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

The general order of reaction is equal to three.

For an elementary reaction the general order coincides with molecularity, and in the kinetic equation the degrees are equal to corresponding stoichiometric coeffi­ cients in equation of the chemical reaction.

Reactions with higher molecularity than three are improbable. Under the kinetic theory a condition of interaction of molecules is their simultaneous collision with each other, but probability of simultaneous collision more than three molecules of the certain kind is insignificantly small.

Reactions of radioactive decay are monomolecular. Stages (20) - (23) in the reac­ tion of bromine with hydrogen are bimolecular. Trimoiecular reactions are recombi­ nation of atoms at collision with some neutral particles, for example:

Br- + Br- + A = Bra + A*.

The molecularity can be considered exactly only after detailed studying of the mechanism of a reaction.

It is necessary to note, that the mechanism of a reaction includes also formation of an intermediate activated complex at each elementary stage, representation about which will be given below in connection with concept about energy of activation.

1.3. Chemical Reaction Rate. Dependence on Temperature

1.3.1. Van-Goff Rule

Rate of chemical reaction, as a rule, strongly depends on temperature. Van-Goff formulated an empirical rule according to which, rate of most of reactions in­ creases in 2-4 times at rise in temperature for 10 degrees if reaction is carried out at the temperature close to room temperature:

(32)

where V [ j and vTo are reaction rales at temperatures Tj and T2 correspondingly; у

is Van-Goff temperature factor for reaction rate (y = 2-4). It is follows from the equation (32), that if Tj - T2 = 10, then

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The temperature factor shows, in how many time speed of chemical reaction in­ creases at rise in temperature on 10 degrees. By Van’t-Goff rule у has the values which are being in interval 2- 4.

Example. To calculate, in how many time the reaction rate will increase at in­ crease in temperature from 313 up to 333 K, the temperature factor is equal 2.

The decision. Dependence of the rate of chemical reaction on temperature is

Therefore the rate of chemical reaction will increase in 4 times at temperature change from 313 up to 333 К (ДТ = 20 К).

1.3.2. Arrhenius equation. Activation energy of chemical reactions. Activated complex

According to S.Arrhenius, only molecules which possess the certain rate and certain energy take part in a reaction.

Excess energy in comparison with average energy of molecules at the given temperature which molecules should possess that their collision could lead to forma­ tion of new substance, refers to as energy of activation of the given reaction. The molecules possessing such energy, refer to as active molecules.

Energy of particles increases with growth of temperature and, accordingly, the number of active molecules increases. Rate of chemical reaction, hence, increases.

Van’t Hoff rule only approximately expresses dependence of rate of reaction on temperature. More exact dependence for constant of chemical reaction has been re­ ceived by S.Arrhenius. Constant of chemical reaction is expressed by the equation

__Ea

к = A • e RT,

(35)

where T - absolute temperature, K; R - the universal gas constant which equals 8,31 j/(moI*K); A - the frequency factor which equals to number of collisions in unit

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of time, multiplied on probability of favorable collision (collision with reaction); Еа - activation energy of particles.

It is possible to receive expression from Arrhenius equation (35) and the equation

R UOO 3

From here the Van’t Hoff rule becomes clear: from the equation (38) follows, that at increase in temperature at 10 degrees and at measurable speeds of reaction (50kJ < Ea <100 Id) the temperature factor is in an interval 2- 4.

From the point of view of the mechanism of chemical reaction an energy of ac­ tivation is necessary for formation of intermediate - the activated complex. We shall consider this process on an example of the reaction of hydrogen radical with deuterium molecule proceeding in a gas phase:

Collision of two active particles, H2 • and D2, originally gives an intermediate state (the so-called activated complex). This complex is characterized by that: in molecules of initial substances a chemical bonds were not yet completely broke, but in molecules of products new chemical bonds have already started to be formed. The activated complex decays with formation of products of reaction. This process is schematically represented on Fig.4.

D-D + H D -D -H — D + D-H

Fig. 4. Scheme of reaction H- + Di —» HD + D* in gaseous phase

Let's consider the energy diagram of exothermal reaction (Fig. 5) at which the levels of average energy of reagents (Ere0gcms), the activated complex (Еде) and prod­ ucts of reaction (Epr0ducts) are represented.

It is apparently from the diagram, that for formation of the activated complex it is necessary to spend energy. Quite the contrary the energy is evolved at transition to end-products. The difference between average value of energy of reagents and the activated complex is an activation energy of reaction (E„).

LAC = Еде - Lrcagcniv

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Since Еде always more than Е ^ с к and Epro<jUC,s the activated complex state is

2. RATE OF HETEROGENEOUS CHEMICAL REACTIONS

The reactions that occur in heterogeneous system are characterized by that inter­ action occurs on phase’s boundary surface.

The quantity of the substance entering into reaction or formed at reaction during a unit of time on a unit of the area of a surface refers to as average speed of heterogeneous reaction:

Vheiorog

SAT

Where

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- S - the area of a surface on which reaction proceeds, square metre; - Anj - the change of quantity of substance in moles;

AT - a time interval in seconds.

As a rate of any chemical reaction has positive size, An; undertakes with a sign "+ " for products of reaction (their quantity grows) and with a sign for reagents (their quantity decreases).

Both reagents are come into contact only on a surface of metal Zn; for this rea­ son speed of heterogeneous chemical reaction includes area of a surface (S) of metal on which process proceeds. Speed by HC1 will be expressed as;

For heterogeneous reaction it is possible to distinguish three basic stages:

1.A supply of reacting substance to a surface.

2.Chemical reaction on a surface.

3.Removal of products.

A kinetics equation for heterogeneous reactions includes only concentra­ tions of substances in solutions and concentration of gaseous substances.

For example the reaction of zinc dissolution in hydrochloric acid solution is

To increase a rale of chemical reaction it is possible not only by rise in tempera­ ture and concentration of reagents, but also by means of the catalyst.

The catalyst is a substance which influences on a rale of reaction, but is not spent during reaction and remains chemically unchanged after reaction. Ca­ talysis is the phenomenon of change of chemical reaction rate under action of the catalyst.

The reactions proceeding under action of catalyst refer to catalytic reaction

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Fig.3. Energy changing in system A + В = D at presence of the catalyst

At presence of the catalyst new mechanisms of reactions are realized, i.e. there are elementary stages with participation of the catalyst. Thus activation energy of reaction decreases as a result of formation of other activated complexes with less energy. It is well visible on an example of the schematic diagram (Fig.3), at which the energy changing in system A + В = D at presence of the catalyst are represented.

All catalytic processes can be divided according to a phase states of the catalyst and reagents into two kinds:

1)homogeneous catalysis;

2)heterogeneous catalysis.

Homogeneous catalysis is called the catalysis in which reacting substances and the catalyst are in one phase states. For example all system is gaseous or a solution.

Heterogeneous catalysis is called the catalysis in which a catalyst and react­ ing substances arc in the different phase states. In this case the catalyst is in a solid state more often.

As well as in case of homogeneous catalysis, reactions proceed through forma­ tion of intermediates with that difference, that these compounds are formed

on a surface of catalyst.

Practically all biochemical reactions both in (single cell) unicellular protozoa and in plants and animals have catalytic character.

The catalysis of biological organisms are enzymes. Enzymes are protein molecules with molecular weights ranging to over a million amu.

Enzymes are characterized by

-high catalytic activity, converting a thousand or so reactant molecules to prod­ ucts in a second;

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- high specificity, each enzyme acts only on specific substance, or a specific type of substance and act in strictly certain conditions.

Enzymes show the highest catalytic activity at the certain temperature (36-38° C) and at the certain value of acidity of environment (pH).

The substance whose reaction the enzyme catalyzes is called the substrate. Fig.4 shows schematically how an enzyme acts.

Fig.7. Mechanism of enzyme action

The enzyme molecule is a protein chain that tends to fold into a roughly spherical form with an active site at which the substrate molecule binds and the catalysis takes place. The substrate molecule, S, fits into the active site on the enzyme molecule, E, somewhat in the way a key fits into a lock, forming an enzyme-substrate complex. ES. In effect, the active site “recognizes” the substrate and gives the enzyme its specificity. On binding to the enzyme, the substrate may have bonds that weaken or new bonds form that help yield the products, P

E + S —»ES —►E + P

The formation of the enzyme-substrate complex provides new pathway to prod­ ucts with lower activation energy.

In biochemistry, Michaelis-Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelisand Ca­ nadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate .

This equation is called the Michaelis-Menten equation. Here represents the maximum rate achieved by the system, at saturating substrate concentration. The

Biochemical reactions involving a single substrate are often assumed to follow Michaelis-Menten kinetics, without regard to the model's underlying assump­

tions.

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Change in concentrations over time for enzyme E, substrate S, complex ES and product P

In 1903, French physical chemist Victor Henri found that enzyme reactions were initiated by a bond (more generally, a binding interaction) between the enzyme and the substrate. His work was taken up by German biochemist Leonor Michaelis and Canadian physician Maud Menten, who investigated the kinetics of an enzy­ matic reaction mechanism, invertase, that catalyzes the hydrolysis of sucrose into glucoseand fructose. In 1913, they proposed a mathe­ matical model of the reaction. It involves an enzyme, E, binding to a substrate, S, to form a complex, ES, which in turn releases a product, P, regenerating the original en­ zyme. This may be represented schematically as where and denote the rate con­ stants,151the double arrows between S (substrate) and ES (enzyme-substrate complex) represent the fact that enzyme-substrate binding is a reversible process, and the single forward arrow represents the formation of P (product).

Under certain assumptions - such as the enzyme concentration being much less than the substrate concentration - the rate of product formation is given by equation

v = A.\, + c(S)■. The reaction order depends on the relative size of the two terms in the denominator. At low substrate concentration. Under these conditions the reaction

rate varies linearly with substrate concentration , the reaction becomes independ­ ent, where is the initial enzyme concentration. This rate is attained when all enzyme

is bound to substrate. The turnover number, is the maximum number of substrate molecules converted to product per enzyme molecule per second. Further addition of substrate does not increase the rate which is said to be saturated.

The Michaelis constant at which the reaction rate is at half-maximum, and is an inverse measure of the substrate's affinity for the enzyme—as a small indicates high affinity, meaning that the rate will approach with lower than those reactions with a larger. The constant is not affected by the concentration or purity of an en­ zyme. The value of is dependent on both the enzyme and the substrate, as well as conditions such as temperature and pH.

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The model is used in a variety of biochemical situations other than enzymesubstrate interaction, including antigen-antibody binding, DNA-DNA hybridization, and protein-protein interaction. It can be used to characterise a generic biochemical reaction, in the same way that the Langmuir equation can be used to model ge­ neric adsorption of biomolecular species. When an empirical equation of this form is applied to microbial growth, it is sometimes called a Monod equation.

CHEMICAL EQUILIBRIUM. THE KINETIC APPROACH

1. Reversible and irreversible reactions

If in chemical interaction even one of reagents is spent completely, reaction is considered as irreversible. This reaction proceeds up to the end only in one direc­ tion. Decomposition of ammonium dichromate at heating is example of irreversible reaction

(NHjiCrjO-tsoMi СГ2О3 <Sondi + + 4 H30 (gas). (1) The aiTOw shows a direction of irreversible reaction.

However in most cases reactions take place reversibly. Reversible reaction is called the reactions that take place in both direction simultaniously under certain conditions (in forward and in reverse directions).

For example, at temperatures about 1000°C hydrogen and oxygen interact with explosion to give water, on the contrary, at 5000°C water with explosion decomposes to hydrogen and oxygen. In an interval of temperatures 2000-4000°C simultaneously two processes occur a) formation of molecules of water from hydrogen and oxygen and b) destruction of water on H? and O?. Thus, at the specified temperatures reaction

becomes reversible. For indication of reversibility two oppositely directed arrows are used:

2H3fmf + 0 2(l,as) 2H 20 (gas) \T = 2000-4000° C ( 2)

The reaction from left to right is named a forward reaction, and from right (o left - reverse. Reversible reactions refer to complex reactions.

2. Chemical Equilibrium. Kinetic Argument. Equilibrium Constant (K)

2.1. Equilibrium in homogeneous system

Consider the reversible reaction o f hydrogen and iodine with formation hy­ drogen iodide in a gas phase. In the kinetic equation the order by each substance co­ incides with stoichiometric coefficients in the equation of reaction.

(3)

IB

Let’s mixture Hi and I2 at the fixed temperature and pressure. Rate of forward

concentrations are maximal, that corresponds to the maximal rate of forward reaction (fig. 8). Since during the forward reaction the concentrations of reagents decrease, the

where kr - constant of reverse reaction. At the initial moment of time rate of reverse reaction is equal to zero, but in process of accumulation of HI it increases according to the kinetic equation (5) (fig. 1). In the certain time the concentrations of H2, b and HI cease to vary, as there comes the moment when the quantity of particles HI formed as a result of forward reaction, is equal to number of particles HI decaying as a result of reverse reaction. From this point, rate of the forward and reverse reac­ tions are equal each other (fig. 8). There condition of chemical equilibrium comes.

Figure 8. Change of rates of forward (vf) and reverse (vr) reactions in gas phase process H; + N 2H1.

At chemical equilibrium point the concentrations of products and re­ agents, despite of continuously occuring processes of formation and decomposition of HI, will remain constant.

In chemical kinetics equilibrium is defined as state at which rates of for­ ward and reverse reactions are equal each other

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