Thermal effect of a chemical reaction. Thermochemical equations

here and below indexes i refer to the starting substances or reagents, and the indices j- to the final substances or products of the reaction; and are the stoichiometric coefficients in the reaction equation for the starting materials and reaction products, respectively.

Example: Let us calculate the thermal effect of the methanol synthesis reaction under standard conditions.

Decision: For calculations, we will use the reference data on the standard heats of formation of the substances involved in the reaction (see Table 44 on page 72 of the reference book).

The thermal effect of the methanol synthesis reaction under standard conditions, according to the first consequence of the Hess law (equation 1.15), is:

When calculating the thermal effects of a chemical reaction, it must be taken into account that the thermal effect depends on the state of aggregation of the reactants and on the type of recording of the chemical equation of the reaction:

According to the second corollary of Hess's law, the thermal effect can be calculated using the heats of combustion ∆ c H, as the difference between the sums of heats of combustion of the initial substances and reaction products (taking into account stoichiometric coefficients):

where ∆ r C p- characterizes the change in the isobaric heat capacity of the system as a result of a chemical reaction and is called temperature coefficient thermal effect of the reaction.

It follows from the Kirchhoff differential equation that the dependence of the thermal effect on temperature is determined by the sign Δ r C p, i.e. depends on which is greater, the total heat capacity of the starting materials or the total heat capacity of the reaction products. Let's analyze differential equation Kirchhoff.

1. If the temperature coefficient Δ r C p> 0, then the derivative > 0 and function increasing. Therefore, the thermal effect of the reaction increases with increasing temperature.

2. If the temperature coefficient Δ r C p< 0, то производная < 0 и функция decreasing. Therefore, the thermal effect of the reaction decreases with increasing temperature.

3. If the temperature coefficient Δ r C p= 0, then the derivative = 0 and . Therefore, the thermal effect of the reaction does not depend on temperature. This case does not occur in practice.

Differential equations are convenient for analysis, but inconvenient for calculations. To obtain an equation for calculating the heat effect of a chemical reaction, we integrate the Kirchhoff differential equation by dividing the variables:

The heat capacities of substances depend on temperature, therefore, and . However, in the range of temperatures commonly used in chemical-technological processes, this dependence is not significant. For practical purposes, the average heat capacities of substances are used in the temperature range from 298 K to a given temperature. given in the reference books. Thermal effect temperature coefficient calculated using average heat capacities:

Example: Let us calculate the heat effect of the methanol synthesis reaction at a temperature of 1000 K and standard pressure.

Decision: For calculations, we will use the reference data on the average heat capacities of the substances involved in the reaction in the temperature range from 298 K to 1000 K (see Table 40 on page 56 of the reference book):

Change in the average heat capacity of the system as a result of a chemical reaction:

Second law of thermodynamics

One of the most important tasks of chemical thermodynamics is to elucidate the fundamental possibility (or impossibility) of a spontaneous chemical reaction proceeding in the direction under consideration. In those cases when it becomes clear that this chemical interaction can occur, it is necessary to determine the degree of conversion of the starting materials and the yield of reaction products, that is, the completeness of the reaction

The direction of the spontaneous process can be determined on the basis of the second law or the beginning of thermodynamics, formulated, for example, in the form of the Clausius postulate:

Heat by itself cannot pass from a cold body to a hot one, that is, such a process is impossible, the only result of which would be the transfer of heat from a body with a lower temperature to a body with a higher temperature.

Many formulations of the second law of thermodynamics have been proposed. Thomson-Planck formulation:

A perpetual motion machine of the second kind is impossible, i.e., such a periodically operating machine is impossible that would allow work to be obtained only by cooling the heat source.

The mathematical formulation of the second law of thermodynamics arose in the analysis of the operation of heat engines in the works of N. Carnot and R. Clausius.

Clausius introduced the state function S, called entropy, the change of which is equal to the heat of the reversible process, referred to the temperature

For any process

(1.22)

The resulting expression is a mathematical expression of the second law of thermodynamics.

THERMAL EFFECT, heat released or absorbed thermodynamic. system during the flow of chemical in it. districts. It is determined under the condition that the system does no work (except possible work extensions), and m-ry and products are equal. Since heat is not a state function, i.e. during the transition between states depends on the transition path, then in the general case the thermal effect cannot serve as a characteristic of a particular district. In two cases, an infinitesimal amount of heat (elemental heat) d Q coincides with full differential state functions: at a constant volume d Q = dU (U-internal energy of the system), and at a constant d Q = dH (H-enthalpy of the system).

Two types of thermal effects are practically important - isothermal isobaric (at constant t-re T and p) and isothermal isochoric (at constant T and volume V). There are differential and integral thermal effects. The differential thermal effect is determined by the expressions:

where u i , h i -acc. partial molar ext. energy and ; v i -stoichiometric. coefficient (v i > 0 for products, v i<0 для ); x = (n i - n i 0)/v i ,-хим. переменная, определяющая состав системы в любой момент протекания р-ции (n i и n i0 - числа i-го компонента в данный момент времени и в начале хим. превращения соотв.). Размерность дифференциального теплового эффекта реакции-кДж/ . Если u T,V , h T,p >0, district called. endothermic, with the opposite sign of the effect, exothermic. The two types of effects are related by the relationship:

The temperature dependence of the thermal effect is given, the application of which, strictly speaking, requires knowledge of the partial molar of all involved in r-tion in-in, but in most cases these quantities are unknown. Since for districts flowing in real solutions and other thermodynamically non-ideal media, thermal effects, like others, depend significantly on the composition of the system and experiment. conditions, an approach has been developed that facilitates the comparison of different districts and the systematics of thermal effects. This purpose is served by the concept of the standard thermal effect (denoted). The standard is understood as the thermal effect, carried out (often hyprthetically) under conditions when all the islands participating in the district are in the given ones. Differential and integral standard thermal effects are always numerically the same. The standard thermal effect is easily calculated using tables of standard heats of formation or heats of combustion in-in(see below). For non-ideal media, there is a large discrepancy between the actually measured and standard thermal effects, which must be kept in mind when using thermal effects in thermodynamic calculations. For example, for alkaline diacetimide [(CH 3 CO) 2 NH (tv) + H 2 O (l) \u003d \u003d CH 3 SOCH 2 (tv) + CH 3 COOH (l) +] in 0.8 n. solution of NaOH in water (58% by mass) at 298 K, the measured thermal effect D H 1 \u003d - 52.3 kJ / . For the same district, under standard conditions, = - 18.11 kJ / was obtained. It means so much. the difference is explained by the thermal effects accompanying the in-in in the indicated p-solvent (heats). For solid, liquid acetic acid and heat are equal respectively: D H 2 = 13.60; D H 3 = - 48.62; D H 4 \u003d - 0.83 kJ / so \u003d D H 1 - D H 2 - D H 3 + D H 4. From the example viewbut that in the study of thermal effects, it is important to measure the thermal effects of concomitant physical. processes.

The study of thermal effects is the most important task. Main experimental method is calorimetry. Modern The equipment makes it possible to study thermal effects in the gas, liquid and solid phases, at the phase boundary, as well as in complex ones. systems. The range of typical measured thermal effects ranges from hundreds of J/ to hundreds of kJ/. In table. calorimetric data are given. measurements of thermal effects of certain districts. Measurement of thermal effects, dilution, and heats allows you to go from actually measured thermal effects to standard ones.

An important role belongs to the thermal effects of two types - the heats of formation Comm. from simple in-in and calorific values ​​of in-in pure with the formation of higher elements, of which is in-in. These thermal effects are reduced to standard conditions and tabulated. With their help it is easy to calculate any thermal effect; it is equal to the algebraic the sum of the heats of formation or heats of combustion of all participating in the district in-in:

Application of tabular values allowscalculate thermal effects pl. thousand districts, although these values ​​themselves are known only for a few. thousand connections. This calculation method is unsuitable, however, for districts with small thermal effects, since the calculated small value obtained as an algebraic. sum of several large values, is characterized by an error, edges in abs. may exceed the thermal effect. Calculation of thermal effects using quantities is based on the fact that there is a state function. This makes it possible to compose thermochemical systems. ur-tions to determine the thermal effect of the required p-tion (see). Calculate almost always the standard thermal effects. In addition to the method discussed above, the calculation of thermal effects is carried out according to the temperature dependence of the equation

7. Calculate the thermal effect of the reaction under standard conditions: Fe 2 O 3 (t) + 3 CO (g) \u003d 2 Fe (t) + 3 CO 2 (g), if the heat of formation: Fe 2 O 3 (t) \u003d - 821.3 kJ / mol; CO (g ) = – 110.5 kJ/mol;

CO 2 (g) \u003d - 393.5 kJ / mol.

Fe 2 O 3 (t) + 3 CO (g) \u003d 2 Fe (t) + 3 CO 2 (g),

Knowing the standard thermal effects of combustion of the initial substances and reaction products, we calculate the thermal effect of the reaction under standard conditions:

16. Dependence of the rate of a chemical reaction on temperature. Van't Hoff's rule. Temperature coefficient of reaction.

Only collisions between active molecules lead to reactions, the average energy of which exceeds the average energy of the participants in the reaction.

When a certain activation energy E is communicated to molecules (excess energy above the average), the potential energy of interaction of atoms in molecules decreases, bonds within molecules weaken, molecules become reactive.

The activation energy is not necessarily supplied from the outside; it can be imparted to some part of the molecules by redistributing the energy during their collisions. According to Boltzmann, among N molecules there is the following number of active molecules N   with increased energy  :

N N e – E / RT

where E is the activation energy, showing the necessary excess of energy compared to the average level that molecules must have in order for the reaction to become possible; the rest of the designations are well known.

During thermal activation for two temperatures T 1 and T 2 the ratio of the rate constants will be:

which allows you to determine the activation energy by measuring the reaction rate at two different temperatures T 1 and T 2 .

An increase in temperature by 10 0 increases the reaction rate by 2–4 times (approximate van't Hoff rule). The number showing how many times the reaction rate (and hence the rate constant) increases with an increase in temperature by 10 0 is called the temperature coefficient of the reaction:

This means, for example, that with an increase in temperature by 100 0 for a conditionally accepted increase average speed 2 times ( = 2) the reaction rate increases by 2 10 , i.e. approximately 1000 times, and when  = 4 - 4 10 , i.e. 1000000 times. The van't Hoff rule is applicable to reactions occurring at relatively low temperatures in a narrow range. The sharp increase in the reaction rate with increasing temperature is explained by the fact that the number of active molecules increases exponentially.

25. Van't Hoff chemical reaction isotherm equation.

In accordance with the law of mass action for an arbitrary reaction

and A + bB = cC + dD

The equation for the rate of a direct reaction can be written:

and for the rate of the reverse reaction:

As the reaction proceeds from left to right, the concentrations of substances A and B will decrease and the rate of the forward reaction will decrease. On the other hand, as reaction products C and D accumulate, the reaction rate will increase from right to left. There comes a moment when the speeds υ 1 and υ 2 become the same, the concentrations of all substances remain unchanged, therefore,

Where K c = k 1 / k 2 =

The constant value K c, equal to the ratio of the rate constants of the forward and reverse reactions, quantitatively describes the state of equilibrium through the equilibrium concentrations of the starting substances and the products of their interaction (in terms of their stoichiometric coefficients) and is called the equilibrium constant. The equilibrium constant is constant only for a given temperature, i.e.

K c \u003d f (T). The equilibrium constant of a chemical reaction is usually expressed as a ratio, the numerator of which is the product of the equilibrium molar concentrations of the reaction products, and the denominator is the product of the concentrations of the starting substances.

If the reaction components are a mixture of ideal gases, then the equilibrium constant (K p) is expressed in terms of the partial pressures of the components:

For the transition from K p to K with we use the equation of state P · V = n · R · T. Insofar as

It follows from the equation that K p = K s, provided that the reaction proceeds without changing the number of moles in the gas phase, i.e. when (c + d) = (a + b).

If the reaction proceeds spontaneously at constant P and T or V and T, then the valuesG and F of this reaction can be obtained from the equations:

where C A, C B, C C, C D are the nonequilibrium concentrations of the initial substances and reaction products.

where P A, P B, P C, P D are the partial pressures of the initial substances and reaction products.

The last two equations are called the van't Hoff chemical reaction isotherm equations. This relation makes it possible to calculate the values ​​of G and F of the reaction, to determine its direction at different concentrations of the initial substances.

It should be noted that both for gas systems and for solutions, with the participation of solids in the reaction (i.e. for heterogeneous systems), the concentration of the solid phase is not included in the expression for the equilibrium constant, since this concentration is practically constant. So for the reaction

2 CO (g) \u003d CO 2 (g) + C (t)

the equilibrium constant is written as

The dependence of the equilibrium constant on temperature (for temperature T 2 relative to temperature T 1) is expressed by the following van't Hoff equation:

where Н 0 is the thermal effect of the reaction.

For an endothermic reaction (the reaction proceeds with the absorption of heat), the equilibrium constant increases with increasing temperature, the system, as it were, resists heating.

34. Osmosis, osmotic pressure. Van't Hoff equation and osmotic coefficient.

Osmosis is the spontaneous movement of solvent molecules through a semipermeable membrane that separates solutions of different concentrations from a solution of a lower concentration to a solution of a higher concentration, which leads to the dilution of the latter. As a semi-permeable membrane, through small holes of which only small solvent molecules can selectively pass and large or solvated molecules or ions are retained, a cellophane film is often used - for high molecular weight substances, and for low molecular weight - a copper ferrocyanide film. The process of solvent transfer (osmosis) can be prevented if an external hydrostatic pressure is applied to a solution with a higher concentration (under equilibrium conditions this will be the so-called osmotic pressure, denoted by the letter ). To calculate the value of  in solutions of non-electrolytes, the empirical Van't Hoff equation is used:

where C is the molar concentration of the substance, mol/kg;

R is the universal gas constant, J/mol K.

The value of osmotic pressure is proportional to the number of molecules (in the general case, the number of particles) of one or more substances dissolved in a given volume of solution, and does not depend on their nature and the nature of the solvent. In solutions of strong or weak electrolytes, the total number of individual particles increases due to the dissociation of molecules; therefore, it is necessary to introduce the appropriate proportionality coefficient, called the isotonic coefficient, into the equation for calculating the osmotic pressure.

i C R T,

where i is the isotonic coefficient, calculated as the ratio of the sum of the numbers of ions and undissociated electrolyte molecules to the initial number of molecules of this substance.

So, if the degree of electrolyte dissociation, i.e. the ratio of the number of molecules decomposed into ions to total number solute molecules is equal to  and the electrolyte molecule decomposes into n ions, then the isotonic coefficient is calculated as follows:

i = 1 + (n – 1) ,(i > 1).

For strong electrolytes, you can take  = 1, then i = n, and the coefficient i (also greater than 1) is called the osmotic coefficient.

The phenomenon of osmosis is great importance for plant and animal organisms, since the membranes of their cells in relation to solutions of many substances have the properties of a semipermeable membrane. AT clean water the cell swells strongly, in some cases up to the rupture of the membrane, and in solutions with a high salt concentration, on the contrary, it decreases in size and shrinks due to a large loss of water. Therefore, when preserving food products added to them a large number of salt or sugar. Cells of microorganisms in such conditions lose a significant amount of water and die.

The heat of reaction (heat effect of the reaction) is the amount of heat released or absorbed Q. If heat is released during the reaction, such a reaction is called exothermic, if heat is absorbed, the reaction is called endothermic.

The heat of reaction is determined based on the first law (beginning) of thermodynamics, whose mathematical expression in its simplest form for chemical reactions is the equation:

Q = ΔU + рΔV (2.1)

where Q is the heat of reaction, ΔU is the change in internal energy, p is the pressure, ΔV is the change in volume.

Thermochemical calculation consists in determining the thermal effect of the reaction. In accordance with equation (2.1), the numerical value of the heat of reaction depends on the method of its implementation. In an isochoric process carried out at V=const, the heat of reaction Q V =Δ U, in isobaric process at p=const thermal effect Q P =Δ H. Thus, the thermochemical calculation is in determining the amount of change in either internal energy or enthalpy during a reaction. Since the vast majority of reactions proceed under isobaric conditions (for example, these are all reactions in open vessels that occur at atmospheric pressure), when bringing thermochemical calculations, ΔН is almost always calculated . If aΔ H<0, то реакция экзотермическая, если же Δ H>0, then the reaction is endothermic.

Thermochemical calculations are made using either Hess's law, according to which the thermal effect of a process does not depend on its path, but is determined only by the nature and state of the initial substances and products of the process, or, most often, a consequence of Hess's law: the thermal effect of a reaction is equal to the sum heats (enthalpies) of formation of products minus the sum of heats (enthalpies) of formation of reactants.

In calculations according to the Hess law, the equations of auxiliary reactions are used, the thermal effects of which are known. The essence of operations in calculations according to the Hess law is that the equations of auxiliary reactions produce such algebraic actions, which lead to a reaction equation with an unknown thermal effect.

Example 2.1. Determination of the heat of reaction: 2CO + O 2 \u003d 2CO 2 ΔH - ?

We use the reactions as auxiliary: 1) C + O 2 \u003d C0 2;Δ H 1 = -393.51 kJ and 2) 2C + O 2 = 2CO;Δ H 2 \u003d -220.1 kJ, whereΔ N/iΔ H 2 - thermal effects of auxiliary reactions. Using the equations of these reactions, it is possible to obtain the equation for a given reaction if the auxiliary equation 1) is multiplied by two and equation 2) is subtracted from the result. Therefore, the unknown heat of a given reaction is:

Δ H = 2Δ H1-Δ H 2 \u003d 2 (-393.51) - (-220.1) \u003d -566.92 kJ.

If a consequence of the Hess law is used in the thermochemical calculation, then for the reaction expressed by the equation aA+bB=cC+dD, the relation is used:

ΔН =(сΔНоbr,с + dΔHobr D) - (аΔНоbr A + bΔН arr,c) (2.2)

where ΔН is the heat of reaction; ΔH o br - heat (enthalpy) of formation, respectively, of the reaction products C and D and reagents A and B; c, d, a, b - stoichiometric coefficients.

The heat (enthalpy) of formation of a compound is the heat effect of a reaction during which 1 mole of this compound is formed from simple substances, which are in thermodynamically stable phases and modifications 1*. for example , the heat of formation of water in the vapor state is equal to half the heat of reaction, expressed by the equation: 2H 2 (g)+ About 2 (g)= 2H 2 O(g).The unit of heat of formation is kJ/mol.

AT thermochemical calculations reaction heats are usually determined for standard conditions, for which formula (2.2) takes the form:

ΔН°298 = (сΔН° 298, arr, С + dΔH° 298, o 6 p, D) - (аΔН° 298, arr A + bΔН° 298, arr, c)(2.3)

where ΔН° 298 is the standard heat of reaction in kJ (the standard value is indicated by the superscript "0") at a temperature of 298K, and ΔН° 298,rev are the standard heats (enthalpies) of formation also at a temperature of 298K. ΔH° values ​​298 rev.are defined for all connections and are tabular data. 2 * - see application table.

Example 2.2. Calculation of standard heat p e shares expressed by the equation:

4NH 3 (r) + 5O 2 (g) \u003d 4NO (g) + 6H 2 O (g).

According to the corollary of Hess's law, we write 3*:

Δ H 0 298 = (4Δ H 0 298. o b p . No+6∆H0 298. code N20) - 4∆H0 298 arr. NH h. Substituting the tabular values ​​of the standard heats of formation of the compounds presented in the equation, we get:Δ H °298= (4(90.37) + 6(-241.84)) - 4(-46.19) = - 904.8 kJ.

negative sign the heat of reaction indicates the exothermicity of the process.

In thermochemistry, it is customary to indicate thermal effects in reaction equations. Such equations with a designated thermal effect are called thermochemical. For example, the thermochemical equation of the reaction considered in example 2.2 is written:

4NH 3 (g) + 50 2 (g) \u003d 4NO (g) + 6H 2 0 (g);Δ H° 29 8 = - 904.8 kJ.

If the conditions differ from the standard ones, in practical thermochemical calculations it allows Xia approximation use:Δ H ≈Δ N° 298 (2.4) Expression (2.4) reflects the weak dependence of the heat of reaction on the conditions of its occurrence.

Any chemical reaction is accompanied by the release or absorption of energy in the form of heat.

On the basis of the release or absorption of heat, they distinguish exothermic and endothermic reactions.

exothermic reactions - such reactions during which heat is released (+ Q).

Endothermic reactions - reactions during which heat is absorbed (-Q).

The thermal effect of the reaction (Q) is the amount of heat that is released or absorbed during the interaction of a certain amount of initial reagents.

A thermochemical equation is an equation in which the heat effect of a chemical reaction is indicated. For example, thermochemical equations are:

It should also be noted that thermochemical equations must necessarily include information about the aggregate states of reactants and products, since the value of the thermal effect depends on this.

Reaction Heat Calculations

An example of a typical problem for finding the heat effect of a reaction:

When interacting 45 g of glucose with an excess of oxygen in accordance with the equation

C 6 H 12 O 6 (solid) + 6O 2 (g) \u003d 6CO 2 (g) + 6H 2 O (g) + Q

700 kJ of heat were released. Determine the thermal effect of the reaction. (Write down the number to the nearest integer.)

Decision:

Calculate the amount of glucose substance:

n (C 6 H 12 O 6) \u003d m (C 6 H 12 O 6) / M (C 6 H 12 O 6) \u003d 45 g / 180 g / mol \u003d 0.25 mol

Those. the interaction of 0.25 mol of glucose with oxygen releases 700 kJ of heat. From the thermochemical equation presented in the condition, it follows that when 1 mol of glucose interacts with oxygen, an amount of heat equal to Q (the heat of the reaction) is formed. Then the following proportion is true:

0.25 mol glucose - 700 kJ

1 mol of glucose - Q

From this proportion follows the corresponding equation:

0.25 / 1 = 700 / Q

Solving which, we find that:

Thus, the thermal effect of the reaction is 2800 kJ.

Calculations according to thermochemical equations

Much more often in USE assignments in thermochemistry, the value of the thermal effect is already known, because the complete thermochemical equation is given in the condition.

In this case, it is required to calculate either the amount of heat released / absorbed with a known amount of the reactant or product, or, conversely, the known value of heat is required to determine the mass, volume or amount of a substance of any involved in the reaction.

Example 1

In accordance with the thermochemical reaction equation

3Fe 3 O 4 (solid) + 8Al (solid) \u003d 9Fe (solid) + 4Al 2 O 3 (solid) + 3330 kJ

formed 68 g of aluminum oxide. How much heat is released in this case? (Write down the number to the nearest integer.)

Decision

Calculate the amount of aluminum oxide substance:

n (Al 2 O 3) \u003d m (Al 2 O 3) / M (Al 2 O 3) \u003d 68 g / 102 g / mol \u003d 0.667 mol

In accordance with the thermochemical equation of the reaction, 3330 kJ are released during the formation of 4 mol of aluminum oxide. In our case, 0.6667 mol of aluminum oxide is formed. Denoting the amount of heat released in this case, through x kJ we will make up the proportion:

4 mol Al 2 O 3 - 3330 kJ

0.667 mol Al 2 O 3 - x kJ

This proportion corresponds to the equation:

4 / 0.6667 = 3330 / x

Solving which, we find that x = 555 kJ

Those. in the formation of 68 g of aluminum oxide, in accordance with the thermochemical equation, 555 kJ of heat is released under the condition.

Example 2

As a result of the reaction, the thermochemical equation of which

4FeS 2 (solid) + 11O 2 (g) \u003d 8SO 2 (g) + 2Fe 2 O 3 (solid) + 3310 kJ

1655 kJ of heat were released. Determine the volume (l) of sulfur dioxide released (n.o.s.). (Write down the number to the nearest integer.)

Decision

In accordance with the thermochemical reaction equation, the formation of 8 mol of SO 2 releases 3310 kJ of heat. In our case, 1655 kJ of heat was released. Let the amount of substance SO 2 formed in this case be equal to x mol. Then the following proportion is valid:

8 mol SO 2 - 3310 kJ

x mol SO 2 - 1655 kJ

From which follows the equation:

8 / x = 3310 / 1655

Solving which, we find that:

Thus, the amount of substance SO 2 formed in this case is 4 mol. Therefore, its volume is:

V (SO 2) \u003d V m ∙ n (SO 2) \u003d 22.4 l / mol ∙ 4 mol \u003d 89.6 l ≈ 90 l(round up to integers, because this is required in the condition.)

More analyzed problems on the thermal effect of a chemical reaction can be found.