CHEMICAL KINITICS Kononova T.O.

Some reactions occur in a fraction of a second, others take several minutes, and some take months or years. Many common chemical reactions, such as acid – base and precipitation reactions, occur very quickly, as shown by the rapid color change of an indicator of the almost instantaneous formation of a precipitate when some reagents are mixed.

𝝑=∓ 𝚫𝒄 𝚫𝒕 =∓ 𝐥𝐢𝐦 ∆𝒕→𝟎 ∆𝒄 ∆𝒕 =∓ 𝒅𝒄 𝒅𝒕 The rate of a chemical reaction equals the change in the number of moles per liter of a product formed, or a reagent consumed, in a given time interval: 𝝑=∓ 𝚫𝒄 𝚫𝒕 =∓ 𝐥𝐢𝐦 ∆𝒕→𝟎 ∆𝒄 ∆𝒕 =∓ 𝒅𝒄 𝒅𝒕

Let us consider a simple reaction in which a single reactant, A, decomposed to one product, B: A → B The concentration of substance A decreases during the reaction, and the concentration of B increases.

If we assume that the molar concentration of the product B is c1 at time t1 and c2 at time t2, the rate of the reaction is: 𝜗= 𝑐 2 − 𝑐 1 𝑡 2 − 𝑡 1 = Δ𝑐 Δ𝑡 The rate of formation of a product is written with a positive sign because the concentration of the product at time t2 is greater then the concentration at time t1.

When the rate of reaction is given as the rate of a reactant (A) whose concentration is decreasing, the rate expression is given a negative sign: 𝜗=− 𝑐 2 − 𝑐 1 𝑡 2 − 𝑡 1 =− Δ𝑐 Δ𝑡 In the expression for the rate of disappearance of a reactant, the difference between the concentration of the reactant at time t2 and that at time t1 is a negative quantity. Therefore write this rate expression with a minus sign so that the rate will be positive.

The important factors, which affect the rates of reactions are as under: The nature of a reactants and a solvent (if the reaction occur in a solution). Concentration of a reactant. Temperature of a system: as a rule, the rates of reactions increase with increase in temperature of a system. Pressure of a system: if reactants one in a gaseous states, the change in pressure of system, changes the rate of reaction.

The surface area of particles of solid reactants: if a solid reactant is used in a finely powdered form, its reaction occurs speedily. Catalytic effect: if a reaction is carried out in the presence of a catalyst, the rate of reaction increases. Intensity of light: rates of some reactions are affected by the intensity of light falling on reactants.

CONCENTRATION AND REACTION RATE Concentration plays an important role in the rate of a chemical reaction; nearly always, increasing the concentration of a reactant will increase the rate of a reaction. Reactions occur between two molecules when they collide. In elementary reactions that involve more than one molecule, the increase in rate is easy to understand: the higher the concentration of reactants, the more collisions occur between reactant molecules and the greater the likelihood of a reaction occurring. The quantitative relation between rate and concentration is called the rate law. A rate law can be derived from a proposed mechanism, but the true rate law is obtained from meticulous experimental work.

LAW OF MASS ACTION 𝝑=𝒌∙ 𝒄 𝒂 (𝑨)∙ 𝒄 𝒃 (𝐁) Fundamental law of chemical kinetics, formulated in 1864-79 by the Norwegian scientists Cato M. Guldberg and Peter Waage. The law states that: The reaction rate of any simple chemical reaction is proportional to the product of the molar concentrations of the reacting substances, each raised to the power corresponding to the number of molecules of that substance in the reaction. For example: aA +bB → cC 𝝑=𝒌∙ 𝒄 𝒂 (𝑨)∙ 𝒄 𝒃 (𝐁)

𝒌=𝝑 temperature; nature of reactants. The "𝑘" is the rate constant. The rate constant depends on: temperature; nature of reactants. If the concentration of each reagent in the rate law is 1M, the rate of the reaction and 𝑘 become equal. The exponents 𝑎, 𝑏 are called the order of the reaction with respect to that particular reactant. The sum of all the exponents is the overall order of the reaction. 𝑛=𝑎+𝑏 where 𝑛 is overall order of reaction. 𝒏=𝟏 𝒏=𝟐 𝒊𝒇 𝒄 𝑨 = 𝒄 𝑩 =𝟏𝒎𝒐𝒍/𝒍 𝒌=𝝑

THE KINETIC EQUATIONS OF 0, 1 AND 2-ORDER REACTIONS. 𝜗=− 𝑑𝑐 𝑑𝑡 =𝑘∙ 𝑐 0 𝑘= 𝑐 0 −𝑐 𝑡 “half-life” time is 𝑡 1/2 = 𝑐 0 2𝑘 For example: 𝐻 2 + 𝐶𝑙 2 →2𝐻𝐶𝑙 (photochemical reactions) 1-st order reactions: 𝜗=− 𝑑𝑐 𝑑𝑡 =𝑘∙ 𝑐 1 𝑘= 1 𝑡 ln 𝑐 0 𝑐 or 𝑘= 2.303 𝑡 log 𝑐 0 𝑐 “half-life” time is 𝑡 1/2 = ln 2 𝑘 = 0.693 𝑘 Example are radioactive reactions.

The 2-nd order reactions. Let us consider the second order reaction: 2𝐴→𝐵 Mass action law is: 𝜗=− Δ𝑐 Δ𝑡 =𝑘∙ 𝑐 2 (𝐴) 𝑘= 1 𝑡 1 𝑐 − 1 𝑐 0 “Half-life” is: 𝑡 1/2 = 1 𝑘∙ 𝑐 0

The molecularity of a reaction. One, two or three molecules may be involved in the elementary event of a reaction. Accordingly, monomolecular, bimolecular, and termolecular reactions are distinguished. The probability of the simultaneous collision of a large number of particles is very small, so that even termolecular reactions are very rare, while tetramolecular reactions are not known. In most cases therefore the stoichiometric equation of a reaction does not define the character of its course, i.e. its mechanism.

The influence of rate of chemical reaction on temperature. Van’t Hoff’s rule: when the temperature rises by 100C, the rate of the reaction increases about two- or four-fold. 𝜗 𝑡2 = 𝜗 𝑡1 ∙ 𝛾 (𝑡2−𝑡1)/10 Were: 𝜗 𝑡2 - rate of a chemical reaction at 𝑡 2 ; 𝜗 𝑡1 - rate of a chemical reaction at 𝑡 1 . γ - temperature coefficient of a rate of a chemical reaction Vant-Hoff

Arrhenius equation. Arrhenius studied the rates of reactions at different temperatures and established the following relationship between rate constant of a reaction and the energy of activation (Ea) of the reaction.

ACTIVATION ENERGY Activation energy is a term introduced in 1889 by the Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction. The activation energy of a reaction is usually denoted by 𝐸 𝑎 and given in units of 𝑘𝐽 𝑚𝑜𝑙 . Activation energy can be thought of as the height of the potential barrier separating to minima of potential energy(of a reactants and products of a reaction). For a chemical reaction to proceed at a reasonable rate, there should exist an appreciable number of molecules with energy equal to or greater than the activation energy.

Types of catalysts Many reactions proceed quite slowly when the reactants are mixed alone, but can made to occur much more rapidly by the introduction of other substances. These substances are called catalysts and are not used up in the reaction. The effect of catalyst is called catalysis. There are two types of catalytic reactions. Homogeneous catalytic reactions: In such catalytic reactions catalyst and the reactants are in a same phase e.g. 2SO2(g) + O2(g) → 2SO3(g) H2(g) + Cl2(g)→ 2HCl(g)

Unsaturated oil(l) + H2(g)→ Saturated fat(s). Heterogeneous catalytic reactions: In such catalytic reactions catalyst and the reactants are in different phases e.g. N2(g) + 3H2(g)→ 2NH3(g) 2SO2(g) + O2(g) → 2SO3(g) Unsaturated oil(l) + H2(g)→ Saturated fat(s).

Types of catalysts Positive catalysts: A catalyst which increases the rate of reaction is called positive catalyst e.g. N2(g) + 3H2(g) → 2NH3(g) 2SO2(g) + O2(g)→ 2SO3(g). Negative catalysts: A catalyst which decreases or retards the rate of reaction is called negative catalyst e.g. 2H2O2(l) → 2H2O(l) + O2(g). Auto-catalysts: When one of the products formed in the reaction acts as a catalyst is known as auto-catalyst e.g. CH3COOC2H5 + H2O → CH3COOH + C2H5OH. (auto-catalyst)

Activation energy and catalysis According to the collision theory, a reaction occurs by the collisions between the reactant molecules (or ions). But the molecules do not react unless they attain a minimum amount of energy. The minimum amount of energy required to cause a chemical reaction is known as the activation energy. The activated molecules on collision first form an activated complex. As a result of breaking and forming of new bonds, the activated complex dissociates to yield product molecules.

Scheme of the catalysis A catalyst lowers the activation energy of the reaction by providing a new pathway (mechanism). Thus larger number of effective collisions occur in the presence of the catalyst than would occur at the same temperature without the presence of the catalyst. In this way the presence of the catalyst makes the reaction go faster, other conditions remaining the same. Scheme of the catalysis A + K ↔ A…K ↔ AK (1) AK + B ↔ AK…B ↔ AB + K (2) Were: A and B – reactants; K – catalyst; A…K – activation complex A with catalyst (transition state); AK – chemical substances A with catalyst; AK…B – activation complex AK with catalyst (transition state);

CHARACTERISTICS OF ENZYME CATALYSIS Numerous organic reactions are taking place in the body of animals and plants to maintain the life process. These reactions being slow are remarkably catalyzed by the organic compounds known as enzymes. All enzymes have been found to be complex protein molecules. Thus: CHARACTERISTICS OF ENZYME CATALYSIS Enzymes are the most efficient catalysts known Enzyme catalysis is marked by absolute specificity The rate of enzyme catalyzed reactions is maximum at the optimum temperature Enzymes are protein molecules which act as catalysts to speed up organic reactions in living cells. The catalysis brought about by enzymes is known as enzyme catalysis.

Rate of enzyme catalyzed reactions is maximum at the optimum pH The rate of an enzyme catalysed reaction is increased with the rise of temperature but up to a certain point. Thereafter the enzyme is denatured as its protein structure is gradually destroyed. Thus the rate of reaction drops and eventually becomes zero when the enzyme is completely destroyed. The rate of an enzyme reaction with raising of temperature gives a bell-shaped curve. The temperature at which the reaction rate is maximum is called the optimum temperature. Rate of enzyme catalyzed reactions is maximum at the optimum pH The rate of an enzyme catalyzed reaction varies with pH of the system. The rate passes through a maximum at a particular pH, known as the optimum pH.

MECHANISM OF ENZYME CATALYSIS The long chains of the enzyme (protein) molecules are coiled on each other to make a rigid colloidal particle with cavities on its surface. These cavities which are of characteristic shape and abound in active groups (-NH2, -COOH, -SH, -OH), are termed active centers. The molecules of substrate which have complementary shape, fit into these cavities just as key fits into a lock (Lock-and-Key theory). By virtue of the presence of active groups, the enzyme forms an activated complex with the substrate which at once decomposes to yield the products. Thus the substrate molecule enters the cavities, forms complex and reacts, and at once the products get out of the cavities.

The Michaelis-Menten Equation 𝑣 𝑆𝑡 = 𝑣 𝑚𝑎𝑥 + 𝑆 𝐾 𝑀 + 𝑆 Where: [S] – concentration of substrate, KM – Michaelis constant, 𝑣 𝑠𝑡 – stationary rate of a enzymes reaction, 𝑣 𝑚𝑎𝑥 – maximal rate of a enzymes reaction. Analysis of the Michaelis-Menten Equation: If 𝐾 𝑀 ≫ 𝑆 𝑣 𝑠𝑡 = 𝑣 𝑚𝑎𝑥 𝑆 𝐾 𝑀 If 𝐾 𝑀 ≪ 𝑆 𝑣 𝑠𝑡 = 𝑣 𝑚𝑎𝑥

Michaels constant is the concentration of substrate when 𝑣 𝑠𝑡 = 1 2 ∙ 𝑣 𝑚𝑎𝑥

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