Sarkisyan Z. M., Prokhorova L. B.. Lecture. Hemical kinetics. Rate of chemical reaction. Chemical equilibriurn

УS= У,.

This is the main characteristic of chemical equilibrium.

At equilibrium composition and concentrations of all components of equilib­ rium mixture do not vary under constant external conditions, but continuing forward and reverse reactions make the equilibrium a dynamic process.

Sometimes the composition of a mixture in which chemical reaction is possible, remains long time constant, but not because process has already ended and there equilibrium has come but because, for example, without the catalyst process proceeds so slowly, that changes cannot be found experimentally.

For an establishment of the fact of equilibrium it is possible to use second characteristic of equilibrium - an attribute of its mobility. If the equilibrium system is being take out from this equilibrium in an insignificant degree by external in­ fluence, than after stopping of this effect the system will come back to equilib­ rium state spontaneously. If with change of external conditions (temperature, pres­ sure, etc.) the structure of a mixture will change, and at returning to old conditions will come back to an initial state it means, that the considered state is equilibrium. If it is not present, the system has not reached still a condition of equilibrium.

The system, which state is characterized by two attributes - stability of composition and mobility is called equilibrium system and it’s composition is called equilibrium composition. The composition of equilibrium system is charac­ terized by that in it concentration of initial substances and concentration of endproducts are in the certain ratio.

Let’s consider this ratio on the example of reaction of hydrogen with iodine (3).

According to the kinetic equation of forward and reverse reactions (4,5) at the equi­ librium concentration equal [H2], [h] and [HI] this equality takes the form

As constants of rates do not depend on concentration, expression (7) is convenient for writing down in the form of

The ratio of constants of rates of forward and reverse reactions is called a constant of equilibrium and is designated as Kc(or K). Apparently from expres­ sion (52), the constant of equilibrium shows a numerical ratio which is established in equilibrium system between equilibrium concentration of substances; for the given equilibrium and temperature this ratio is constant. The subscript "c" shows, that the composition of an equilibrium mixture is expressed through molar concentration of corresponding substances.

For reaction in general form

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at equilibrium v,= к/[A]“[B]band vr = kr [ Pf [Of!; V/= vr, so

k, [A]a[B]h = к, [РГ10Г : so constant of forward reaction

The constant of equilibrium, as well as constants of rate, depends on nature the substances participating in reaction, and temperature.

To make the constant of equilibrium in numerator of fraction it is necessary to write the product of equilibrium concentration values of reaction products,

The Equilibrium Constant Kp

In discussing gas-phase equilibrium, il is often convenient to write the equilib­ rium constant in terms of partial pressures of gases rather than concentrations. Note that the concentration of gas is proportional to its partial pressure at fixed tempera­ ture.

2.2. Equilibrium in heterogeneous system

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A heterogeneous equilibrium is an equilibrium ivolving reactants and products in more than one phase. For example, the reaction of iron metal filings with steam to produce iron oxide

+ 4H <-■>FGjO-tisoinii "**

In writing the equilibrium constant expression for a heterogeneous equilibrium, we omit concentration terms for pure solid and liquids.

They are constant at given temperature. For reaction of iron with water

K. _= KJ

For heterogeneous reaction of iron preparation from iron oxide

The concentrations of Fe and FejOjare omitted:

(14)

Equilibrium constant depends on nature of substances and temperature and does not depend on concentration. Note that catalyst has no effect on the constant value. A catalyst merely speeds up the attainment of an equilibrium.

3. Shifts of Chemical Equilibrium. Le Chatelier’s Principle.

The equilibrium state of system is a stable state, and a system may be in equilib­ rium for infinitive period of time if the environment does not change. Temperature, pressure, concentrations of substance concentrations must be constant. When even one of this factors is changed the system go out of equilibrium state because the rales of forward and reverse reaction are changes, usually, unequally. Changes in equilib­ rium system as result of changes of outer conditions refer as equilibrium shift, if the rate of forward reaction becomes more than the rate of reverse reaction, we say that equilibrium shifts to the right (vr > vr). Oppositely, when rate of reverse reac­ tion becomes more than rate of forward reaction (vr > vf) equilibrium shifts to the left. At that, after some time a new equilibrium is established with new equilibrium concentrations. So, by changing the reaction conditions we can to change the direc­ tion of reaction

Let's consider the main factors.

3.1. Equilibrium shifts by changing the concentration of substances

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Change of concentration of one of components can be earned out, for example, by its addition in equilibrium system or its conclusion from a reactionary mix. We shall enter into the system (3) which are being at equilibrium, some quantity of Ь or l-k

The equilibrium constant does not depend on concentration of substances and con­ nects their values by the ratio

' ■' (l5)

So constant value of K(.at increasing of [H2] and/or [I2] concentrations (in denomi­ nator) demands the increasing of numerator ([HI]), and the decreasing of the denomi­ nator. So equilibrium will be displaced to the right towards H2 and/or I2 consumption.

On the contrary, we shall diminish concentration of any substance, for example HI. At transition to a new condition of equilibrium the concentration of H2 and/or l2 will decrease and concentration of HI will increase in accordance with KL.expression

. So equilibrium will be displaced to the right towards the formation of HI. Only in this case after a while the parity of concentration equal to a constant of balance will be reached.

Following law is generally observed:

- at increase of concentration of any substance-participant in reaction mixture, the equilibrium is shifts towards the consumption of this substance;

- at decrease of concentration of any substances in reaction mixture, the equilib­ rium is shifts towards the formations of this substance.

To a similar conclusion it is possible to come on the basis of the kinetic equations of direct and return reactions.

3.2. Equilibrium shifts by changing the volume of gaseous system

If gases participate in a reaction, equilibrium can be shifted by change of vol­ ume of system. For gaseous substances reduction or increase in volume of system means accordingly increasing or decreasing of concentration of gaseous substances, and also increasing or reduction of pressure in a system.

Let the mixture of gases NO, 0 2 and N 02 is in equilibrium.

times concentration of all gases will increase also. Pressure also will increase in sys­ tem in 2 times. Having substituted initial values after the concentration’s changes, the ratio of Kuis equal

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we can see, that the numerator has increased in 4 times, and a denominator - in 8 times. The condition of a constancy of Kc is not earned out now. Equilibrium is bro­ ken, and process will go towards the increase of N 03 concentration and decreasing of NO and O2concentrations until rates of forward and reverse reactions again will be equal. It is easy to notice, that thus equilibrium will be shifts to the right, towards de­ creasing of moles number of gas. Considering various equilibriums from the point of view of a Kc constancy, and analyzing changes of rates of forward and reverse reac­ tions with participation of gases, it is possible to come to the generalized conclusions:

1.At increasing o fpressure by compression o f system (reduction o f volume), an equilibrium is shifted towards the reduction o f total moles o f gases.

2.At decreasing ofpressure by expansion o fsystem (increase o f volume), an equilibrium is shifted towards increases o f total moles o fgases.

3. In case reaction proceeded without change of total moles o fgases, an equilibrium is not shifted at change ofpressure. For example, in system (3), balance is not shifted neither at compression, nor at expansion of system because two moles of H2{gns> and b(gas> give two moles gaseous HI.

3.3. Equilibrium shift by changing the tem perature

Temperature has a profound effect on most reactions. In the first place, reac­ tion rates usually increase with an increase in temperature, meaning that equilibrium is reached sooner. Equilibrium constants vary with temperature. But if the reaction is exothermic, the equilibrium constant usually increases less than equilibrium constant of endothermic reaction. So shift of equilibrium is connected with dependence of an equilibrium constant on temperature. The factor defining a direction of shift is the sign of thermal effect (ДН0).

For an endothermic reaction (ДН0 positive -absorption of energy), the amounts of products are increase at equilibrium by an increase in temperature (Kc is lager at higher T).

For an exothermic reaction (ДН° negative - desorption of energy), the amounts of products are increase at equilibrium by a decrease in temperature (Kc is lager at lower T).

By terms of equilibrium shifts: at increase in tem perature, equilibrium shifts towards the endothermic reaction (ДН0 positive) and at decrease in tem­ perature, equilibrium shifts towards the exothermic reaction (ДН° negative).

Example. How to displace equilibrium to the left in the system

Nugas) + Oilgas* «-» 2 NO(gas); AH° > 0?

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The decision. The thermal effect of forward reaction is known; the reaction is endothermic (AH0 >0). Thermal effects of a forward and reverse reactions are con­ nected by the expression

AH lyfwurd -A H reverse

Therefore it is possible to draw a conclusion that reverse reaction is exothermic (AH0 <0). So equilibrium is shifted to the left when temperature is increased.

In the table there are several examples of equilibrium shifts by temperature changing.

Table. Examples of equilibrium shifts by temperature changing

Besides concentration of substances, pressure and temperatures, other factors can in greater or lesser degree influence on chemical equilibrium. For example in some systems this is electric or magnetic fields.

Considered rules are the examples of general principle - Le Chatclier’s principle.

Le Chatelier’s principle state that when a system in equilibrium is disturbed by a change o f temperature, pressure, or concentration variable, the system shifts in equilibrium in away that tends to counteract this change o f variable.

Le Chatelier’s principle is true for both chemical and physical equilibrium.

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Bibliography

1.Chemistry. Fundamentals of living substances chemistry. V.I. Slesarev. SPb. Khimizdat. 2007.768 p. (in Russian)

2.Popkov V.A., Puzakov S.A. Geotar-Media. 2010. 976 p. (in Russian).

3.Reuveni, Shlomi; Urbakh, Michael; Klafter. Joseph (2014). "Role of Substrate

Unbinding in Michaelis-Menten Enzymatic Reactions". Proceedings of the National Academy of Sciences. III (12): 4391-4396.

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