Gibbs energy formula chemistry. Gibbs free energy

Table 7. Standard absolute entropies S 0 298 of some substances

Example Z. Based on the standard heats of formation (Table 5) and the absolute standard entropies of substances (Table 7), calculate G reaction proceeding according to the equation

CO(g) + H 2 O(l) = CO3(g) + H 2 (g).

Solution. G° = H° - TS°;

H and S are state functions, therefore

H 0 h.r. = H 0 cont. - H 0 ref. ;

S 0 x. R. = S 0 cont. - S 0 ref. . H 0 x. R.

= (-393.51 + 0) - (-110.52 - 285.84) = +2.85 kJ; S 0 x. R.

= (213.65+130.59) -(197.91+69.94) =+76.39 = 0.07639 kJ/(mol∙K); G 0

Example 4. = +2.85 – 298 - 0.07639 = -19.91 kJ.

The reduction reaction of Fe 2 O 3 with hydrogen proceeds according to the equation

Fe 2 O 3 (k) + ZN 2 (g) = 2Fe (k) + ZN 2 O (g); H= +96.61 kJ. S = Is this reaction possible under standard conditions if the change in entropy 

Solution. 0.1387 kJ/(mol. K)? At what temperature will the reduction of Fe 2 Oz begin? G° We calculate 

reactions:

G =H-TS= 96.61 - 298. 0.1387 = +55.28 kJ.

Since G > 0, the reaction is impossible under standard conditions; on the contrary, under these conditions a reverse reaction of iron oxidation (corrosion) occurs. Let's find the temperature at which G = 0:
H = TS; T=

TO.

Example Consequently, at a temperature T = 696.5 K (423.5 0 C), the reduction reaction of Fe 2 O 3 will begin. This temperature is sometimes called the temperature at which the reaction begins.

5. Calculate H 0, S 0, G 0, - the reaction proceeding according to the equation

Fe 2 Oz(k) + 3 C = 2 Fe + 3 CO.

Solution. Is the reduction reaction of Fe 2 Oz with carbon possible at 500 and 1000 K?

H 0 h.r. and S 0 h.r. we find from relations (1) and (2): H 0 h.r.

S 0 = - [-822.10 + 30]= -331.56 + 822.10 = +490.54 kJ; h.r. = = (2 ∙ 27.2 +3 ∙ 197.91) - (89.96 + 3 ∙ 5.69)

541.1 J/(mol∙K).

The Gibbs energy at the corresponding temperatures is found from the relation G 500 = 490.54 – 500

= +219.99 kJ; = 490,54 –1000 ∆G 1000

= -50.56 kJ.< 0, то восстановление Fе 2 Оз возможно при 1000 К и невозможно при 500 К.

Since G 500 > 0, and G 1000 Gibbs free energy or isobaric-isothermal potential (G). It characterizes the direction and limit of spontaneous occurrence of processes under isobaric-isothermal conditions (p = const and T = const). The Gibbs free energy is related to the enthalpy and entropy of the system by the relation

G = H – TS. (9)

It is impossible to measure the absolute value, so the change in function during the course of a particular process is used:

DG = DH – TDS. (10)

Gibbs free energy is measured in kJ/mol and kJ. Physical meaning of Gibbs free energy: free energy of a system that can be converted into work. For simple substances, the Gibbs free energy is assumed to be zero.

The sign of the change in the Gibbs free energy DG and its value at P = const determine the thermodynamic stability of the system:

· if in a chemical process there is a decrease in the Gibbs free energy, i.e. DG< 0, процесс может протекать самопроизвольно, или говорят: процесс термодинамически возможен;

· if the reaction products have a greater thermodynamic potential than the starting substances, i.e. DG >

· if DG = 0, then the reaction can proceed in both forward and reverse directions, i.e. the reaction is reversible.

Hence, Spontaneous processes at P = const occur with a decrease in the Gibbs free energy. This conclusion is valid for both isolated and open systems.

The change in the Gibbs energy of a system during the formation of 1 mole of a substance from simple substances that are stable under given conditions is called the Gibbs energy of formation of the substance DG arr. , measured in kJ/mol.

If the substance is under standard conditions, then the Gibbs energy of formation is called the standard Gibbs energy of formation of the substance (DG 0 sample 298). The standard Gibbs energy of formation of a simple substance that is stable under standard conditions is zero. The values ​​of DG 0 sample 298 substances are given in reference books.

Gibbs energy change, as well as the change in enthalpy and entropy, does not depend on the process path, therefore, the change in the Gibbs energy of a chemical reaction DG is equal to the difference between the sum of the Gibbs energies of the formation of the reaction products and the sum of the Gibbs energies of the formation of the starting substances, taking into account the stoichiometric coefficients:

DG 0 298 = S(n i . DG i 0 298) ex. - S(n i . D G i 0 298) ref. . (eleven)

Helmholtz free energy

The direction of isochoric processes (V = const and T = const) is determined by the change in Helmholtz free energy, which is also called isochoric-isothermal potential (F):

DF = DU – TDS.

The sign of the change in the Helmholtz free energy DF and its value at V = const determine the thermodynamic stability of the system:

· if in a chemical process there is a decrease in the Helmholtz free energy, i.e. D F< 0, процесс может протекать самопроизвольно, или говорят: процесс термодинамически возможен;

· if the reaction products have a greater thermodynamic potential than the starting substances, i.e. D F > 0, the process cannot proceed spontaneously, or they say: the process is thermodynamically impossible;

· if D F = 0, then the reaction can proceed both in the forward and in the reverse direction, i.e. the reaction is reversible.

Consequently, spontaneous processes at V=const occur with a decrease in the Helmholtz free energy. This conclusion is valid for both isolated and open systems.

CHEMICAL KINETICS

Basic concepts of chemical kinetics

Chemical kinetics is a branch of chemistry that studies the rates and mechanisms of chemical reactions.

There are homogeneous and heterogeneous chemical reactions:

· homogeneous reactions occur in a homogeneous environment throughout the entire volume of the system (these are reactions in solutions, in the gas phase);

· heterogeneous reactions occur in a heterogeneous environment, at the interface (combustion of a solid or liquid substance).

The basic concept of chemical kinetics is the concept of the rate of a chemical reaction. The rate of a chemical reaction is understood as the number of elementary acts of interaction per unit time per unit volume (if the reaction is homogeneous) or the number of elementary acts of interaction per unit time per unit interface surface (if the reaction is heterogeneous).

The reaction rate is characterized by a change in the concentration of any of the starting substances or final reaction products per unit time and is expressed: for homogeneous reactions - mol/l s (mol/m 3 s, etc.), for heterogeneous reactions - mol/cm 2 s (mol/m 2 s).

V av =± (C 2 – C 1)/(t 2 - t 1) = ± DC/Dt. (1)

The average speed is a rough approximation because in the time interval t 1 ÷ t 2 it does not remain constant. The true or instantaneous speed at time t (V) is determined as follows:

V = lim (± DC/D t) = ± dС/dt = ± С" t = tg a, (2)

those. the instantaneous rate of a chemical reaction is equal to the first derivative of the concentration of one of the substances with respect to time and is defined as tg the angle of inclination of the tangent to the curve CA = f (t) at the point corresponding to a given time t: dС/dt = tga.

The speed of a chemical reaction depends on various factors:

The nature of the reacting substances;

Their concentrations;

Process temperatures;

Presence of a catalyst.

Let us consider in more detail the influence of each of the listed factors on the rate of a chemical reaction.

One of the most important problems solved by thermodynamics is the establishment of the fundamental possibility (or impossibility) of the spontaneous occurrence of a chemical process.

As stated earlier, the course of a chemical process is favored by an increase in the entropy of the system. An increase in entropy is achieved by the separation of particles, the breaking of chemical bonds, the destruction of crystal lattices, the dissolution of substances, etc. However, all these processes are inevitably accompanied by an increase in the enthalpy of the system, which impedes the process. It is obvious that in order to solve the question of the fundamental possibility of a chemical process occurring, it is necessary to simultaneously take into account the change in both entropy and enthalpy of the system. At constant temperature and pressure, a thermodynamic function called the Gibbs free energy (sometimes simply the Gibbs energy) is used for this purpose. Gibbs free energy (G) is related to enthalpy and entropy by the following equation:

The change in Gibbs energy during the transition of a system from the initial state to the final state is determined by the relation:

ΔG = ΔH - TΔS

Since the equation is valid for processes occurring at constant temperature and pressure, the function G is called isobaric-isothermal potential. In the resulting equation, the value ΔH evaluates the influence of the enthalpy factor, and the value TΔS - the entropy factor on the possibility of the process occurring. In its physical meaning, Gibbs free energy is that part of ΔH that, under certain conditions, can be converted into work done by the system against external forces. The rest of ΔH, equal to TΔS, represents “unfree” energy, which goes to increase the entropy of the system and cannot be converted into work. Gibbs free energy is a kind of potential that determines the driving force of a chemical process. Like physical potentials (electric, gravitational), the Gibbs energy decreases as the process proceeds spontaneously until it reaches a minimum value, after which the process stops.

Let some reaction spontaneously occur in the system at constant pressure and temperature (non-equilibrium process). In this case ΔH< TΔS, соответственно ΔG <0. Таким образом, изменение функции Гиббса может служить критерием при определении направления протекания реакций: in an isolated or closed system at constant temperature and pressure, reactions occur spontaneously for which the change in Gibbs free energy is negative (ΔG< 0).

Let the reaction occurring in the system be reversible. Then, under given conditions, a direct reaction is fundamentally feasible if ΔG< 0, а обратная - если ΔG >0; at ΔG = 0 the system will be in a state of equilibrium. For isolated systems ΔН = 0, therefore ΔG = - TΔS. Thus, in an isolated system processes occur spontaneously leading to an increase in entropy(second law of thermodynamics).

Since the Gibbs energy equation includes the enthalpy of the system, it is impossible to determine its absolute value. To calculate the change in free energy corresponding to the occurrence of a particular reaction, the Gibbs energies of formation of the compounds participating in the interaction are used. The Gibbs energy of formation of a compound (ΔG f) is the change in free energy corresponding to the synthesis of a mole of a given compound from simple substances. The Gibbs energies of formation of compounds referred to standard conditions are called standard and are designated by the symbol. Values ​​are given in reference literature; they can also be calculated from the enthalpies of formation and entropies of the corresponding substances.

Example No. 1. It is required to calculate for Fe 3 O 4 if the enthalpy of formation of this compound is known ΔH o f (Fe 3 O 4) = -1117.13 kJ/mol and the entropies of iron, oxygen and Fe 3 O 4 are equal to 27.15; 205.04 and 146.19 J/mol. K. Accordingly

(Fe 3 O 4) = (Fe 3 O 4) - T·,

where Δ is the change in entropy during the reaction: 3Fe + 2O 2 = Fe 3 O 4

The entropy change is calculated using the following equation:

Δ = (Fe 3 O 4) - =

146.19 - (3.27.15 + 2.205.04) = -345.3(J/mol . TO);

Δ = -0.34534 kJ/mol K

(Fe 3 O 4) = -1117.13 - 298(-0.34534) = -1014.2 (kJ/mol)

The result obtained allows us to conclude that the reaction is fundamentally possible under standard conditions. In this case, the enthalpy factor favors the reaction (< 0), а энтропийный - препятствует (Т < 0), но не может увеличить до положительной величины

Since G is a state function, then for the reaction: aA + bB = dD + eE the change in Gibbs energy can be determined by the equation

= Σi (pr) - Σj (react)

Example No. 2. Let us evaluate the fundamental possibility of producing ozone through the interaction of nitric acid with oxygen (standard conditions) using the equation:

4HNO 3 (l) + 5O 2 (g) = 4O 3 (g) + 4NO 2 (g) + 2H 2 O (l)

Let us calculate the change in the Gibbs energy under standard conditions:

= - =

4 162.78 + 4 52.29 - = 1179.82 (kJ)

Spontaneous reaction under standard conditions is fundamentally impossible. At the same time, nitrogen dioxide can be oxidized by ozone to nitric acid, since for the reverse reaction the ΔG value is negative.

CHEMICAL KINETICS

any chemical reaction is accompanied by the release or absorption of energy. Most often, energy is released or absorbed in the form of heat (less often in the form of light or mechanical energy). This heat can be measured. The measurement result is expressed in kilojoules (kJ) for one mole of reactant or (less commonly) for one mole of reaction product. This quantity is called the thermal effect of the reaction.

Thermal effect is the amount of heat released or absorbed by a chemical system when a chemical reaction occurs in it.

Thermal effect is indicated by the symbols Q or DH (Q = -DH). Its value corresponds to the difference between the energies of the initial and final states of the reaction:

DH = H end - H ref. = E con. - E ref.

Icons (d), (g) indicate the gaseous and liquid states of substances. There are also designations (tv) or (k) - solid, crystalline substance, (aq) - substance dissolved in water, etc.

The designation of the state of aggregation of a substance is important. For example, in the combustion reaction of hydrogen, water is initially formed in the form of steam (gaseous state), upon condensation of which some more energy can be released. Consequently, for the formation of water in the form of a liquid, the measured thermal effect of the reaction will be slightly greater than for the formation of only steam, since when the steam condenses, another portion of heat will be released.

A special case of the thermal effect of the reaction is also used - the heat of combustion. From the name itself it is clear that the heat of combustion serves to characterize the substance used as fuel. The heat of combustion is referred to 1 mole of a substance that is a fuel (a reducing agent in an oxidation reaction), for example:

The energy (E) stored in molecules can be plotted on the energy scale. In this case, the thermal effect of the reaction (E) can be shown graphically

This law was discovered by Hess in 1840 based on a synthesis of many experimental data.

7.Entropy. Gibbs free energy. Thermodynamic criterion for the direction of a chemical process.

Entropy is the reduction in the available energy of a substance as a result of energy transfer. The first law of thermodynamics states that energy cannot be created or destroyed. Therefore, the amount of energy in the universe is always the same as it was when it was created. The second law of thermodynamics states that the efficiency of no real (irreversible) process can be 100% when converting energy into work.

where Δ S- entropy change, Δ Q- change in heat, T- absolute thermodynamic temperature.

Consequently, the amount of energy to be converted into work or heat continuously decreases with time as heat spontaneously moves from a warmer region to a colder region

Gibbs energy and direction of reaction

In chemical processes, two opposing factors act simultaneously - entropic() And enthalpic(). The total effect of these opposing factors in processes occurring at constant pressure and temperature determines the change Gibbs energy():

From this expression it follows that, that is, a certain amount of heat is spent on increasing entropy (), this part of the energy is lost to perform useful work (dissipated into the environment in the form of heat), it is often called bound energy. Another part of the heat () can be used to do work, which is why Gibbs energy is often also called free energy.

The nature of the change in the Gibbs energy allows us to judge the fundamental possibility of carrying out the process. When the process can proceed, when the process cannot proceed (in other words, if the Gibbs energy in the initial state of the system is greater than in the final state, then the process can fundamentally proceed, if vice versa, it cannot). If, then the system is in a state of chemical equilibrium.

Gibbs free energy(or simply Gibbs energy, or Gibbs potential, or thermodynamic potential in the narrow sense) is a quantity that shows the change in energy during a chemical reaction and thus gives an answer to the question about the fundamental possibility of a chemical reaction occurring; This is the thermodynamic potential of the following form:

Gibbs energy can be understood as the total chemical energy of a system (crystal, liquid, etc.)

The concept of Gibbs energy is widely used in thermodynamics and chemistry.

The spontaneous occurrence of an isobaric-isothermal process is determined by two factors: enthalpy, associated with a decrease in the enthalpy of the system (ΔH), and entropy T ΔS, due to an increase in disorder in the system due to an increase in its entropy. The difference between these thermodynamic factors is a function of the state of the system, called the isobaric-isothermal potential or Gibbs free energy (G, kJ)

The classic definition of the Gibbs energy is the expression

where is internal energy, is pressure, is volume, is absolute temperature, is entropy.

Gibbs differential energy for a system with a constant number of particles, expressed in eigenvariables - pressurep and temperatureT:

For a system with a variable number of particles, this differential is written as follows:

Here is the chemical potential, which can be defined as the energy that must be expended to add another particle to the system.

In the process of chemical reactions, two tendencies operate:

1.Н min (enthalpy factor);

2.S max (entropy factor).

Both of these factors act in mutually opposite directions and the course of the reaction is determined by whichever one prevails in a given particular case. The change in enthalpy and entropy during a chemical reaction takes into account the Gibbs energy ∆G 0 (kJ): ∆G 0 = ∆H 0 – T∆S 0, where T is the absolute temperature, ∆S 0. – standard change entropy; ∆Н 0 – standard enthalpy change.

The magnitude and sign of G determine the possibility of spontaneous occurrence of a chemical reaction and its direction. At constant temperature and pressure, the reaction proceeds spontaneously in the direction corresponding to the decrease in the Gibbs energy.

G< 0 - реакция идет самопроизвольно в прямом направлении;

G > 0 - under these conditions the reaction does not proceed in the forward direction;

G = 0 - the reaction is reversible (chemical equilibrium).

The change ∆ r G does not depend on the path of the process and can be calculated by a consequence of Hess’s law: Gibbs energy change as a result of a chemical reaction is equal to the sum of the Gibbs energies of formation of the reaction products minus the sum of the Gibbs energies of the formation of the starting substances.

R G 0 = Σ∆ f G 0 reaction products – Σ∆ f G 0 starting substances,

where ∆ f G 0 – standard Gibbs energy of formation, kJ/mol; reference value. ∆ f G 0 of simple substances is equal to zero.

Lecture No. 6 . RATE OF CHEMICAL REACTIONS

Chemical kinetics -a branch of chemistry that studies the rate and mechanism of chemical reactions.Speed ​​of chemical reaction called change in the amount of reactant per unit time per unit volume(for homogeneous reaction) or per unit interface(for a heterogeneous system). The reaction rate depends on the nature of the reactants, their concentration, temperature, and the presence of catalysts.

Dependence of the rate of a chemical reaction on the nature of the reacting substances due to the fact that each reaction is characterized by a certain activation energy value. Reactions proceed in the direction of destruction of less strong bonds and the formation of substances with stronger bonds. In order to destroy one bond and form another bond, certain energy costs are required. Activation energy E a - this is the excess energy that molecules must have in order for their collision to lead to the formation of a new substance. If the activation energy is very small (< 40 кДж/моль), то реакция идет с очень большой скоростью, если энергия активации очень велика (>120 kJ/mol), then the reaction rate is immeasurably low.

Dependence of reaction rate on concentration reactants is expressed law of mass action (LMA): at constant temperature, the rate of a chemical reaction is directly proportional to the product of the concentrations of the reacting substances.

In general, for homogeneous reactions nA (g) + mB (g) = pAB (g)

The dependence of the reaction rate on concentration is expressed by the equation:

,

where C A and C B are the concentrations of reactants, k is the reaction rate constant. For a specific reaction 2NO (g) + O 2 (g) = 2NO 2 (g), the mathematical expression of the ZDM has the form: υ ​​= k∙∙

The reaction rate constant k depends on the nature of the reactants, temperature and catalyst, but does not depend on the concentrations of the reactants. The physical meaning of the rate constant is that it is equal to the reaction rate at unit concentrations of the reactants.

For heterogeneous reactions, the reaction rate depends only on the concentration of gases or dissolved substances, and the concentration of the solid phase is not included in the mathematical expression of the ZDM. For example, the rate of combustion of carbon in oxygen is proportional only to the oxygen concentration:

C (k) + O 2 (g) = CO 2 (k), υ = k

Dependence of reaction rate on temperature. As the temperature increases, the speed of movement of molecules increases, which in turn leads to an increase in the number of collisions between them. Increasing temperature increases the number of active molecules, and, therefore, increases the rate of a chemical reaction.

The dependence of the rate of a chemical reaction on temperature is expressed van't Hoff's rule: for every 10 °C increase in temperature, the reaction rate increases by 2-4 times.

,

where υ 2 and υ 1 are reaction rates at temperatures t 2 and t 1,

γ is the temperature coefficient of the reaction rate, showing how many times the reaction rate increases when the temperature increases by 10 0 C

The dependence of the reaction rate on temperature is described more strictly Arrhenius equation, which relates the reaction rate constant to the activation energy:

where A is a constant factor that is equal to the number of collisions of molecules per unit time multiplied by the probability of chemical interaction during a collision.

Dependence of reaction rate on catalyst.Substances that increase the rate of a reaction, but remain chemically unchanged after it, are called catalysts. The change in reaction rate under the influence of catalysts is called catalysis. There are catalysis homogeneous And heterogeneous.

If the reactants and the catalyst are in the same state of aggregation, then catalysis homogeneous:

2SO 2 (g) + O 2 (g) 2SO 3 (g)

If the reactants and the catalyst are in different states of aggregation, then catalysis heterogeneous:

N 2(g) + 3H 2(g) 2NH 3(g)

The effect of a catalyst is that it reduces the activation energy, and at the same time the reaction rate increases.

Lecture No. 7. CHEMICAL EQUILIBRIUM

Chemical reactions are divided into irreversible And reversible. Irreversible flow only in the forward direction (until one of the reactants is completely consumed), reversible proceed in both forward and reverse directions (in this case, none of the reacting substances is completely consumed). Consider the following reaction:

The mathematical expression of the law of mass action for the speed of direct υ forward and reverse υ reverse reactions has the form:

υ pr = υ arr =

At the moment of mixing substances A and B, the rate of the direct reaction will be maximum. Substances A and B are then gradually consumed and the rate of the forward reaction decreases. The resulting substances D and F will begin to react with each other, and the rate of the reverse reaction will continuously increase as the concentration of substances D and F increases. At a certain point in time, the rate of the forward reaction will become equal to the rate of the reverse reaction.

The state of the system in which the rate of the forward reaction (υ 1) is equal to the rate of the reverse reaction (υ 2), called chemical equilibrium.The concentrations of reactants that are established at chemical equilibrium are are called equilibrium.

Law of mass action for reversible processes: in a state of chemical equilibrium at a constant temperature, the ratio of the product of the concentrations of reaction products to the product of the concentrations of the starting substances is a constant value. This quantity is called equilibrium constant. Equilibrium concentrations are usually denoted not by the symbol “CA”, but by the formula of the substance placed in square brackets, for example, and the equilibrium constant expressed in terms of concentrations - K C. For a reversible reaction aA + bB dD + fF, the mathematical expression of the law of mass action has the form :

.

For a specific homogeneous reaction:

2CO (g) + O 2 (g) ↔ 2CO 2 (g)

For the heterogeneous reaction CO 2 (g) + C (k) = 2CO (g). The concentration of the solid phase is not included in the mathematical expression of the ZDM for heterogeneous systems.

Chemical equilibrium is unchanged as long as the equilibrium conditions ( concentration, temperature, pressure), are kept constant. When conditions change, the balance is disrupted. After some time, equilibrium again occurs in the system, characterized by new equality of speeds and new equilibrium concentrations of all substances. Transition of a system from one equilibrium state to another called shift of balance.

The direction of the equilibrium shift is determined Le Chatelier's principle: If an external influence is exerted on a system that is in equilibrium (concentration, pressure, temperature changes), then the equilibrium shifts towards the reaction that weakens the effect produced.