allows you to calculate the true speed at each moment in time.

For heterogeneous reactions:

S-mass interface

The law of active masses.

The law of mass action is the basic law of formal kinetics.

Consider a homogeneous reaction where all substances are in gaseous states. The formulation of the law: the reaction rate is directly proportional to the concentration of the reactants in degrees equal to the stoichiometric coefficients.

The physical meaning of the rate constant is the rate of a reaction if the concentration is 1.

A task. How will the rate of a direct reaction change if the pressure is tripled?

If the pressure increases by 3 times, then the concentration increases by 3 times (Mendeleev-Claiperon equation)

Answer: will increase by 27 times

For heterogeneous reactions, the rate depends only on the concentration of gaseous substances, since in solids it is a constant value.

The reaction order, denoted n, is determined by the sum of the exponents in the law of mass action. For elementary reactions that proceed in one stage, the order and molecularity coincide, for complex ones they do not.

Studying the order of a reaction is a method of studying its mechanism.

1) Kinetic equation of the first order (all decay reactions)

Let the concentration at the initial moment of time be a moles/liter. If at the time

X moles of substance a, then

Thus, for a reaction of the first order, the graph in InC() coordinates is a straight line with a negative slope, and tg allows us to calculate the rate constant

2) Kinetic reaction equation of the second order

We assume that the initial concentration of substances is equal.

If a moles / liter reacted at the moment of time, then

3) Kinetic equation reactions III order. The reaction proceeds in several stages. The overall rate of the entire reaction is equal to the sum of the rates of all stages.

The second characteristic of a first order reaction is the half-life

Effect of temperature on the reaction rate. Van't Hoff equation.

For every 1C increase in temperature, the reaction rate increases by 2-4 times.

Van't Hoff rule

Arrhenius theory.

Basic provisions:

• 1) In order for a chemical interaction of substances to occur, they must collide
• 2) The energy of the particles must be greater than or equal to the activation energy of the reaction
• 3) Collisions of particles must occur on the functional group

The activation energy is the minimum energy that must be given to a molecule in order for a chemical interaction to occur.

As the temperature increases, the activation energy increases.

where K is the rate constant, A is the pre-exponential factor, R is the universal gas constant, T is the temperature in Kelvin.

1) Analytical

Divide the (1) equation by (2)

If the values ​​of the two rate constants at two temperatures are known, then the activation energy of the reaction can be calculated.

2) Graphic

Disadvantages of the Arrhenius theory:

• 1) Real speed often turns out to be lower than that calculated by the Arrhenius theorem
• 2) the theory does not explain the phenomenon of catalysis.

Some reaction takes 16 minutes at a temperature of 2 How long will this reaction take at a temperature of 5 if =3.

If the gas consists of a mixture of several gases, then Dalton's law will help calculate the pressure of the mixture

where p v p 2 , p b - partial pressures gases in the mixture.

Partial pressure called the pressure that a gas would have if it alone occupied the entire volume provided.

Molecular Kinetic Theory(MKT) originated in the 19th century. and presented the structure of matter (mainly gases) in terms of three positions:

• all bodies are made up of particles: atoms and molecules;
• particles are in continuous chaotic motion (thermal);
• particles interact with each other by absolutely elastic collisions.

The MKT has become one of the most successful physical theories and has been confirmed by a number of experimental facts. A clear experimental confirmation of the chaotic thermal motion of atoms and molecules was Brownian motion.

Brownian motion - this phenomenon was discovered by Robert Brown 1 in 1827. While observing the movement of pollen suspended in water through a microscope, he saw disordered zigzag trajectories of particles.

Cause brownian motion is the thermal motion of the molecules of the medium, which is due to pressure fluctuations. Impacts of the molecules of the medium lead the particle into random motion: its speed rapidly changes in magnitude and direction. A complete theory of Brownian motion was given later by Albert Einstein and Marian Smoluchowski.

Basic equation of the MKT. The gas pressure on the vessel wall is determined by the momentum imparted by the gas molecules to the vessel wall when they collide with it. The higher the speed of the molecule, the greater the momentum it carries, the stronger it acts on the wall, i.e. R ~ v. Moreover, the larger the mass of the molecule t, the higher the momentum, R ~ t. The higher the concentration of molecules P, the more collisions occur, therefore, R ~ P. Assuming that the pressure is distributed equally in all directions in space (x, r/, r), we finally write

Kinetic energy of one molecule E \u003d mv / 2. Connecting the last two equations, we obtain

The last equation is called the basic equation of the MKT. This equation shows that the average kinetic energy ideal gas molecules (E) proportional to its temperature T. Note that the equation is written for a monatomic ideal gas. For a polyatomic gas, it takes the form

where i- already known to you the number of degrees of freedom of the molecule. From equality

follows that root mean square speed molecules of a monatomic gas is

The Maxwell distribution 1 is a probability distribution, often found in equal branches of physics (and not only), underlies the MKT. The Maxwell distribution is also applicable to electronic transport processes, to describe the properties of individual molecules in a gas. Usually, this distribution is understood as the energy distribution of molecules in a gas, but it can also be applied to the distribution of velocities, momenta, and momentum modulus of molecules. It can also be expressed as a discrete distribution over a set of discrete energy levels, or as a continuous distribution over some energy continuum.

We will confine ourselves to considering only one application of the Maxwell distribution - the distribution of gas molecules over velocities.

Mathematically, the Maxwell distribution function (Fig. 4.1) is written as follows:

Rice. 4.1.

Let us explain the mathematical meaning of the distribution function. Any distribution function (including Maxwell's) shows the probability that some quantity (in our case, the velocity of gas molecules v) takes on a certain set value. Maxwell velocity distribution function f(v) shows the probability that the velocity of a gas molecule is v.

On fig. 4.1, three characteristic points are marked on the velocity distribution curve: o - most likely the speed of the molecule (it corresponds to the maximum, since it has the highest probability, hence the name), r> sr - average speed molecules (its probability is slightly less) and r; kv - root mean square speed (even less likely).

Let's define mathematical expressions for all three speeds. To find the most likely speed that corresponds to the maximum value /( v), need to calculate df/dv, equate it to zero and solve for v

James Clerk Maxwell (1831 - 1879) - British physicist and mathematician. He laid the foundations of modern classical electrodynamics (Maxwell's equations), introduced the concepts of displacement current and electromagnetic field into physics, predicted the existence electromagnetic waves, the electromagnetic nature of light, is one of the founders kinetic theory gases and the author of the principle of color photography.