Kinetics of heterogeneous catalytic reactions. Laboratory training guidance

Nernst suggested that liquid near the surface of the solid body forms a so-called custom diffusion layer, outside of which the concentration with good stirring is maintained throughout the same. In addition, he believed that the dissolution rate is much more than the diffusion rate, therefore directly at the surface of a solid body solution is close to saturation. Since the diffusion is considered to be the slowest stage, the speed of the overall process can be taken for the rate of diffusion.

Further studies have shown that the Nernst`s theory is not entirely true. Diffusion layer thickness calculated on the basis of this theory is so large (about one million molecular layers) that it cannot be considered as a not attracting in the process of mixing. In fact, the mass transfer between the interface and internal regions is ensured not only by molecular diffusion, but also by convection associated with the movement of layers of substances (convective diffusion). Despite the fact that the equation (22) is often performed a certain value of the δ = D / k obtained with this equation does not correspond to the actual near-surface layer and may be called a diffusion layer effective thickness.

Catalytic reactions

In the presence of the catalyst the reaction rate increases significantly. Catalysts are substances involved in the reaction, altering the reaction rate, but not expendable in the reaction and remaining chemically unchanged thereafter reaction. Catalysts interact with reactants, form with them certain intermediates, are included in the active complex composition, and are reallocated after the reaction. A positive catalysis accelerates the reaction, while a negative catalysis slows down the reaction (i.e., inhibition occurs).

Catalysis divided into homogenous (all reactants and the catalyst itself are in the same phase) and heterogenous (reactants and the catalyst are in separate phases, and the catalytic reaction occurs at the interface).

General features of catalytic reactions.

1.Catalyst reduces the activation energy of the reaction, which leads to a significant increase in reaction rate.

2.Catalyst has no effect on the thermodynamic equilibrium. It changes only the rate to reach equilibrium, i.e. rates forward and reverse reactions.

3.Catalyst`s action is specific. Catalyst selectively enhances only a few of all the possible reactions of the reactants.

4.Very small amount of catalyst is usually sufficient for appreciable catalytic action.

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5.Catalyst`s action is strongly affected by the presence of foreign matter. Certain substances, known as promoters, enhance the action of the catalyst. Substances that reduce the activity of the catalyst are called catalytic poisons.

6.For heterogeneous catalytic reactions the catalyst`s action depends from the surface area.

Mechanisms of catalytic reactions

Chemical reactions proceed with breaking certain chemical bonds in the initial compounds and the formation of new bonds in the reaction products. The activation energy is usually much less than the energy used to break chemical bonds. Progress of the reaction is due to the fact that when driving along the reaction way (via transition state) a path of the energy required to break old bonds is compensated by the energy liberated during the formation of new bonds. The degree of compensation determines the reactivity of substances. Interacting with the reactants entering into the activated complex catalyst increases the degree of compensation, reduces the activation energy, and thereby increases the rate of chemical conversion.

Consider these reasons for the increased rates of catalytic reactions for the two mechanisms of catalytic reactions (stepwise and confluent).

Stepwise (separate) mechanism of the catalytic reactions is substitution of one catalytic reaction by several consecutive stages of interaction between initial reactants and the catalyst with the possible formation of an activated complex at each stage.

In the catalysis reaction of the A + B → C + D type can occur in the following two stages

1)A + K → (AK)≠ → AK,

2)AK + B → (ABK)≠ → C + D + K,

where AK is intermediate stable compound with catalyst, (AK)≠ and (ABK)≠ are intermediate activated complexes.

According to confluent (synchronous) mechanism the simultaneous interaction of all the initial reactants with the catalyst and the formation of single activated complex occur during the reaction:

A + B + K → (ABK) ≠ → С + D.

Thus, at least not less than two activated complexes are formed during the stepwise catalytic reactions, while there cannot be more than one activated complex occurrence at the confluent catalytic reactions (Fig. 4).

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Any heterogeneous catalytic reactions occurring at the presence of a solid catalyst comprising a number of stages:

1.mass transfer of the initial reactants by diffusion from the bulk of liquid phase or gas to the external surface of the catalyst granules;

2.mass transfer by diffusion through the pores of the granules to the inner surface of the catalyst;

3.adsorption of reactants on the surface of the catalyst;

4.chemical act on the surface with one or more chemisorbed species;

5.desorption of the reaction products and the reverse mass transfer of them into the bulk of the liquid or gaseous phase.

Adsorption

Adsorption is a process of spontaneous concentrating of substances from the bulk of the phases at the interface. Adsorption is the second (after diffusion) stage of many heterogeneous chemical reactions.

Differences between physical adsorption and chemisorption.

At the physical adsorption absorbing molecules (adsorbate) are held by absorber surface (adsorbent) due to weak molecular forces of attraction.

In the case of chemisorption absorbing molecules form a surface chemical compound, usually with considerable overcome the energy barrier and it is called activated adsorption.

Consider the relatively simple case of adsorption, which is explained by the theory of Langmuir, whose main provisions are as follows.

1.The surface of the adsorbent (absorbing material) has a limited number of the adsorption centers, i.e. sites where adsorption takes place.

2.Only one molecule of adsorbate (a substance that is absorbed) can be adsorbed on the each adsorption center.

3.All adsorption centers are identical.

4.The adsorbed molecules do not affect each other.

5.Adsorbed molecules are in dynamic equilibrium with the adsorbate molecules located in the environment from which absorption occurs.

Adsorption is characterized by the degree of surface filling Θ, which is the ratio of the number of occupied adsorption centers to the total number of adsorption centers in a given surface.

Adsorption rate is proportional to the concentration of the substance and to the number of free centers on the surface of the adsorbent, i.e.

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while desorption rate (an inverse process of adsorption) is proportional to the degree of surface filling Θ, i.e.

where k1 and k2 are the rate constants.

At equilibrium, the rate of adsorption and desorption are equal to each

k2 k1c

Dividing the numerator and denominator of this equation for k2 and entering the equilibrium constant for adsorption (adsorption coefficient)

Since υdes=k2Θ, i.e. the rate is proportional to the degree of filling, the order (true order) of chemical transformation is unity. Using (29), we obtain

kbc 1 bc ,

comprising a rate dependent from the concentration of the initial substance. At low concentrations (bc << 1) and υ ≈ kbc. In these conditions, the reaction has an apparent order of unity. When bc >> 1 υ ≈ k = const, hence the apparent order is zero. Obviously, at average concentrations the apparent order must be fractional and lies between zero and one.

Theory of heterogeneous catalysis

There are several general theories of heterogeneous catalysis. Most common in the past years have three theories. The multiplet theory, the active ensembles theory, and the electron theory.

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According to the multiplet theory of heterogeneous catalysis (A.A. Balandin) it is assumed that the formation of the surface compound (complex multiplet) involved a group of active surface atoms (multiplets) with certain geometric and energetic properties. The multiplet theory covers the principles of geometrical and energy compliance.

The theory of active ensembles (N.I. Kobozev) assumes that the catalytically active center is a collection (ensemble) of free atoms of the catalyst located on a separate block of the surface area of the solid. These atoms are not included in the crystal lattice and can migrate freely within each block.

The electron theory of catalysis is based on a quantum-mechanical band theory of solid (semiconductor). When temperature is different from absolute zero in the conduction band of the crystal there are electrons providing free valences on its surface. The initial molecules interacting with them on the surface of the catalyst are adsorbing with the formation of free radicals or atoms. Interaction of the particles adsorbed and weakly coupled to the surface can lead to formation of reaction products.

Lab 15

Dissolution rate of hard-soluble salt

Purpose. In this lab you will determine the dissolution rate constant at given temperature using the concentration dependence of the resistivity (or conductivity) of a hard-soluble salt (gypsum) solution.

Background. To calculate the rate of the dissolution process following equation is used

where k is the dissolution rate constant, с0 is the solute concentration at the surface, с is the solute concentration in the bulk. Equation (30) was obtained by Shchukarev under the assumption that the diffusion rate of dissolution products in the bulk of solvent is small in comparing with rates of the other stages.

The dissolution rate constant corresponding to equation (30) is calculated as follows

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For poorly soluble substances, such as gypsum, the rate constant can be determined by measuring of the aqueous solution resistance at various times. Equipment for studying of the dissolution kinetics includes a temperature control system, a reaction vessel, and apparatus for measurement of the solution resistance (conductometer). The reaction vessel is a glass with a capacity of 300-400 mL, which contains the stirrer.

Procedure.

1.Turn on the thermostat system and set the temperature (20-25 ° C).

2.Prepare reaction vessel. Rinse the vessel several times with distilled

water.

3.Fill the vessel by 250 mL of distilled water heated to a temperature of the thermostat and turn on the stirrer setting a uniform mixing mode. Insert the solute plate that has been previously soaked with water into the vessel so that it is above the water surface.

4.Put pre-prepared cylindrical vessel with a saturated solution of gypsum into the thermostat.

5.Put electrode to the reaction vessel with distilled water and turn on the conductometer.

6.After equilibration of the reaction vessel at constant temperature during 15 to 20 minutes start the measurements. For this lower the gypsum plate in the glass of water. Moment of the dive is considered as the start time of the process. Three minutes later from the beginning of the process make the first measurement of the resistance of the solution. Since at the beginning of process the solution resistance is rapidly changing, several first measurements should be carried out every 3-5 minutes, while subsequent measurements should be carried out every 10-15 minutes. Measurements should continue for an hour (9-10 measurements). Solution resistance will decrease with time.

7.Determine the resistance of a saturated solution of gypsum. The electrode previously rinsed by separate portions of the gypsum saturated solution should be lowered into the cylindrical vessel with the saturated solution.

8.At the end of the experiment drain solution from the reaction vessel and rinse it with water.

9.Store the measurement results in the Table 1 using following example:

The solute _____________________

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Temperatute _______ºС

Resistance of the saturated solution, Rs =__________Ω

The volume of solution, __________ mL

kaver.=

10.Calculate the rate constant using the equation (31), which is modified in accordance with the experimental relation between the resistance and the concentration of the solution

compare this value with the average value of the rate constant (kaver.) calculated by the equation (32).

12. Calculate the relative error in the determination of the constants from

the equation k t 2 Rs k t Rs

Resistance is measured with an accuracy of 1%, t = 1 min.

Questions

1.What kind of processes is called heterogeneous?

2.From what stages comprise heterogeneous reactions?

3.What is a limiting stage?

4.What is the difference between reactions occurring in the diffusion and kinetic areas?

5.What is the diffusion process?

6.What is the First Fick 's law?

7.Which conditions hold the Second Fick's law?

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8.What is the steady-state diffusion?

9.Write Shchukarev`s equation.

10.What is the diffusion layer?

11.How changes the character of diffusion with stirring?

12.How is it possible to determine experimentally the rate of diffusion?

13.Which procedure should be expected for reactions in the diffusion limitations?

14.How affects the temperature on the diffusion processes?

15.What factors effect on the rate of dissolution of solids?

Lab 16

Kinetics and catalysis of hydrogen peroxide decomposition

Purpose. In this lab you will study a rate of the hydrogen peroxide decomposition at the presence of catalyst.

Background. Hydrogen peroxide in aqueous solution spontaneously decomposes slowly according to the equation

In the presence of cations and anions of certain organic compounds, as well as a number of solid substances (glass, metals, carbon, salts, metal oxides) hydrogen peroxide decomposition is greatly accelerated. Depending on the catalyst taken for the reaction can be homogeneous or heterogeneous catalytic reaction.

Measurement of the rate of hydrogen peroxide decomposition is based on determination of the amount of oxygen liberated in the reaction. It is necessary to take into account that the total volume of oxygen evolved during the reaction (V∞) corresponds to the amount of hydrogen peroxide having at the beginning of the reaction (c0), while the difference between the total volume of evolved oxygen and its volume at the moment (V∞–Vt) corresponds to the amount of hydrogen peroxide (c) that is still undecomposed at this moment of time t. In order to calculate the rate constants of the first order reaction we replace the concentration ratio c0/c in the eq.(6) by the proportional values of V∞ and (V∞ – Vt) and obtain

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The V∞ value (volume of overall the oxygen released during the decomposition) can be found by determination of the hydrogen peroxide concentration in the initial solution using titration method or gasometric method by fully decomposing of hydrogen peroxide. The choice of method is carried out as directed by the teacher.

In this lab, the process of decomposition of the Н2О2 with given concentration are studied in the presence of activated carbon or other solid catalyst. For this purpose we use gasometric method which allows to control with sufficient accuracy the reaction rate of hydrogen peroxide decomposition. Amount of the Н2О2 decomposed at a given moment is proportional to the volume of the evolved oxygen. The equipment setup for measurements of the oxygen volume is shown in Fig. 5. The equipment consists of a reaction vessel (1), a gas burette (2) with a valve (3), and the equalizing vessel (4).

Certain parts of the equipment are interconnected by rubber tubes. Burette and the equalizing vessel are filled with water. The volume of oxygen is determined by the volume of water displaced from the burette into the equalizing vessel at equal liquid levels in both of them. Equal levels are achieved by moving the vessel (4) vertically that provides equal pressure from atmospheric within the system.

Figure 5. The experimental setup for the study of the catalytic decomposition of hydrogen peroxide.

Procedure.

1. Prepare a sample of the hydrogen peroxide solution by diluting (as directed by the teacher) of 1-3 mL concentrated hydrogen peroxide solution (perhydrol) with water in a volumetric flask to 50 mL and mix it thoroughly.

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