Dalton's laws

Dalton's laws

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This section is intended for those who often encounter incomprehensible abbreviations, abbreviations and terms and would like to better understand their meanings.

Dalton's laws- two physical laws that determine the total pressure and solubility of a mixture of gases. Formulated by John Dalton at the beginning of the 19th century.

Formulation of laws

Law on the total pressure of a mixture of gases

The pressure of a mixture of chemically non-interacting ideal gases is equal to the sum of the partial pressures.

Law on the solubility of gas mixture components

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

Limits of applicability

Both Dalton's laws are strictly satisfied 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.

History of discovery

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

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 the 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*

Task. Combustion of 2 g of metal consumes 400 ml of oxygen. Find the metal equivalent.

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

M=28 g/mol

Chemical thermodynamics

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

Basic concepts.

A system is a material part of the Universe that is subject to theoretical and experimental study.

The boundaries between the system and the environment can be both real and fictitious (imaginary) in nature.

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

If a 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, it is called closed.

An exothermic reaction is a reaction that occurs with the absorption of heat.

An endothermic reaction is a reaction that releases heat.

The state function F (p,V,T...) is called a state function if its value does not depend on the path of transition of the system from one state to another, but depends only on the values ​​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 of thermodynamic equilibrium if the equilibrium mechanism (the pressure at all points of the system is the same), thermodynamic and chemical equilibrium (this is the composition of the starting substances and reaction products at all points is the same) is simultaneously carried out.

A reversible process is a process in which a 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 amount. Otherwise, the process is called irreversible.

A system in which the components are in the same phase is called homogeneous. A system in which the components are in different phases is called heterogeneous. Let's consider whether heat and work are functions of state. Both work and heat are forms of energy transfer. Work is in the form of ordered movement of particles, heat is in the form of chaotic movement.

Let's consider the process of expansion of an ideal gas at t=const

1. The process is reversible

d-infinitesimal of the state function

p int = p int

2. The process is irreversible

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

First law of thermodynamics.

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

Let's consider special cases.

1. When р=const

Enthalpy

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

2. When V=const

Physical meaning - thermal effect of reaction at V=const

Thermochemistry. Hess's law.

The thermal effect of a 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 a reaction passes through a number of intermediate states, then the thermal effect of the reaction does not depend on the path of transition of the system from one state to another, but depends only on the values ​​of the parameters of the system in the final and initial states.

I consequence of Hess's law: the thermal effect of a reaction is equal to the difference in the sums of the heats of formation of products and reagents, 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 mole 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 mole in 1 liter, for solids the most stable crystallographic modification is selected)

In thermochemistry, the heat of formation of simple substances is conventionally assumed to be equal to zero.

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

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.

Task. Determine the heat of combustion

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

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

Dependence of the thermal effect of the reaction on temperature. Kirchhoff's equation.

Heat capacities

the heat that must be imparted to 1 mole of a substance to heat it up.

In order to calculate the thermal effect of a reaction at temperature, it is necessary to calculate the thermal effect at 298 K of the change in the heat capacity of the reaction (the difference in the sums of the thermal effects of products and reagents, 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 we will take the temperature to be 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 greater the chaos, the greater the S.

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

The standard entropy values ​​of all substances at 298 K are given in the reference book of thermodynamic quantities.

III law of thermodynamics.

The entropy of an ideal crystal at absolute 0 Kelvin temperature 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 oscillatory, rotational, translational motion of particles, i.e., one single microstate is described by one single macrostate.

Calculation of entropy change during heating.

The processes of phase transitions are isobaric-isothermal and reversible, therefore 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.

Change in Gibbs energy 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

State of balance

The physical meaning of the change in Gibbs energy: the maximum useful work performed by the system.

If there is a phase transition

Physical meaning: if enthalpy characterizes the system’s desire for order (i.e., to reduce the energy reserve), then entropy characterizes the system’s desire for chaos, and 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 (according to the sign of the Gibbs energy), but also to quantitatively calculate the system in a state of 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 substances to degrees equal to their stoichiometric coefficients.

Conditions for shifting chemical equilibrium (Le Chatelier's principle)

Formulation: if a force is applied to a system in equilibrium from outside, then the equilibrium shifts in the direction that weakens the applied force.

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

An increase in temperature promotes the occurrence of that reaction, which reduces the heat required and shifts the equilibrium towards an isothermal reaction.

The higher the temperature, the more the temperature influences the equilibrium shift.

II. The 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.

As pressure increases, the equilibrium shifts towards those substances that occupy less volume (toward a decrease in the number of molecules).

III. Influence of composition.

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

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

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

(kJ) (J/mol)

7.22 J/mol K

Upon substitution we get:

Answer: - 84%

The greater the negative Gibbs energy, the greater the value of the equilibrium constant; therefore, reaction products will predominate in the equilibrium system.

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 occurrence of processes over time.

Average rate is the 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 the concentration of starting substances or products (“-” - starting substances, “+” - products). The tangent of the tangent to the curve allows you to calculate the true speed at each moment in time.

For heterogeneous reactions:

S-mass interface.

Law of mass action.

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

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

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

Task. How will the rate of the direct reaction change if the pressure is increased by 3 times?

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

Answer: will increase 27 times

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

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

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

1) First order kinetic equation (all decomposition reactions)

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

X moles of substance a, then

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

2) Kinetic equation of the second order reaction

We assume that the initial concentration of substances is equal.

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

3) Kinetic equation of a third-order reaction If in none of the cases InC does a straight line work out, then the reaction mechanism is complex, i.e. The reaction occurs in several stages. The total 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

The 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.

Key points:

• 1) For chemical interaction of substances to occur, their collision must occur
• 2) The energy of the particles must be greater than or equal to the activation energy of the reaction
• 3) Particle collisions must occur on the functional group

Activation energy is the minimum energy that must be imparted to a molecule 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 equation (1) by (2)

If the values ​​of 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) The actual speed is often lower than that calculated by the Arrhenius theorem
• 2) the theory does not explain the phenomenon of catalysis.

A certain reaction takes 16 minutes at a temperature of 2. How long will this reaction take to take place at a temperature of 5 if =3.

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

Where p v p 2 , ръ - partial pressures gases included in the mixture.

Partial pressure is the pressure that a gas would have if it alone occupied the entire available volume.

Molecular kinetic theory(MKT) arose in the 19th century. and presented the structure of matter (mainly gases) from the point of view of three provisions:

• all bodies consist of particles: atoms and molecules;
• particles are in continuous chaotic motion (thermal);
• particles interact with each other through perfectly elastic collisions.

MCT 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. Observing through a microscope the movement of flower pollen suspended in water, he saw disordered zigzag trajectories of particles.

The cause of Brownian motion is the thermal motion of the molecules of the medium, which is caused by pressure fluctuations. The impacts of the molecules of the medium lead the particle into random motion: its speed quickly changes in magnitude and direction. A complete theory of Brownian motion was given later by Albert Einstein and Marian Smoluchowski.

Basic MKT equation. The pressure of a gas on the wall of a vessel is determined by the impulse that gas molecules impart to the wall of the vessel when they collide with it. The higher the speed of the molecule, the greater the impulse it carries, the stronger it acts on the wall, i.e. r ~ v. In addition, the greater the mass of the molecule T, the higher the impulse, r ~ T. The higher the concentration of molecules n, the more often collisions occur, therefore, r ~ p. Assuming that the pressure is distributed equally in all directions in space (x, z/, z), we finally write

Kinetic energy of one molecule E = mv / 2. Connecting the last two equations with each other, we get

The last equation is called basic equation of MKT. This equation indicates that the average kinetic energy of 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 will take the form

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

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

The Maxwell distribution 1 is a probability distribution, often found in equal parts of physics (and not only), and underlies MCT. The Maxwell distribution is also applicable to electronic transfer processes, to describe the properties of individual molecules in a gas. Typically this distribution refers to the distribution of energies of molecules in a gas, but it can also be applied to the distribution of velocities, momenta, and modulus of molecules. It can also be expressed as a discrete distribution over many discrete energy levels or as a continuous distribution over some continuum of energy.

We will limit ourselves to considering only one application of the Maxwell distribution - the velocity distribution of gas molecules.

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 a certain quantity (in our case, the speed of gas molecules v) takes on a certain specified value. Maxwell velocity distribution function f(v) shows the probability that the speed of a gas molecule is v.

In Fig. 4.1 on the speed distribution curve, three characteristic points are marked: o - most likely 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 g; kv - mean square speed (with even less probability).

Let's define mathematical expressions for all three speeds. To find the most probable speed that corresponds to the maximum value /( v), need to calculate df/dv, set it equal 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 of electromagnetic waves, the electromagnetic nature of light, is one of the founders of the kinetic theory of gases and the author of the principle of color photography.

It is worth mentioning two more gas laws. One of them concerns the number of molecules of different gases at the same pressures and temperatures, and the other concerns the mixture of gases.

Avogadro's law

At the beginning of the 19th century. the rule of multiple ratios was established for gases that enter into a chemical reaction. If the temperatures and pressures of gases combining with each other are equal, then their volumes are in simple ratios: 1:1, 1:2, 1:3, etc. Based on this rule, Avogadro in 1811 expressed a bold statement for this time hypothesis: Equal volumes of gases at the same temperatures and pressures contain the same number of molecules. At a ratio of 1:1, the molecules of the reacting gases are connected in pairs. If the volume ratio is 1:2, then each molecule of the first gas attaches to itself two molecules of the second, etc.

Currently, Avogadro's conjecture has been strictly proven and is called Avogadro's law.

According to Avogadro's law different gases, taken in an amount of 1 mole, have the same volumes at the same pressuresr and temperaturest , since the number of molecules in them is the same. Under normal conditions, i.e. at a temperature of 0 °C and an atmospheric pressure of 101,325 Pa, this volume, as measurements show, is equal to

Volume V M 0 called molar.

Why is it that in equal volumes of gases at the same pressures and temperatures the same number of molecules is always found, regardless of which gas is taken? This can only be explained using molecular kinetic energy (see §4.5).

Dalton's law

More often they deal not with pure gas - oxygen, hydrogen, etc., but with a mixture of gases. Atmospheric air, in particular, is a mixture of nitrogen, oxygen and many other gases. Each of the gases in the mixture makes its own “contribution” to the total pressure on the walls of the vessel. The pressure that each of the gases making up the mixture would have if the remaining gases were removed from the vessel is called partial (i.e. private) pressure.

The simplest assumption that can be made is that the pressure of the gas mixture r equal to the sum of the partial pressures of all gases p 1 , p 2 , p 3 ...:

(3.8.2)

The English chemist D. Dalton found that for sufficiently rarefied gases this is exactly the case in reality. Relationship (3.8.2) is called Dalton's law.

From the point of view of molecular kinetic theory, Dalton's law is satisfied because the interaction between the molecules of an ideal gas is negligible. Therefore, each gas exerts the same pressure on the wall of the vessel as if there were no other gases.

A mole of any gas under normal conditions occupies a volume 22.4 l. This volume value was established experimentally. In a mixture of gases, each of them exerts pressure on the walls of the container, regardless of the presence of other gases.

§ 3.9. Ideal gas equation of state

The state of a given mass of gas is characterized by three macroscopic parameters: pressure p, volumeVand temperature T. Now we will find the connection between them.

Equation of state

In § 3.5 and 3.6 you became familiar with the behavior of an ideal gas under specially created conditions. Two parameters out of three (p, V or V, T) changed at a constant value of the third (G or p). Typically, in nature and technology, gas changes all three parameters at once. For example, when air heated at the surface of the Earth rises, it expands, its pressure decreases and the temperature decreases.

Using gas laws (3.5.2) and (3.7.8), we can obtain an equation relating all three parameters p, V And T, characterizing the state of a gas of a given mass. This equation is called the ideal gas equation of state.

The partial pressure of each gas included in the mixture is the pressure that would be created by the same mass of a given 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 gas mixture 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 gases making up the mixture.

This law was called law of partial pressures of gases

Dalton's law The partial pressure of each gas included in a mixture is the pressure that would be created by the same mass of a given 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 components in the mixture do not change.

Dalton's two laws

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 mole 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 were formulated by J. Dalton resp. in 1801 and 1803.

Dalton's Law Equation

As already noted, the individual components of a 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 of the i gas component. This equation is Dalton's law.

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

Let there be i component in a mixture of gases, then the Mendeleev-Cliperon equation will have the form:

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

where \(m_i\) are the masses of the components of the gas mixture, \((\mu )_i\) are the molar masses of the components 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 we write equation (3) in the form:

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

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 \(x_i-molar\ concentration\ of the i-th\) 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 of \(i-th \) gas in the mixture.

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