Energy changes in chemical reactions


Химия и фармакология

The energy of system is the sum of ll individul kinetic nd potentil energies of the prticles present in the system. Het is the term used to describe the process of energy trnsfer to or from the system. Temperture is mesure of the verge kinetic energy of the prticles in the system; temperture difference then gives n indiction of the direction of het flow.



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Energy changes in chemical reactions

General definitions

One of the important characteristic of a chemical changes is that energy exchange takes place between the reacting system and its surroundings. The exchange can either be to or from the system. Thus, chemical reactions usually involve the absorption or release of heat.

The energy of a system is the sum of all individual kinetic and potential energies of the particles present in the system.

Heat is the term used to describe the process of energy transfer to or from the system.

Temperature is a measure of the average kinetic energy of the particles in the system; a temperature difference then gives an indication of the direction of heat flow.

The energy available from a chemical reaction is a chemical potential energy.

So, reactions proceeding with the liberation of energy are called exothermic, and reactions in which energy is absorbed are called endothermic one .

Let we introduce the others important notions such as system,  surroundings and phase. A system in chemistry is defined as the substance or combination of substances being considered. The surroundings—the substances surrounding the system, are opposed to a system. A system is usually separated physically from its surroundings. By a phase is meant a part of a system separated from its other parts by an interface upon passing through which the properties change in a jump.


The branch of chemistry devoted to a quantitative study of the heat effects of reactions is called thermochemistry. The results of thermochemical measurements—the heat effects of reactions—are customarily related to one mole of the substance formed.

The amount of heat liberated in the formation of one mole of a compound from simple substances is called the heat of formation of the given compound.

Heat effects can be included in the equations of reactions.

Chemical equations in which the amount of liberated or absorbed heat is indicated are known as thermochemical equations. The value of the heat effect is usually indicated in the right-hand side of an equation with a plus sign for an exothermic reaction and a minus sign for an endothermic one.

For instance, the expression "the heat of formation of water is 285,8 kJ/mol" signifies .that 285.8 kJ are liberated in the formation of 18 g of liquid water from 2 g of hydrogen and 16 g of oxygen.

If an element can exist in the form of several simple substances, then the heats of formation of the most stable simple substances in the given conditions are taken equal to zero. The heats of formation of the less stable simple substances are thus taken equal to the heats of their formation from the stable ones.

A very important characteristic of substances used as fuel is their heat of combustion. This quantity is also customarily related to one mole of the substance. For example,

The magnitude of the heat effect depends on the nature of the reactants (initial substances) and the reaction, products, their state of aggregation, and temperature.

The crystalline state is indicated by the symbol (c) next to the formula of the relevant substance, the liquid state by the symbol (lq), and the gaseous state by (g). It is obvious that the difference between at 25 °C related to one mole (18 g).the heat of formation of liquid water (285.8 kJ/mol) and of water vapour (241.8 kJ/mol) is the heat of vaporization of water

Thermochemical Calculations

The fundamental principle on which all thermochemical was established in 1840 by the Russian chemist, G. Hess. This principle is a particular case of the law of energy conservation and is known as Hess's law or principle of additivity of reaction heats:

The heat effect of a reaction depends only on the initial and the final state of substances and does not depend on the intermediate stages of the process.

Like the conventional equations of chemical reactions, thermochemical equations can be summated. Hess's law allows us to calculate the heat effects of reactions when they cannot be measured directly. For example, the oxidation of graphite and diamond can be combined to obtain heat effect for the transformation between these two forms of solid carbon (a reaction that cannot be studied experimentally).

C(graphite) + O2 (g)® CO2 (g) DHo = - 393:51 kJ mol-1 

C(diamond) + O2 (g) ®CO2 (g) DHo = - 395:40 kJ mol-1

Subtraction of the second reaction from the first (i.e., writing the second equation in reverse and adding it to the first one) yields

C(graphite) ® C(diamond) DHo= 1:89 kJ mol-1 

For instance, by combining the heats of combustion of carbon, hydrogen, and methane, we obtain the heat of formation of methane, which cannot be determined directly:

Tables of heats of formation, atomization, and combustion can be found in most textbooks.

Consider the other practically important corollary of Hess's law:

The heat effect of a chemical reaction equals the sum of the heats of formation of the products less the sum of the heats of formation of the reactants.

Both sums are determined with account taken of the number of moles of the substances participating in the reaction in accordance with its equation.


The purpose of thermodynamics is to predict the equilibrium state of a system from the properties of its components. It means that we can say with complete certainty whether or not a given change is possible, and if it is possible, to what extent it will occur.

Factors determining the direction of chemical reaction

The direction of the spontaneous proceeding of chemical reactions is determined by the combined action of two factors: by the tendency of a system to pass over to a state having the lowest internal energy, and by the tendency to achieve the most probable state, i.e. to a state which the maximum disorder in the distribution of particles correspond to. 

Both factors considered above, as well as the result of their combined action, can be expressed quantitatively. The quantities involved are studied in the branch of physics called thermodynamics and are known as thermodynamic quantities. They include, particularly, the internal energy, the enthalpy, the entropy, and the Gibbs energy.

Thermodynamic quantities. Internal energy and enthalpy

The internal energy U of a substance (or system) is the total energy of the particles forming the substance. It consists of the kinetic and potential energies of the particles. The kinetic energy is the energy of transactional, vibration, and rotational motion of the particles; the potential energy is due to the forces of attraction and repulsion acting between the particles.

The internal energy depends on the state of a substance. The change in the internal energy of a system DU in a process can be determined. Assume that as a result of a process, a system passes from the initial state 1 to the final state 2, doing the work W and absorbing the heat Q from the surroundings1 If we designate the difference U2 — U1 by DU, the equation can be written in the form

This equation expresses the law of energy conservation according to which the change in the internal energy is independent of the way of conducting the process and is determined only by the initial and final states of a system. Particularly, if the volume of the system does not change, then

where Qv is the heat absorbed by the system in conditions of a constant volume.

The last equation allows us to determine the change in the internal energy in different processes. For instance, when a substance is heated at constant volume, the change in the internal energy is determined from the heat capacity of this substance:

Here Cv is the molar heat capacity of the substance at constant volume, n is the number of moles of the substance, and DT is the difference between the final and initial temperatures.

For a chemical reaction proceeding without a change in the volume of the system, a change in the internal energy equals the heat effect of the reaction taken with the opposite sign.

The total heat content of a system is called its enthalpy. It can be regarded as the sum of the internal and external energies of the system determined by the relationship

H = U + PV 

The external energy, PV, or the work of expansion, W=pDV2, is a measure of the energy of the system possesses as result of the space it occupies. We have to do with processes occurring at a constant pressure more often in chemistry, however. Here it is convenient to use an enthalpy. At constant pressure and provided that only the work of expansion is performed in the course of a process, we have


comparing the last equation with the equation for the internal energy

we see that in the conditions indicated above


where Qp is the heat absorbed by the system at constant pressure. When a substance is heated, the change in its enthalpy is determined from the heat capacity of this substance at constant pressure

where n is the number of moles of the substance, and Cp is its molar heat capacity at constant pressure.

Upon changes in the state of aggregation of a substance and in allotropic transitions, the change in the enthalpy is equal in magnitude, but opposite in sign, to the heat of the relevant transformation (fusion, boiling, transformation from one modification into another).

Finally, in a chemical reaction, the change in the enthalpy equals the heat effect of the reaction conducted at a constant temperature and constant pressure taken with the opposite sign.

Like the internal energy, the enthalpy is determined by the state of a system and does not depend on how this state was reached.

Thermodynamic quantities. Entropy and Gibbs energy

The number of particles in macroscopic amounts of a substance is colossal. It was found more convenient to characterise the state of a system in this sense not by the probability itself of achieving a given macrostate, but by a quantity proportional to its logarithm. This quantity is called the entropy.

The entropy (S) is related to the number (P) of equally probable microscopic states by means of which the given macroscopic state of a system can be achieved by the equation

S = k log P

where k is a proportionality constant, P is a thermodynamic probability. The entropy has the dimension J/mol×K.

So, according to the tendency to achieve the most probable state entropy of spontaneous processes always grows. The entropy always grows with increasing temperature because the intensity of motion of the particles grows. It also grows when a substance transforms from the liquid state to the gaseous one, figure 1. The entropy also changes when chemical processes occur. These changes are especially great in reactions leading to a change in the number of molecules of gases: an increase in the number of gas molecules For example, ozone (O3) gas can spontaneously decompose into molecular oxygen (O2):

2O3(g) → 3O2(g).

This reaction occurs because the molecular order is diminished, resulting in a higher level of entropy.

All entropies converge to zero as the temperature approaches absolute zero. This principle is the basis of the Third law of thermodynamics, which states that the entropy of a perfect crystal at 0 oK is zero.

Like the internal energy and enthalpy, the entropy depends only on the state of a system.

A process when it is conducted in infinitely small steps from one equilibrium state to another infinitely close to the preceding state is called a thermodynamically reversible, or simply a reversible one.

If a process is also conducted reversibly at a constant temperature (isothermally), the change in entropy is related to the heat absorbed by the equation.

where Qrev is the amount of heat absorbed by the system in an isothermal reversible process, and T is the absolute temperature. The last equation shows that when a certain amount of heat is absorbed, the entropy of a system grows the more, the lower is the temperature at which the heat is absorbed.

Energy disorder. At the atomic and molecular level, all energy is quantized; each particle possesses discrete states of kinetic energy and is able to accept thermal energy only in packets whose values correspond to the energies of one or more of these states.

All natural processes that involve more than a few particles 2 occur in a direction that leads to a more random distribution of matter and energy; that is, they lead to an increase in the entropy of the world. Once initiated, this process will tend to continue until any further change would produce a decrease in disorder, and thus in the entropy. At this point, no further change will occur, and the system will be in its equilibrium state.

In any spontaneous macroscopic change, the entropy of the world increases. If a process is endothermic or exothermic, heat is exchanged with the surroundings, and we have to consider the entropy change of the surroundings as well as that of the system in order to predict what the direction of change will be.

If this is the case, how can we explain the occurrence of processes that seem at first glance to result in a decrease in disorder? Examples are the freezing of a liquid, the formation of a precipitate, and the growth of an organism. It is important to understand that the criterion for spontaneous change is the entropy change of the system and the surroundings that is, of the universe:

DStotal = DSsystem +DSsurroundings

The only way the entropy of the surroundings can be detected is by exchange of heat with the system; if the system absorbs a quantity of heat q, then DSsurroundings = - Qrev /T. Note that it does not matter whether or not the change in the system occurs reversibly or irreversibly. As mentioned previously, it is always possible to define an alternative pathway in which the same amount of heat is exchanged with the surroundings reversibly, yielding the same value of DS.

Failure to take the surroundings into account is what leads to the apparent paradox that freezing of a liquid, compression of a gas, and growth of an organism are all processes in which entropy decreases. It is only the entropy of the system that undergoes a decrease when these processes occur.

As a specific example, let us consider the freezing of water. We know that liquid water will spontaneously change into ice when the temperature drops below 0 oC at 1 atm pressure. Since the water molecules are far more ordered in ice than they are in the liquid, the entropy of the water (the system here) is decreasing. The amount of decrease is found by dividing the heat of fusion of ice by the temperature for the reversible pathway, which occurs at the normal freezing point:

DSsystem =  - = - 21:978 J 1K-1mol-1

If the process actually occurs at 0 ±K , then the heat of fusion is transferred to the surroundings at the same temperature, and the entropy of the surroundings increases by

DS surroundings =   = + 21:978 J 1K-1mol-1

so that DStotal = 0. Under these conditions, the ice and water are in equilibrium, and no net change will occur.

We consider the heat content of a system as the sum of external and internal energies. But there is an alternative way of dividing up the heat content. It can be represented as the sum of the energy that can be converted into external work (free energy) and the energy unavailable for conversion. The “unfree energy” associated with a system heat content can be written as TS, where S is an entropy, T is an absolute temperature.

The Gibbs energy G (other names of this function are the free energy, the isobaric-isothermal potential, the isobaric potential) was introduced for isothermal reactions proceeding at a constant pressure. The sign of the change in this a function in a reaction can be a criterion of the possibility of the reaction proceeding spontaneously.

The Gibbs energy is related to the enthalpy, entropy, and temperature by the equation

G = H - TS

The change in the Gibbs energy in the reaction will be

In the reversible and isothermal conducting of a process, DG is equal in magnitude, but opposite in sign, to the maximum useful work that the system does in the given process:

By useful work is meant all the work done in the course of a process less the work of expansion p DV.

It can be proved that in conditions of a constant temperature and pressure, reactions proceed spontaneously in the direction of diminishing of the Gibbs energy  ( DG < 0).


Only those reactions can proceed spontaneously at the expense of whose energy useful work can be performed.

If DG equal to zero a system is in the state of chemical equilibrium. If    DG > 0 proceeding of a reaction is impossible at a standard conditions. The possibility of proceeding of such reaction depend on the DG value. The positive value nearly 40kJ/mol signifies that reaction is possible owing to, for example change in concentration of reagents, temperature and etc.

It is evident that if proceeding a reaction is impossible in the forward direction the reverse reaction is expected to proceed spontaneously according to the energy conservation law.

For a rough assessment of the direction in which a reaction will proceed at low and at high temperatures, approximate equations of the Gibbs energy of a reaction can be used. For low temperatures in the expression

the second term may be ignored. This yields

For sufficiently high temperatures, we have the opposite relationship:

Ignoring now the first term in the expression of the Gibbs energy, we get

These approximate equations show that for low temperatures the criterion of the direction in which a reaction proceeds simultaneously in a first approximation is the sign of the heat effect of the reaction, and for high temperatures is the sign of the change in the entropy.

This signifies that at low temperatures exothermic reactions can proceed spontaneously, and at high temperatures—reactions attended by an increase in the entropy.

We must add to what has been said above that a negative value of DG for a reaction points only to the possibility of its occurring. Actually, the reaction may not be observed. In these cases, an appropriate catalyst must be found to increase the rate of the reaction.

For the vaporization of water, both DHo and DSo are positive. At higher temperatures, TDSo will eventually overtake DHo, driving DGo negative; all reactions of this kind will therefore become spontaneous at higher temperatures. At 373K, the free energies of liquid water and water vapour at 1 atm partial pressure are identical, thus establishing the normal boiling temperature, Figure 2. 

Standard thermodynamic quantities. Chemico-thermodynamic calculations

The state of a substance in standard conditions is called its standard state. Thermodynamic quantities characterising a substance in its standard state are called standard quantities. Standard quantities and their changes are customarily designated by means of the superscript "°". For instance, the standard change in the enthalpy by DHo, and the standard change in the Gibbs energy by DG°. The temperature 25 °C (298 K) has been adopted as the standard one. The temperature is indicated in the form of a subscript:

The standard change in the Gibbs energy of a reaction is related to the equilibrium constant of the reaction by the equation

where R = 8.31 J/(mol×K) the molar gas constant. This equation makes it possible to calculate the equilibrium constant if we know DG0 and, conversely, to determine DG° for a reaction using the experimentally found value of the equilibrium constant.

In calculating the standard changes in the enthalpy and Gibbs energy for reactions, the standard enthalpies and Gibbs energies of formation of the relevant substances are generally used.

According to Hess's law,

the standard change in the enthalpy of a reaction (or simply the standard enthalpy of a reaction) equals the sum of the standard enthalpies of formation, of the products less the sum of the standard enthalpies of formation of the reactants.

For the chemical reaction  

 aA + bB = cC + dD

Similar relations can be proved exist for Gibbs energy, entropy and other state functions.

All summations are performed with account taken of the number of moles of the substances participating in the reaction in accordance with its equation. Table 1 gives the values of the standard enthalpies and Gibbs energies of formation of selected substances at 25 °C (298 K).

Table  1. Standard enthalpy of formation and standard gibbs energy of formation of selected substances at 298k(25°c)

The symbols used to denote the states of aggregation of the substances are: g — gaseous, lq — liquid, c — crystalline

* Some reference books give the values of the standard enthalpy of formation (DHoform) and the standard entropy (S°) of substances. To calculate the standard Gibbs energy oi formation (DGoform) of a substance, it is necessary to first compute the standard entropy of formation <DSoforn>) of the substance, and then use the formula

Since the change in the enthalpy of a reaction is equal in magnitude, but opposite in sign, to its heat effect at constant temperature and pressure (see p. 207). the thennochemical equation of the reaction can be written as follows:

1 In thermochemical equations  the heat liberated by a system is considered to be positive. In equations of thermodynamics, the opposite condition has bees adopted: the heat absorbed by a system is considered to be positive.

2 The work (W) against the force of external pressure equals the magnitude of this force (F) multiplied by the path (Dl), i.e. W == FDl. But the force equals the pressure (p) multiplied by the area (S) which it acts on: F = pS. whence W== pSDl, or W = pDV.


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