Kinetics of heterogeneous catalytic reactions. Laboratory training guidance

UDK 66.061.1.012.7

BBK 35.115

Contributors: Radik R. Shamilov, Docent

Azat V. Bilalov, Professor

Ramzya I. Yusupova, Docent

Yuriy G. Galyametdinov, Professor

Kinetics of heterogeneous catalytic reactions : laboratory training guidance / R. R. Shamilov [et al.]; The Ministry of education and science of the Russian Federation, Kazan National Research Technological University. – Kazan : KNRTUPublishing house, 2016. – 28 p.

The basic concepts and laws of chemical kinetics and catalysis are considered. Guidelines for laboratory works namely "A dissolution rate study of hard soluble salt" and "Kinetics and catalysis of hydrogen peroxide decomposition" are presented. The guidelines are designed for full-time training bachelors and Ms.-students of technological specialties studying the disciplines "Physical Chemistry", "Additional chapters of physical chemistry" and "Theoreticaland experimental methods of investigation in chemistry".

The manual is developed at the department of physical and colloid chemistry.

The manual is approved for publication by the decision of the educational methodology commission of the institute of polymers

Reviewers: professor of department of Inorganic Chemistry KNRTU R. R. Nazmutdinov

PhD in chemistry, docent of department of Inorganic Chemistry KNRTU T. T. Zinkicheva

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Kinetics of chemical reactions

Chemical kinetics is a section of physical chemistry devoted to studying of the chemical reaction rates depending on various factors (nature and concentration of reactants, temperature, reaction time, presence of catalysts, the reactant surface value for heterogeneous reactions, the pressure for the gaseous reactants, etc.).

Chemical kinetics determines the kinetic parameters of the most important chemical reactions, the reaction molecularity, the order of reaction, the rate constants, the activation energy, the half-life, etc.

A rate of chemical reaction (υ) is determined as the change in concentration of one of the starting materials or reaction products in the time unit

If the reaction rate is calculated from the concentration change of the starting substances a negative sign in the equation should be chosen, while a plus should be chosen in the case of the reaction products.

Dependence of the chemical reaction rate from the reactant concentrations is determined by following law. The reaction rate is proportional to a multiplication of the reactant concentrations (Ci) taken in some exponents (ni), which are determined experimentally. For example, in the case of reaction

aA + bB → products

the dependence of the reaction rate from the reactant concentrations is described by the equation

which is called the kinetic equation of a chemical reaction; where k is the rate constant of a chemical reaction, CA and CB are concentrations of substances A and B, respectively, n1 is the reaction order at substance A and n2 is the reaction order at substance B.

Reaction rate constant is numerically equal to the reaction rate at reactants concentrations equal to unity. The rate constant as well as the reaction rate is dependent from the nature of the reactants, temperature,

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presence of a catalyst, but does not depend on the concentration and reaction time.

The partial reaction order (ni) is determined by the exponent at the concentration in the kinetic equation of reaction. The total reaction order (n) is equal to a sum of the exponents at the reactant concentrations (sum of the partial orders), e.g. for the above shown reaction

In the general case n = 0, 1, 2, 3, but may be a fractional number also. Only in the case of simple elementary reactions the partial order value coincides with the stoichiometric coefficient in the reaction equation, i.e. n1 = a and n2 = b.

To determine the order of reaction it is necessary to exam the concentration change of reactants (or reactant) with time.

If the chemical reaction rate depends upon the concentration of only one component, for experimental data processing often use the chemical reaction rate equation for a first order reaction (A products)

where k is the rate constant of a first order reaction, СA is concentration of substance A at the time t.

Integration of the equality (4) leads to the equation

where х is concentration of unreacted substance at time t.

The rate constant of a first order reaction has dimension of (time)-1.

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Constancy of the k values calculated at different times is a proof for a first order of the investigated reaction. This method of the reaction order determination is called the substitution method.

The order of reaction can be also defined graphically.

The equation (5) converted into a linear form looks as follows

On the base of experimental data using equation (7) the dependence of lnC as function from t is plotted (Fig. 1). A straight line indicates that the reaction is a first order reaction.

Figure 1. The logarithm of the concentration versus time for first order reactions.

Besides the reaction rate constant a half-life (t1/2) is a useful characteristic of the reaction rate. A half-life is a time interval during which a half of the initial substance quantity was reacted.

The half-life of first-order reactions may be determined using the equation

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As seen, the half-life for first order reactions is not dependent from the initial concentration of the starting substance.

In order to determine the half-life by the graphical method it is necessary to construct the C=f(t) dependence. The time value corresponding to a half of the whole concentration is the half-life (Fig. 2).

Figure 2. Graphical determination of the half-life.

The half-life can be found also from the first graph (Fig. 1). The time which corresponds to the ln(C0/2) is the half-life.

Effect of temperature on the rate of chemical reactions

As the temperature increases the rate of most reactions increase. Van't Hoff rule indicates that the rate constant of the chemical reaction increases in 2-4 times when temperature increases on 10 degrees,

where γ is a temperature coefficient of the chemical reaction rate.

In the common case of temperature increasing from T1 to T2 the constants ratio is equivalent to

Van't Hoff rule is approximation and applicable only in a limited temperature range since the temperature coefficient varies with temperature. For most reactions, a temperature dependence of the rate constant is described by the Arrhenius equation

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This equation contains two parameters that do not depend on the temperature; A is a pre-exponential factor, which is determined only by the type of reaction, Ea is the activation energy of a chemical reaction that characterizes the height of the energy barrier for the reaction.

Pre-exponential factor A has the same dimension as the rate constant. Arrhenius equation (12) in differential form can be written as

The activation energy of a chemical reaction can be calculated from the rate constants at two different temperatures. We write the equation (13) for temperatures T1 and T2, and subtract the first equation from the second:

The equation for the activation energy of the chemical reaction is as follows:

If the data about the rate constant values are not known, then a rate constant in the Arrhenius equation may be substituted by other associated parameters. For example, the initial reaction rate at different temperatures, or the time at which the reaction yield will have a predetermined value at different temperatures.

The activation energy (Ea) in the Arrhenius equation is the minimum energy that must have reacting molecules to their clash led to a reaction. Thus, during transition from the initial to the final state system must overcome kind of an energy barrier (Fig. 3).

The activation energies in the Arrhenius equations for the forward and reverse reactions are connected with each other through the change in internal energy for the overall reaction.

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Diffusion is important in heterogeneous processes since it occurs due to the change in concentration in the interface layer, which affects the kinetics of the process. Diffusion is described by Fick's laws.

The First Fick's law states that the mass of the substance dm, transported by diffusion in the x direction through the area perpendicular to this direction, is proportional to the value of this area S, time dt and the

concentration gradient dc along the chosen direction:

where D is a diffusion coefficient, υdiff = dm/dt is a diffusion rate. The minus sign in equation (16) indicates that the diffusion process is directed toward reducing of the concentration.

The diffusion coefficient depends from temperature. However, the activation energy of the diffusion process is significantly less than the activation energy of most chemical reactions. Therefore, the temperature has less influence on the rate of diffusion processes than on the chemical process rate.

The Second Fick's law states the time dependence of the concentration in the volume of one of the contacted phases:

At steady-state diffusion the concentration varies only with the distance x, and is independent from time. In this case, the dc/dt = 0 and equation (17) yields dc/dx = a = const, after the integration

where с0 corresponds to the coordinate х = 0.

Thus, at steady-state diffusion the concentration changes linearly in the direction of diffusion and a concentration gradient may be written using finite values,

where δ is a finite value of the x.

Substituting this equation in (16), we obtain steady-state diffusion equation,

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where β is so called a mass transfer coefficient.

Consider that the heterogeneous chemical reaction is a first order reaction and proceeds steadily. Suppose that only two successive stages (a chemical reaction and a diffusion process) can be identified in the total process. Since the process is stationary there is no accumulation of the raw materials or reaction products at the interface, and the rates of both stages are the same, kc = β(с0 – с). Hence, we find the concentration of the

substance at the interface between phases с βс0 , and insert into an k β

equation of the first order reaction rate:

where 1/β is the diffusion resistance, 1/k is the chemical resistance.

When k >> β the heterogeneous reaction rate is equivalent to βc0 and it is determined only by the β value characterizing diffusion. The process occurs in the diffusion region. Otherwise β >> k, υ = kc0 and the overall process is determined by the chemical stage and proceeds in the kinetic region. In other cases the rate of the overall process depends from the rates of the both considered stages.

Dissolution of solids in liquids

A. N. Shchukarev experimentally established the following equation for dissolution rate of a solid in a liquid

where S is the contact surface area between the solid body and a liquid, c is concentration of solute in the bulk of liquid, csat is concentration of the saturated solution, k is a coefficient that depends on the temperature, the nature of the bodies and the dissolution conditions.

In accordance with this equation, the greater the contact surface area between the phases and the concentration difference between reached in the given time and maximum possible values of the concentrations, the greater the rate of dissolution.

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