The criterion for the occurrence of processes in an isolated system is. Second law of thermodynamics
Thermodynamic equilibrium - a state of a system in which the macroscopic quantities of this system (temperature, pressure, volume, entropy) remain unchanged over time under conditions of isolation from the environment. In general, these values are not constant, they only fluctuate (oscillate) around their average values. If an equilibrium system corresponds to several states, in each of which the system can remain indefinitely, then the system is said to be in metastable equilibrium. In a state of equilibrium, there are no flows of matter or energy in the system, nonequilibrium potentials (or driving forces), or changes in the number of phases present. Distinguish between thermal, mechanical, radiation (radiant) and chemical equilibria. In practice, the isolation condition means that the processes of establishing equilibrium proceed much faster than changes occur at the boundaries of the system (that is, changes in conditions external to the system), and the system exchanges matter and energy with its surroundings. In other words, thermodynamic equilibrium is achieved if the rate of relaxation processes is sufficiently high (as a rule, this is typical for high-temperature processes) or the time to achieve equilibrium is long (this case occurs in geological processes).
In real processes, incomplete equilibrium is often realized, but the degree of this incompleteness can be significant or insignificant. In this case, three options are possible:
1. equilibrium is achieved in any part (or parts) of a relatively large system - local equilibrium,
2. incomplete equilibrium is achieved due to the difference in the rates of relaxation processes occurring in the system - partial equilibrium,
3. both local and partial equilibrium take place.
In nonequilibrium systems, changes occur in the flow of matter or energy, or, for example, phases.
The criterion for the direction of a spontaneous process in these cases is the sign of the change in the Gibbs energy dG or Helmholtz energy dA in the system.
Gibbs energy G = Н –ТS = U + рV –ТS.
Helmholtz energy A = U –
ТS, with G = f(р,Т); A = f(V,T).
The equations can also be presented as: H = G + TS; U = A +
TS . Where the TS value characterizes the energy associated with the particles of the system, i.e. that part of the total energy of the system that is dissipated in the environment in the form of heat (the so-called lost work).
In a closed system, the sign of the change in the Gibbs energy is a criterion for the direction of a spontaneous process when carried out under isobaric-isothermal conditions:
- at dG = 0 (G=Gmin, the Gibbs energy has a minimum value) the system is in a state of thermodynamic equilibrium;
- at dG< 0 (Ga Gmin , энергия Гиббса убывает) процесс самопроизвольно протекает в прямом направлении, т.е. термодинамически возможен;
- at dG > 0 (Ga Gmin, the Gibbs energy increases), only the reverse process occurs spontaneously; the direct process is thermodynamically impossible.
Many processes take place without supplying energy from an external source. Such processes are called spontaneous.
Examples of spontaneous processes include the fall of a stone from a height, the flow of water downhill, the transfer of heat from a more heated body to a less heated one.
Human experience has shown that spontaneous processes in the opposite direction cannot occur spontaneously, i.e. Water will not spontaneously flow uphill, a stone will not fly upward, and heat will not transfer from a cold body to a heated one.
(although from the point of view of the first law of thermodynamics, both the process of heat transfer from a hot body to a cold one and the reverse process are equally plausible, i.e. transition from heat from a cold body to a hot one, because in both cases the law of conservation and transformation of energy is observed)
Many chemical reactions also occur spontaneously, For example, rust formation on metals, reaction of sodium with water, dissolution of salt in water, etc.
To understand and control chemical processes, you need to know the answer to the question: what are driving forces and criteria spontaneous processes?
One of the driving forces chemical reaction is what we discussed earlier decrease in system enthalpy, those. exothermic heat effect of reaction ii.
Experience shows that most exothermic reactions (?H<0) протекают самопроизвольно. – Why?
However, the condition?<0 не может быть критерием! Самопроизвольного течения реакций, так как существуют самопроизвольные эндотермические химические реакции, у которых?Н >0, for example, the interaction of methane with water vapor at high temperatures.
Therefore, in addition to the decrease in the enthalpy of the system (enthalpy factor), there is another the driving force of a spontaneous process.
With such strength is particle aspiration(molecules, ions, atoms) to chaotic movement, and systems - to a transition from a more ordered state to a less ordered one.
For example, let's imagine the space in which the substance is placed in the form of a chessboard, and the substance itself in the form of grains. Each cell of the board corresponds to a certain position and energy level of particles. If particles are distributed throughout space, then the substance is in a gaseous state; if the particles occupy only a small part of the space, the substance will go into a condensed state. All poured grains are distributed more or less evenly on the board. There will be a certain number of grains on each square of the board. The position of the grains after each scattering corresponds to microstate system, which can be defined as an instantaneous snapshot that records the location of particles in space. Every time we get the system in the same macrostate. The number of similar microstates that satisfy the expected macrostate (with a sufficiently large number of particles) is very large.
For example, a box with cells in which balls are located: so there are 4 balls in 9 cells - this is a model macrosystems. Balls can be arranged into cells in 126 different ways, each of which is microstate.
The number of microstates through which a given macrostate is realized is associated with thermodynamic probability W. Entropy is determined by thermodynamic probability: she the higher the more ways to implement a macrostate.
Therefore they believe that entropy is a measure of the disorder of a system.
The mathematical connection between entropy and the number of microstates was established by L. Boltzmann at the end of the 19th century, expressing it by the equation:
S= k* lnW,
Where W- thermodynamic probability of a given state of the system for a certain supply of internal energy U and volume V;
k – Boltzmann constant equal to 1.38*10 -23 J/K.
The example with balls is, of course, very clear, but it insidious since, based on it, intuitively, the orderliness of a system is sometimes understood arrangement of particles in space.
However, in reality, the thermodynamic state refers mainly to the arrangement of particles (for example, molecules) according to possible energy levels ( Each type of movement - oscillatory, rotational, translational - is characterized by its own level of energy).
Entropy also depends on the mass of particles and their geometric structure.
Crystals have the lowest entropy (so their particles can only oscillate around a certain equilibrium state), and gases have the highest, since all three types of motion are possible for their particles. S T
Every substance can be assigned a certain absolute value of entropy.
Of course, the entropies of substances are not usually calculated based on the Boltzmann equation. They are determined using the equation of classical thermodynamics, taking into account the heat capacity of a given substance and the heats of phase transitions.
The entropy value of various substances at 298 K and a pressure of 1 atm. (S 0 298) are tabular data.
Based on data on the standard entropy of substances, it is possible to calculate the change in entropy of various chemical processes. Because the entropy is a function of state, then its change does not depend on the path of the process and is equal to the difference in the entropies of the reaction products and starting materials:
?S 0reaction .= ? ? i S 0 - ? ? jS 0
In many cases, the change in the entropy of a process can be assessed qualitatively:
· Thus, entropy always increases during the transition from a condensed state (solid or liquid) to a vapor state.
· Entropy always increases when a solid or liquid substance is dissolved, and the greater the degree of dissociation, the more noticeably the entropy increases. When gases dissolve, on the contrary, entropy decreases.
· The more complex the composition of a substance, the greater the entropy. For example, for manganese oxides MnO, Mn 2 O 3, Mn 3 O 4, the entropy is respectively 61.50; 110.5; 154.8 kJ/mol*K.
· In chemical reactions, entropy increases if, as a result, the amount of gaseous substances increases. For example, in the reaction of thermal decomposition of calcium carbonate:
CaCO 3 (t) = CaO (t) + CO 2 (g)
Second law (law) of thermodynamics regulates the fundamental possibility of various processes occurring. In the mid-19th century, this law was formulated in the form of several postulates. The most famous of them are the following:
· It is impossible to transfer heat from a colder body to a hotter one without spending work on it.
(R. Clausius)
and using the concept of entropy:
· In isolated systems, processes occur spontaneously in which entropy increases. (? S insulated >0)
Any isolated system spontaneously tends to adopt a state characterized by maximum thermodynamic probability.
Based on the Boltzmann equation, it can be shown that any irreversible process that occurs spontaneously in an isolated system is characterized by an increase in entropy. Let there be two chemically non-interacting gases, for example helium and neon, in an isolated system, under identical conditions, separated by a partition. In this state, the thermodynamic probability of the system is w 1. When the partition is removed, the gases begin to spontaneously diffuse into each other until the molecules of each gas are evenly distributed throughout the entire volume. In the final state, the thermodynamic probability w 2. The system spontaneously moved from a less probable state to a more probable one (w 2 > w 1). There is no energy exchange between the system and the external environment; therefore, the only reason for this process is an increase in entropy.
In other words, processes proceed spontaneously only towards a less ordered state, i.e. growing disorder. That is why the evaporation of a liquid, the dissolution of salt in water or the mixing of gases occurs spontaneously, and at the same time, reverse processes without an exchange of energy with the environment are impossible.
Consequently, an increase in entropy is a criterion for the spontaneous occurrence of processes only in isolated systems, i.e. not exchanging energy with the external environment, and this is a rather rare case. In open and closed systems, in addition to changes in entropy, the direction of the process is also affected by changes in enthalpy.
Question 5. Gibbs and Helmholtz energy. Criterion for the spontaneous occurrence of processes.
What processes occur spontaneously in non-isolated systems? When hydrogen reacts with oxygen, water spontaneously forms:
2H 2 (g) + O 2 (g) = 2H 2 O (g)
In this reaction, entropy decreases, but a large amount of heat is released ( ? S<0, ?Н <0), т.е. самопроизвольному протеканию процесса способствует уменьшение энтальпии.
Ammonium chloride dissolves spontaneously in water:
NH 4 Cl (s) + aq = NH 4 + (r) + Cl - (r)
This process is accompanied by a decrease in temperature (heat absorption) and an increase in entropy ( ? S> 0, ?N > 0), with the last factor playing the main role.
In thermodynamics, a new function is introduced that connects the two previous quantities - Gibbs energy.(G)
G= H – T.S.
The main value of this function is that its change at constant temperature and pressure defines spontaneity of processes.
? G = ( ? H–T ? S) <0
· In classical thermodynamics, entropy is understood as a property of a system, the change in which during a reversible process is numerically equal to the ratio of heat to the temperature of the process:
? S=Q/T ;T? S=Q
· In thermodynamics reversible is a process that is carried out infinitely slowly and so that the system is practically in a state of equilibrium all the time.
Thus, the value? G characterizes that part of the change in internal energy that can be converted into useful work.
Assuming constant volume, use a thermodynamic function called Helmholtz energy (F ):
F=U –T? S
In an isochoric process, useful work is determined by a change in the Helmholtz energy, and the condition for the process to be spontaneous is its decrease ? F<0.
In chemistry, Gibbs energy is usually used, since chemical reactions are most often carried out at constant (atmospheric) pressure.
So, in a non-isolated system, the process predominantly occurs spontaneously if it corresponds decrease in Gibbs energy. (?G<0.)
At ? G =0 state of the system corresponds to equilibrium.
At ? G > 0 - the process predominantly does not proceed in the forward direction
Equation Analysis ? G =( ? H – T ? S) shows that the sign of the quantity ? G, which means that the thermodynamic possibility of a spontaneous reaction depends on two factors: enthalpy(energy) and entropy. On the one hand, the system strives to reach a minimum level of energy, releasing part of it in the form of heat or work ( ? H <0). С другой стороны, система стремится занять наиболее вероятное состояние, характеризующееся максимумом молекулярного беспорядка, т.е. максимумом энтропии (? S>0). In this case, the enthalpy and entropy factors act in a direction favorable to the reaction.
Let's consider the options:
A) ? H<0; ? S>0; in this case ? G<0 at all temperatures, the process is thermodynamically possible at any temperature.
b) ? H<0; ? S<0; in this case ? G<0 at T < , those . when the reaction is thermodynamically possible at a relatively low temperature;
V) ? H>0; ? S>0; in this case ? G<0 at T > , the process is possible at high temperatures;
G) ? H>0; ? S<0; in this case ? G<0 - both factors act in an unfavorable direction, the reaction is thermodynamically impossible at any temperature.
First way calculation is similar to the method of estimating the change in the enthalpy of a reaction from the tabulated enthalpies of formation of various substances. The tables also summarize the values of ? G 0 sample 298 and it is also accepted that for simple substances ? G 0 sample 298 =0
? G 0 reaction =?? i?G 0 return prod.- ?? j? G 0 return ref.
ij
Second way is based on first calculating the quantities ? H reaction.. and ? S reaction for a given process, and then, based on them, the values ? G 0 reaction according to the formula :
? G 0 reaction =? H 0 reaction – 298? S 0 reaction
This method is good because it allows you to evaluate how the sign will change ? G 0 reaction when the temperature changes.
Although the enthalpy and entropy of substances depend on temperature, for a reaction the change in these quantities is insignificant, therefore it is approximately believed that in a certain temperature range ? H reaction.. and ? S reaction values are practically constant.
For simple substances in thermodynamically stable states ? G 0 =0.
Considering spontaneously occurring processes, we identified:
1) a pattern in accordance with the 2nd law of thermodynamics of their occurrence with increasing entropy.
2) the pattern of spontaneous occurrence of exothermic reactions that occur with a decrease in entropy.
For example, the process of evaporation occurs spontaneously (an endothermic process with increasing entropy), in which chaos in the environment decreases, but increases within the system itself. On the other hand, the above-described exothermic reaction for the production of ammonia proceeds with a decrease in entropy - a more complex, ordered structure is formed, and 2 gas molecules are formed from 4. As mentioned above, there is no disobedience to the 2nd law of thermodynamics here, just a decrease in entropy in the reaction is compensated by a significantly greater release of thermal energy into the environment and, accordingly, greater world disorder.
However, it is desirable to have some criterion that allows quantitative
predict the possibility of spontaneous processes occurring
Such a criterion is G - Gibbs free energy (free enthalpy or isobaric potential), which is derived from the equality
H=G+TS or
H, T and S are enthalpy, temperature and entropy, respectively.
Gibbs free energy change
DG = DH - TDS
In the first equality, enthalpy (internal energy) is the sum of free energy G and bound energy TS.
Free energy G represents that part of the total supply of internal energy that can be entirely converted into work (this is a technically valuable part of internal energy).
Bound energy TS, in turn, represents the rest of the internal energy of the system. Bound energy cannot be converted into work. It is capable of converting only into thermal energy, in the form of which it dissipates (dissipates).
Free energy is contained in the system in the form of potential energy. It decreases as the system performs work. So, for example, a more rarefied gas at the same temperature and the same internal energy contains less free energy and more bound energy than a compressed gas. This is quite understandable, since in the second case we can get more work than in the first.
But since G decreases, this decrease DG = G 2 – G 1 is expressed by the sign minus, since the energy of the second system is lower than in the first
Based on the above, we can formulate the following principle of minimum free energy:
In an isolated system, only processes directed towards a decrease in the free energy of the system occur spontaneously.
What do these functions express?
By the value of DG one can judge the fundamental possibility of the reaction occurring. If DG = 0, then an equilibrium reaction occurs, the direction of which is determined only by the concentration of its individual components. If DG< 0, то реакция идёт спонтанно с выделением энергии в форме полезной работы (или более упорядоченной химической структуры). Если DG >0, then a change in the state of the system occurs only when work is expended from the outside.
The second principle of thermodynamics can be extended to social processes, but it should be remembered that this method of considering the behavior of society will be of a philosophical, cognitive nature, and does not pretend to be strictly scientific.
Consider, for example, a problem that directly concerns lawyers - the problem of the growth of crime and the fight against it.
Let me remind you of the formulas of the 1st law: DН = Q – A and the change in Gibbs free energy DG = DH - TDS
Or DH = DG + TDS
Let's assume that the initial crime level is H 1, and the final crime level is H 2. Then DH = Н 2 – Н 1 = DG + TDS, where DG is the change in the creative activity of the population, T is the degree of excitement of citizens, DS is the change in the destructive activity of the population.
If the creative activity (potential energy) of citizens is high, that is, DG<0, то она тратится на создание благополучного общества; в этом случае степень возбуждения Т не очень высока, поскольку люди заняты полезным делом, низка и разрушительная деятельность (митинги, излишняя политизированность общества и т.д.) иначе говоря, энтропия общества постоянна. В этом случае DH ≤ 0 (роста преступности практически нет).
- a) In an isolated system, only processes with an increase in entropy occur spontaneously. S > 0 - the process is possible, S
- b) Where heat exchange with the environment is possible, this is no longer entirely true. Exothermic processes with a decrease in S are possible, for example, crystallization of a liquid, condensation of steam. Therefore, the Berthelot criterion was initially introduced: only exothermic processes occur spontaneously, that is, processes with a decrease in U or H. This criterion is often justified at low temperatures. Indeed, it is easier to lose energy than to gain it. A simple mechanical analogy: an object on the table has greater potential energy than on the floor; it can roll and fall on the floor spontaneously, but it cannot jump from the floor to the table on its own. But still, this criterion is not entirely correct. Endothermic processes are also possible, for example, evaporation of liquid.
Both tendencies operate simultaneously - the desire for a minimum of energy (U or H) and the desire for a maximum of disorder (S). We need criteria that take into account both trends at once. These criteria are:
Helmholtz energy F = U - TS for isochoric-isothermal processes and Gibbs energy G = H - TS = U + pV - TS = F + pV - for isobaric-isothermal.
In the old literature they are also called thermodynamic potentials (isochoric-isothermal and isobaric-isothermal), as well as Helmholtz and Gibbs free energies.
There is a more direct analogy with mechanical potential energy: macrobodies spontaneously roll into a hole, to a minimum of potential energy, and physicochemical systems - to a minimum of thermodynamic potential.
Under isochoric-isothermal conditions, only processes with a decrease in F occur spontaneously: F< 0 - процесс возможен, F >0 - the process is impossible. When F reaches a minimum, equilibrium occurs.
Similarly, under isobaric-isothermal conditions, only processes with a decrease in G occur spontaneously.
G=H-TS< 0 - условие самопроизвольного протекания процесса в изобарно-изотермических условиях. Возможны четыре варианта (рис. 5):
- 1) H > 0, S
If T 0, then G H and Berthelot’s principle is valid. In this case, the direct process can proceed, but the reverse process cannot.
If T, then G -TS, and the direction of the process is determined by the growth of entropy. In this case, only the reverse process can occur.
4) N< 0, S < 0. Случай, обратный предыдущему. Процесс идёт самопроизвольно лишь при высоких температурах.
But where is the border between “low” and “high” temperatures? This depends on the ratio of H and S. Temperature at which the forward and reverse processes are equally probable (G = 0): T 0 = H/S.
Below this temperature, the equilibrium shifts towards the exothermic reaction, above - towards the endothermic one. In qualitative form, this is known as a special version of Le Chatelier's principle. Obviously, with different signs of H and S, such a temperature cannot exist.
Demonstration: reversible decomposition of NH 4 Cl NH 3 + HCl and irreversible decomposition of (NH 4) 2 Cr 2 O 7 N 2 + Cr 2 O 3 + 2H 2 O. The sign of S is obvious from the release of gases, the sign of H in the second case is also obvious - self-heating .
Question. How do H, S and G change during the reaction BaCl 2 (p-p) + H 2 SO 4 (p-p) > BaSO 4 (solid) + 2HCl (p-p) under isobaric-isothermal conditions? in an isolated system? The process occurs spontaneously, which means under isobaric-isothermal conditions G< 0. Но образование кристаллов позволяет утверждать, что S < 0. Тогда однозначно Н < 0. Будет ли Н < 0 в изолированной системе? Нет, Н = 0, т.к. нет теплообмена.
The system cannot release heat to the environment, so the temperature rises. But if the process proceeds spontaneously, then S > 0. But can crystallization occur with an increase in entropy?
Crystallization is unlikely, but the solution heated up, and the increase in its entropy outweighed the decrease in entropy from crystallization. Here G = - TS< 0.
For F, G and S, as well as for U, H, Hess's law is valid.
The change in entropy unambiguously determines the direction and limit of spontaneous occurrence of the process only for the simplest systems - isolated ones: if, as a result of the calculation, it turns out that D S> 0, the process will proceed spontaneously, with D S= 0 – equilibrium state, if D S < 0, процесс самопроизвольно протекать не будет.
In practice, we have to deal primarily with systems that interact with the environment. Thermodynamic potentials are used as a criterion for assessing the direction of spontaneous processes in such systems.
Thermodynamic potential is called a state function, the decrease of which, at constant certain parameters, is equal to the maximum useful work.
The two main thermodynamic potentials are of greatest importance: Helmholtz energy F (T, V) and Gibbs energy G (T, p). Parameters whose functions are thermodynamic potentials are indicated in parentheses.
To get an idea of thermodynamic potentials, we will use the combined mathematical expression of the first and second laws of thermodynamics.
or
.
Let's consider the corresponding processes .
Isobaric – isothermal process ( p, T = const).
Equation (1.23) will be written
,
,
Where H – TS = G– Gibbs free energy. At p, T = const the change in Gibbs energy is associated with the performance of useful work:
.
In a reversible process . Then
,
.
Thus, the Gibbs free energy is an isobaric-isothermal potential, since its decrease characterizes the maximum work of this process.
If the only type of work is expansion (compression), i.e. , then in an irreversible, and therefore spontaneously occurring process
. (1.24)
Isochoric – isothermal process ( V, T = const).
Equation (1.23) will take the form
,
Where U – TS = F– Helmholtz free energy. At V, T = const a change in Helmholtz energy is associated with the performance of useful work:
.
In a reversible process
,
.
Thus, the Helmholtz free energy is an isochoric-isothermal potential.
If , then in a spontaneously occurring process
. (1.25)
Inequalities (1.24), (1.25) are a condition for the spontaneous occurrence of a process with constant corresponding parameters: only those processes that lead to a decrease in the free energy of the system can occur spontaneously; the system reaches a state of equilibrium when the free energy reaches a minimum value (Fig. 1.7.).
F |
F min |
Processes that are accompanied by an increase in thermodynamic potentials occur only when work is performed from outside on the system.
The change in the corresponding thermodynamic potential during any process occurring at temperature T, calculated using the Gibbs-Helmholtz equation:
– for an isobaric-isothermal process
D G= D H–T D S, (1.26)
– for an isochoric-isothermal process
D F= D U–T D S. (1.27)
Based on the Gibbs-Helmholtz equation (1.26), (1.27), it is possible to estimate the contribution of the enthalpy and entropy factors to the value Δ G(or Δ F) and draw some general conclusions about the possibility of spontaneous occurrence of chemical processes.
1. Exothermic reactions, Δ H < 0.
If Δ S> 0, then Δ G always negative; exothermic reactions accompanied by an increase in entropy always occur spontaneously.
If Δ S < 0, реакция будет идти самопроизвольно при DH>T D S(low temperatures).
2. Endothermic reactions, Δ H > 0.
If Δ S> 0, the process will be spontaneous for D H<T D S(high temperatures).
If Δ S < 0, то ΔG always positive; Spontaneous occurrence of endothermic reactions accompanied by a decrease in entropy is impossible.
Thermodynamic potentials can play the role of characteristic functions. This means that with the help of their derivatives it is possible to express the properties of the system necessary for its characteristics.