Lecture 40 min.
Definitions
Chemical thermodynamics is the science of how the direction and limits of
transformations of substances depend on the conditions in which these substances find themselves.
The term was proposed in 1851 by the Englishman William Thomson (Lord Kelvin from 1892) (1824-
1907) when he formulated the second law. Rudolf Julius Emanuel Clausius (1822-
1888), a German, called the new science the "mechanical theory of heat." The first
prerequisites for the creation of thermodynamics were laid in 1760-1762, when the Scotsman
Joseph Black (1728-1799) introduced the distinction between quantity of heat and temperature,
measured the heat of fusion of ice, and introduced the concept of "heat capacity."
Unlike other branches of physical chemistry (the structure of matter and
chemical kinetics), chemical thermodynamics can be applied without knowing anything
about the molecular structure of matter. Such a description requires considerably less
initial data.
A specific object of thermodynamic study is called
a thermodynamic system, or simply a system, separated from the surrounding world by
real or imaginary surfaces. A system may be
a gas in a vessel, a solution of reagents in a flask, a crystal of a substance, or even a mentally
isolated part of these objects.
According to their level of interaction with the environment, thermodynamic systems
are usually divided into:
– open systems, which exchange both matter and energy with the environment
(for example, living objects);
– closed systems, which exchange only energy (for example, a reaction in a closed
flask or a flask with a reflux condenser), the most common object of chemical
thermodynamics;
– isolated systems, which exchange neither matter nor energy and keep a
constant volume (an approximation is a reaction in a thermostat).
For a system to be describable thermodynamically, it must
consist of a large number of particles, that is, obey the laws of statistics.
The properties of a system are divided into extensive (additive), for example
total volume and mass, and intensive (equalizing), such as pressure, temperature,
concentration, etc.
The set of properties of a system determines its state. Many properties are
interrelated, so for a homogeneous one-component system with a known
amount of substance n it is sufficient to choose two of the three properties to characterize the state:
1. Voronin G.F. Modern Chemical Thermodynamics. In: Modern Natural Science:
Encyclopedia in 10 vols. Moscow: Flinta: Nauka, 1999-2000, vol. 1. Physical Chemistry. 328 pp.
2
temperature T, pressure p, and volume V. The equation that connects the properties
is called the equation of state; for an ideal gas it is:
pV = nRT
The most important for calculations are state functions, that is,
thermodynamic functions whose values depend only on the state of the system and
do not depend on the path of transition between states.
A process in thermodynamics is not the development of an event in time but
a sequence of equilibrium states of the system leading from an initial set of
thermodynamic variables to a final one. Thermodynamics allows a problem to be solved completely
if the process under study as a whole is described by
a set of equilibrium stages. For example, the operation of a jet engine is
a sequence of nearly equilibrium processes in each small section of the engine
(fast reactions quickly establish equilibrium).
According to V.A. Kireev: An equilibrium state is a
thermodynamic state of a system that does not change in time, and this
constancy is not caused by the occurrence of any external process.
In stable equilibrium, any states adjacent to it are
less stable, and a transition to them from a state of stable equilibrium is always
associated with the need to expend work from outside.
In principle, stable equilibrium can be approached from two
opposite directions.
According to E.N. Eremin: The general conditions for the realization and properties of equilibrium
processes are:
1. An infinitesimally small difference between the acting and opposing forces.
2. Performance of the greatest, maximum work in the forward process.
3. An infinitely slow course of the process, associated with an infinitesimal difference of
the acting forces and an infinitely large number of intermediate states.
4. The absolute values of the work of the forward and reverse processes are the same.
5. A change in the external force by an infinitesimal amount reverses the direction of the
process.
6. The paths of the forward and reverse processes coincide.
Calculations use numerical (tabulated) data on the thermodynamic
properties of substances. Even small sets of such data make it possible to calculate
many different processes.
To calculate an equilibrium composition, it is not necessary to write the equations of
possible chemical reactions; it is enough to take into account all the substances that can in
principle make up the equilibrium mixture.
Thus, chemical thermodynamics does not give a purely computational
(non-empirical) answer to the question "why?" and still less "how?"; it solves problems
on the principle "if ..., then ...".
2. Kireev V.A. A Short Course of Physical Chemistry. Moscow: Khimiya, 1970. 638 pp., p. 224
3. Eremin E.N. Fundamentals of Chemical Thermodynamics. Textbook for universities. Moscow: Vysshaya Shkola, 1974.
341 pp., p. 62
3
Laws of Thermodynamics
Most courses on chemical thermodynamics consider three laws.
However, for a rigorous definition of thermal equilibrium, in 1931 the Englishman R. Fowler
formulated a law that is called the zeroth law:
Two systems that are in thermal equilibrium with a third system
are in thermal equilibrium with each other.
The first law of thermodynamics is one of the forms of the law of conservation of energy.
Its formulations:
Energy is neither created nor destroyed.
A perpetual motion machine (perpetuum mobile) of the first kind is impossible.
In any isolated system the total amount of energy is constant.
The law of conservation of mechanical energy was established by G.W. Leibniz (1686), and the law of
conservation of energy for nonmechanical phenomena by J.R. Mayer (1842),
J.P. Joule (1843-50) and H.L. Helmholtz (1847).
For thermochemical calculations the law of conservation of energy is used in
the formulation of G.I. Hess:
"When any chemical compound is formed, the same amount of heat is always
released, regardless of whether the formation of this compound occurs directly or
indirectly and in several
steps." Hess announced this law of "constancy of heat sums" in a report at
a Conference of the Academy of Sciences on 27 March 1840.
The energy effect of a chemical reaction can appear as purely
thermal, associated with a change in the internal energy of the system, for example the reaction of
neutralization in a dilute solution:
H+ + OH- = H2O + 57 kJ
For this case one can write that the entire thermal effect ΔQ at constant
volume equals the change in internal energy ΔU:
ΔQv = ΔU
However, if aqueous solutions of sodium carbonate and hydrochloric
acid are mixed in a test tube and the tube is quickly closed with a stopper, then after some time the system
will perform mechanical work by "shooting" out the stopper. In this case the temperature of the
solutions after the reaction hardly changes. Work is done when the
elevated pressure in the closed tube equalizes with atmospheric pressure after
the stopper flies out. Thus the work can be described as the work of expansion of a
gas performed at constant pressure (an isobaric process):
pΔV
In the general case, the work performed by a chemical reaction at constant
pressure consists of the change in internal energy and the work of expansion:
ΔQp = ΔU + pΔV
For most chemical reactions carried out in open vessels, it is convenient to
use a state function whose increment is equal to the heat received
4. Eremin E.N. Fundamentals of Chemical Thermodynamics, 1974, p. 26
5. In 1840 Julius Robert Mayer worked as a ship's doctor. On the island of Java the venous blood was lighter
than in northern latitudes. Mayer's conclusion: in a warm climate the blood is less saturated with oxygen,
because less food is needed to maintain body temperature. In 1842 Mayer formulated
the law of the interconversion of heat and work.
6 Trifonov D.N. "A Straightforward and Noble Character" (On the 200th Anniversary of G.I. Hess)
http://www.1september.ru/ru/him/2002/27-28/no27-28_1.htm
4
by the system in an isobaric process. This function is called enthalpy (from the Greek
"enthalpo," to heat):
ΔQp = ΔH = ΔU + pΔV
Another definition: the difference of enthalpies in two states of a system equals
the heat effect of the isobaric process.
There are extensive tables containing data on the standard
enthalpies of formation of substances ΔHo
298 . The indices mean that for chemical
compounds the enthalpies of formation of 1 mol of them from simple substances taken in the
most stable modification are given (except white phosphorus, which is not the most stable but the
most reproducible form of phosphorus), at 1 atm (1.01325.105 Pa or 760 mm Hg) and
298.15 K (25oC). For ions in solution, the standard is a
concentration of 1 M (1 mol/L).
In principle, one can try to calculate absolute values of enthalpies for
chemistry (the heat effect of forming 1 mol of a compound from infinitely distant
atoms taken at 0oK) or for physics (starting from elementary particles taken at
0oK), but for real calculations the generally accepted arbitrary reference level is quite
convenient.
The sign of the enthalpy is defined "from the point of view" of the system itself: when
heat is released the enthalpy change is negative, when heat is absorbed the
enthalpy change is positive.
Standard enthalpy changes for the most important processes:
Enthalpy of formation: the enthalpy change on formation of one mole of
a substance from the elements in their standard states.
Bond enthalpy, or bond dissociation enthalpy: the enthalpy change on
breaking one mole of bonds in the gas phase.
Enthalpy of hydration, or dissolution: the enthalpy change on dissolving
one mole of a substance in water up to infinite dilution.
Lattice enthalpy: the enthalpy change on breaking down
a crystal into its constituent particles and removing them to an infinite distance from
each other.
Enthalpy of atomization: the enthalpy change on forming one mole of atoms in
the gas phase from an element in its standard conditions.
Let us now return to the reaction of a soda solution with a hydrochloric acid solution:
Na2CO3 + 2 HCl = 2 NaCl + H2O + CO2 ↑
For such an equation we will most likely not find the necessary tabulated data: there are
values of ΔHo
298 for the solid salts and gaseous hydrogen chloride, whereas our reaction
took place on mixing two solutions. To make a correct calculation,
we need to determine what actually reacts (the carbonate ion with the acid):
CO3
2- + 2 H+ = H2O(l) + CO2 ↑
Substance ΔHo
298 , kJ/mol
CO3
2- -677
H+ 0
H2O(l) -286
CO2 -394
By Hess's law we obtain for the reaction
7. The name "enthalpy" was proposed by the Dutch physicist Heike Kamerlingh Onnes (1853-1926).
8. Lewis M. Chemistry. A School Course in 100 Tables, Moscow, "AST-PRESS", 1997
5
ΔHo
298 = ΣΔHo(prod.) - ΣΔHo(init.) = (-286 + -394) - (-677 + 0) = -3 kJ.
An example of a thermochemical calculation for an extremely complex reaction:
The enthalpy of formation of glucose cannot be determined by direct experiment:
6 C + 6 H2 + 3 O2 = C6H12O6 (ΔHx - ?) Such a reaction is impossible
6 CO2 + 6 H2O = C6H12O6 + 6 O2 (ΔHy - ?) the reaction occurs in green leaves, but
together with other processes
Using Hess's law, it is enough to combine three combustion equations:
1) C + O2 = CO2 ΔH1 = -394 kJ
2) H2 + 1/2 O2 = H2O(vapor) ΔH2 = -242 kJ
3) C6H12O6 + 6 O2 = 6 CO2 + 6 H2O ΔH3 = -2816 kJ
We add the equations, "flipping" the third one, then
ΔHx = 6 ΔH1 + 6 ΔH2 - ΔH3 = 6(-394) + 6(-242) -(-2816) = -1000 kJ/mol
Obviously ΔHy corresponds to the process reverse to photosynthesis, that is, the combustion
of glucose. Then ΔHy = -ΔH3 = +2816 kJ
No data on the structure of glucose were used in the solution; the
mechanism of its combustion was not considered either.
The Second Law of Thermodynamics
It is quite obvious that reactions with an overall decrease in enthalpy
(exothermic) can proceed spontaneously, like a stone rolling down a hill. However,
it is well known that some reactions also proceed spontaneously
that are accompanied by an increase in enthalpy and cooling of the reactor
(endothermic).
To characterize endothermic processes and to determine the conditions for their
spontaneous occurrence, a new state function was introduced:
entropy (from the Greek "en," "in," "inward," and "trope," "turning," "transformation").
The change in entropy equals (by definition) the minimum heat supplied to
the system in a reversible (all intermediate states are equilibrium) isothermal
process, divided by the absolute temperature of the process:
ΔS = Qmin./T
The appearance of such a state function is connected with the need to describe heat
by the method of generalized forces, analogous to any work (A), through a generalized force (F) and
a generalized coordinate (in this case a thermal one) [10]:
dA = Fdx
For thermal reversible processes we obtain:
dQ = TdS
That is, entropy is the thermal coordinate of state, introduced for
standardizing the mathematical apparatus of thermodynamics.
At this stage of studying thermodynamics one should accept as a postulate [11] that
there exists a certain extensive property of the system S, called entropy,
whose change is related to the processes in the system as follows:
In a spontaneous process ΔS > Qmin./T
9. The term "entropy" was introduced by Rudolf Clausius in 1865 to denote the transformation of energy into less
valuable forms: "transformation into"
10. Poltorak O.M., Thermodynamics in Physical Chemistry. Textbook for chemistry and chemical technology university specialties, Moscow:
Vysshaya Shkola, 1991. 319 pp., pp. 36-37
11. Eremin E.N. Fundamentals of Chemical Thermodynamics, 1974, p. 72
6
In an equilibrium process ΔS = Qmin./T
In a nonspontaneous process ΔS < Qmin./T
For an isolated system, where dQ = 0, we obtain:
In a spontaneous process ΔS > 0
In an equilibrium process ΔS = 0
In a nonspontaneous process ΔS < 0
In the general case the entropy of an isolated system either increases or remains
constant:
ΔS ≥ 0
The concept of entropy arose from the previously obtained formulations of the second law
(principle) of thermodynamics. Entropy is a property of the system as a whole, not of an individual
particle.
The second law according to W. Thomson (1851): "in nature a process is impossible
whose only result would be mechanical work performed at
the expense of cooling a heat reservoir."
According to R. Clausius (1850): "heat cannot by itself pass from a colder
body to a warmer one," or: "it is impossible to construct a machine that,
operating by means of a cyclic process, will only transfer heat from a colder
body to a warmer one."
The earliest formulation of the second law of thermodynamics appeared before the
first law, based on the work of the Frenchman S. Carnot (1824) and its mathematical
interpretation by the Frenchman E. Clapeyron (1834) as the efficiency of an ideal heat engine:
Efficiency = (T1 - T2)/T1
Carnot and Clapeyron formulated the law of conservation of caloric, an imponderable
indestructible fluid whose content determines the temperature of a body. The caloric
theory dominated thermodynamics until the middle of the 19th century, while the laws and
relations derived from ideas about caloric turned out to be
valid within the molecular-kinetic theory of heat as well.
The Third Law of Thermodynamics (Planck's Postulate)
In 1911 Max Planck proposed the following postulate: the entropy of a properly
formed crystal of a pure substance at absolute zero equals zero. This
postulate can be explained by statistical thermodynamics, according to which
entropy is a measure of the disorder of a system at the microlevel:
S = kblnW "Boltzmann equation", derived by M. Planck in 1900.
W is the number of different states available to the system under the given conditions, or
the thermodynamic probability of the macrostate of the system.
kb = R/NA = 1.38·10^-16 erg/deg – the Boltzmann constant
In 1872 L. Boltzmann proposed a statistical formulation of the second law of
thermodynamics: an isolated system evolves predominantly in the
direction of greater thermodynamic probability [12].
One should always remember that the second law of thermodynamics is not
absolute; it loses its meaning for systems containing a small number of particles, and for
12. Carlo Cercignani, the modern biographer of Ludwig Boltzmann, a physicist, writes: "Only by properly understanding
the second law of thermodynamics can one answer the question of why life is possible at all." In 1906
Boltzmann committed suicide because he was "deceived in love; he had devoted his life to atomic theory,
but his love went unrequited, because his contemporaries could not grasp the scale of his picture of the
world" (Simon Schaffer, Ludwig Boltzmann and the Second Law of Thermodynamics) Internet:
http://if.russ.ru/issue/6/20010816_cha-pr.html
7
systems of cosmic scale [13]. The second law, especially in its statistical
formulation, is not applicable to living objects, which are open
systems and constantly decrease entropy by creating perfectly ordered
molecules, for example, using the energy of sunlight.
Living systems are characterized by self-organization, which the Chilean
neurobiologist Humberto Maturana called autopoiesis in 1970
(self-creation). Living systems not only constantly move away themselves from
classical thermodynamic equilibrium, but also make the surrounding
environment non-equilibrium. As early as 1965 the American atmospheric chemistry specialist
James Lovelock proposed, as a criterion for the presence of life on Mars,
assessing how close the composition of the atmosphere is to equilibrium [14].
The Earth's atmosphere contains simultaneously oxygen (21% by volume), methane
(0.00018%), hydrogen (0.00005%), and carbon monoxide (0.00001%) – this is clearly a
non-equilibrium mixture at temperatures from -50 to +40 °C [15]. The Earth's atmosphere is an open
system, in the formation of which living organisms constantly take part.
The atmosphere of Mars is dominated by carbon dioxide (95% - compare with 0.035% on Earth),
it contains less than 1% oxygen, and reducing gases (methane) have not yet been detected [16].
Consequently, the atmosphere of Mars is practically in equilibrium – all reactions between
the gases contained in it have already taken place.
From these data Lovelock concluded that there is currently no life on Mars.
At the same time, it is possible to apply the laws of classical
thermodynamics to living objects. Open living systems over certain
time scales can be considered quasi-closed with respect to processes for
which local equilibria are established quickly (Gladyshev G.P. [17]).
Structures of a higher hierarchy form a "thermostat" for the lower ones, within
which the processes can be considered quasi-equilibrium.
However, let us return to "normal" chemical systems.
The introduction of entropy made it possible to establish criteria that allow one to
determine the direction and extent of any chemical process (for a
large number of particles at equilibrium).
Macroscopic systems reach equilibrium when the change in energy is
compensated by the entropy component:
At constant volume and temperature:
ΔUv = TΔSv or Δ(U-TS) ≡ ΔF = 0 Helmholtz energy [18] or
isochoric-isothermal potential
At constant pressure and temperature:
ΔHp = TΔSp or Δ(H-TS) ≡ ΔG = 0 Gibbs energy or
Gibbs free energy or
isobaric-isothermal potential
The change in Gibbs energy as a criterion of the possibility of a chemical reaction
13. Eremin E.N. Fundamentals of Chemical Thermodynamics, 1974, p. 193
14. Capra Fritjof. The Web of Life. A New Scientific Understanding of Living Systems. Transl. from English – Kyiv: "Sofia";
Moscow: "Gelios" Publishing House, 2002. – 336 pp., Chapter 5. Models of Self-Organization
15. Encyclopedia for Children: Vol. 3 (Geography). – Moscow: Avanta+, 1994. – 640 pp., p. 305
16. Encyclopedia for Children: Vol. 8. Astronomy. – Moscow: Avanta+, 1998. – 688 pp., p. 540
17. Gladyshev G.P. Supramolecular Thermodynamics – the Key to Understanding the Phenomenon of Life. Moscow-
Izhevsk: Institute of Computer Research, 2003, 144 pp., pp. 27, 125.
18. First introduced by Massieu (1869), then by J. Gibbs in 1875, it became widely known after the article by
H. Helmholtz in 1882.
8
For a given temperature ΔG = ΔH - TΔS
At ΔG < 0 the reaction is possible;
at ΔG > 0 the reaction is impossible;
at ΔG = 0 the system is in equilibrium.
The possibility of a spontaneous reaction in an isolated system is determined by
the combination of the signs of the energetic (enthalpy) and entropy factors:
Sign of ΔH Sign of ΔS Possibility of a spontaneous
reaction
+ – No
– + Yes
– – Depends on the ratio of ΔH and TΔS
+ + Depends on the ratio of ΔH and TΔS
There are extensive tabulated data on the standard values of ΔG0 and S0 (for
entropy, according to the third law there is a zero reference level and, accordingly,
absolute values), which make it possible to calculate ΔG0 of a reaction.
If the temperature differs from 298 K and the concentrations of the reactants from 1
M, for a process in the general form:
aA + bB → xX + yY
ΔG = ΔG0 + RT ln(C(X)
x C(Y)
y )/(C(A)
a C(B)
b)
At the equilibrium position ΔG = 0 and ΔG0 = -RTlnKp, where
Kp = (C(X)
x
eq. C(Y)
y
eq. )/(C(A)
a
eq. C(B)
b
eq. ) the equilibrium constant
Kp = exp(-ΔG0/RT)
Using the formulas given, one can determine the temperature above which
an endothermic reaction in which entropy increases becomes readily
feasible. The temperature is determined from the condition:
ΔG0 = ΔH0 - TΔS0 = 0; T = ΔH0/ΔS0
It should be taken into account that for accurate calculations at temperatures noticeably
different from 298 K, it is necessary to use for all thermodynamic
functions their dependences on temperature. For example, for the reaction:
2 CH4 = C2H4 + 2 H2
In the first approximation ΔH0 = 48.3 kcal/mol C2H4;
in the second approximation ΔHT = 46370 + 6.47T cal/mol [19]
COMMENT: The "problem" of weak electrolytes:
Dissociation of acetic acid:
CH3COOH ↔ CH3COO– + H+
ΔG0 -377 kJ -369 0 [20]
Calculation by Hess's law: (-369 + 0) - (-377) = + 8 kJ (!)
But this is obtained if all concentrations are 1 mol/L
We refine it using the concentration of CH3COO– ions (Kdiss = 1.8*10–5) :
ΔG = ΔG0 + RT ln(C(X)
x C(Y)
y )/(C(A)
a C(B)
b) = ΔG0 + RT ln(Kdiss)
ΔG = -369 + 2.478 ln (10–5) = -369 + 2.478*(-11.5) = -369 + (-28) = -397
19. Eremin E.N. Fundamentals of Chemical Thermodynamics, 1974, p. 53
20. A Concise Handbook of Physicochemical Quantities, 8th ed., Leningrad: Khimiya, 1983. – 232 pp.
9
ΔG (of the reaction) = (-397 + 0) - (-377) = -20 kJ
COMMENT: The expression for the Gibbs energy ΔG = ΔG0 + RTlnKp
arises as follows [21]:
The differential expression of the first and second laws of thermodynamics:
dU = TdS – PdV; substituting G = U + PV – TS we get dG = + VdP – SdT ;
at constant temperature dG = VdP. Then for an ideal gas
dG = (RT/P)dP and after integration G2 = G1 + RTln(p2/p1) or G = G0 + RTln(p/p0).
Since p0 = 1 atm, the ratio (p/p0) is numerically equal to the pressure in atmospheres. It is
called the activity. Activity is a dimensionless quantity. For a condensed
state (liquids and solids), the activity of a substance is understood as the ratio of
its concentration to the concentration in the standard state.
Then the molar Gibbs energy: G = G0 + RTlna
Since for a reaction ΔGreact = Σ ΔGprod - Σ ΔGinit , for the process
aA + bB → xX + yY
we obtain: ΔG = ΔG0 + RT ln(a(X)
x a(Y)
y )/(a(A)
a a(B)
b). Further – see the table:
Table 1
Standard states and activities adopted for calculating the Gibbs energy
and equilibrium constants
Substance Standard state Activity
Gas, pure or in a mixture Partial pressure p0 = 1 atm a = (p/p0)
Pure liquid or
solid substance
Pure liquid or
solid substance
a = 1
Solvent in a
dilute solution
Pure solvent a = 1
Substance in solution Concentration 1 mol/L For dilute
solutions numerically a = c
Chemical Kinetics
The predictions of chemical thermodynamics are most reliable in their
"prohibiting" part. If, for example, for the reaction
N2 + O2 = 2 NO ΔG0 = +176 kJ,
then this reaction will not proceed spontaneously, and no catalyst will help it.
The well-known industrial process for obtaining NO from air requires enormous expenditure of
energy and a non-equilibrium way of carrying out the process ("quenching" of the products by rapid
cooling after passing the gas mixture through an electric arc).
On the other hand, by no means all reactions for which ΔG < 0 "hurry"
to occur in practice. Pieces of coal can lie in air for centuries,
although for the reaction C + O2 = CO2 ΔG0 = -395 kJ
Predicting the rate of a chemical reaction, as well as clarifying how
this rate depends on the conditions under which the reaction is carried out, is the task of
chemical kinetics – the science of the chemical process, its mechanism and
the regularities of its course in time.
21. See, for example: Inorganic Chemistry: In 3 vols. / Ed. Yu.D. Tretyakov. Vol. 1: Physicochemical
Foundations of Inorganic Chemistry. / M.E. Tamm, Yu.D. Tretyakov, Moscow, 2004. – 240 pp., p. 32
10
The rate of a chemical reaction is defined as the change in the concentration of
one of the substances participating in the reaction (a starting substance or a reaction product) per
unit time.
For a reaction in the general form aA + bB → xX + yY
the rate is described by the kinetic equation:
v = -Δ C(A)/ Δt = Δ C(X)/ Δt = k C(A)
mC(B)
n
Strictly speaking, the rate is defined not as a finite difference of concentrations, but
as their derivative v = -d C(A)/ dt;
the exponents m and n usually do not coincide with the stoichiometric
coefficients.
The order of a reaction is the sum of all the exponents m and n.
The order of the reaction with respect to reactant A is m .
The number of reactant molecules participating in a simple one-step reaction
consisting of a single elementary act is called the molecularity of the reaction.
Unimolecular reaction:
C2H6 = 2 CH3
.
Bimolecular reaction:
CH3
. + CH3
. = C2H6
Examples of relatively rare termolecular reactions:
2 NO + O2 = 2 NO2
2 NO + Cl2 = 2 NOCl
H. + H. + Ar = H2 + Ar
In the simplest cases, for the initial concentration C0
(A) and the current
concentration C(A), the following equations can be obtained for elementary
first- and second-order reactions [22] (Table 2)
Table 2
Simple kinetic equations for elementary reactions of the 1st and 2nd order
Ord.
Kinetic
equation in
differential
form
Kinetic equation
in integral form
Typical
units of
measurement of
the rate
constant
Half-
life
1 -d C(A)/ dt = k C(A) kt = ln (C0
(A)/ C(A)) C-1 t1/2 = 0.693/k
2 -d C(A)/ dt = k (C(A) )2 kt = (C0
(A) - C(A))/ C(A)*
C0
(A)
dm3 /(mol*s) t1/2 = 1/(k*C0
(A) )
Most reactions are multistep, even if they are described by
simple stoichiometric equations. In this case a complex kinetic
equation of the reaction is usually obtained.
For example, for the reaction H2 + Br2 = 2 HBr
dC(HBr)/dt = kC(H2) C(Br2)
0.5/ (1 + k' C(HBr)/ C(Br2))
Such a complex dependence of the rate on concentrations indicates a multistep
mechanism of the reaction.
22. Avery H. Basic Reaction Kinetics and Mechanisms / Transl. from English by V.V. Smirnov, Moscow, 1978,
214 pp., p. 21
11
A chain mechanism has been proposed for this reaction:
Br2 → Br. + Br. chain initiation
Br. + H2 → HBr + H. chain propagation
H. + Br2 → HBr + Br. chain propagation
H. + HBr → H2 + Br. inhibition
Br. + Br. → Br2 chain termination
Even now many textbooks present the so-called law of
mass action, which is called the basic law of chemical kinetics. In
1867, when this law was formulated by the Norwegian scientists, the mathematician Cato
Maximilian Guldberg (1836-1902) and the chemist Peter Waage (1833-1900), they called concentrations
"active masses".
According to the law of mass action, the rate for a reaction written in the general
form: aA + bB → xX + yY ,
should be expressed by the kinetic equation: v = k C(A)
a C(B)
b
In this form the law is valid only for elementary reactions, and
the total order should not exceed 3 (a + b ≤ 3)
Many enzymatic reactions proceed through a stage in which an
intermediate enzyme-substrate complex SE is formed between the substrate (the reactant entering the reaction) S and the enzyme (catalyst) E,
which then decomposes with
regeneration of the enzyme E and formation of the product P:
S + E ↔ SE
SE ↔ E + P
For such reactions, in 1913 a kinetic equation was derived (the Michaelis-
Menten equation) for the steady-state rate [23]:
vss = vmaxC(S)/(KM + C(S))
KM – the Michaelis constant
A typical complex multistep reaction is the interaction of
hydrogen with oxygen. This is an example of a branched chain process, to which
the explosion of a nuclear bomb also belongs.
For the study of this type of reaction, in 1956 N.N. Semenov and the Englishman Cyril
Hinshelwood received the Nobel Prize.
H2 + 1/2 O2 = H2O(vapor) + 241 kJ
The sequence of processes in the combustion of hydrogen in oxygen [24]:
1) H2 + O2 → 2 .OH
2) H2 + M → 2 H. + M Chain initiation
3) O2 + O2 → O + O3
4) .OH + H2 → H2O + O Chain propagation
5) H. + O2 → .OH + O Chain branching
6) O + H2 → .OH + H.
7) H. + wall → Chain termination on the wall
8) .OH + wall →
23. Leonor Michaelis (1875-1949) – German biochemist.
24. Panchenkov G.M., Lebedev V.P. Chemical Kinetics and Catalysis. 2nd ed. – Moscow: Khimiya, 1974. – 592 pp.,
p. 273
12
9) H. + O2 + M → HO2
. + M Termination in the volume
10) 1/2 H2O2 + 1/2 O2
HO2
. + wall →
11) 1/2 H2O + 3/4 O2
12) HO2
. + H2 → H2O2 + H. Chain propagation by means of a
13) HO2
. + H2O → H2O2 + .OH low-activity radical
Knowledge of the mechanisms of such reactions is important for creating powerful jet
engines.
On July 21, 1969, the first Earthling, N. Armstrong, walked on the Moon. The Saturn-5 launch
vehicle had 3 stages. The first used kerosene and oxygen, the second and third used
liquid hydrogen and oxygen. In total 468 t of liquid O2 and H2.
Since April 1981 the Space Shuttle has been flying in the USA: 713 t of liquid O2 and
H2, as well as two solid-fuel boosters of 590 t each (total mass of solid fuel 987 t). The first 40 km on
the solid rocket boosters, from 40 to 113 km – hydrogen and oxygen.
On May 15, 1987, the first launch of Energia; on November 15, 1988, the first and
only flight of Buran. Launch mass 2400 t, mass of fuel (kerosene in the
side boosters, liquid O2 and H2) 2000 t. Engine power 125000 MW, payload
105 t [25].
Temperature Dependence of Reaction Rates
Most practically important reactions are accelerated by heating. Since the end of the
19th century the van 't Hoff rule has been known: the rate of many reactions on heating by
10° increases by a factor of 2-4: v2/v1 = γΔT/10 (γ is the van 't Hoff coefficient)
The temperature dependence of the reaction rate constant is expressed more precisely and more universally
by the Arrhenius equation (1889):
k = Aexp(-Ea/RT)
The factor A is related to the frequency of collisions of particles and their orientation during
collisions; Ea is the activation energy of the given chemical reaction.
To determine the activation energy of a given reaction, it is enough to measure its
rate at two temperatures.
A simple calculation shows that the van 't Hoff rule at temperatures near
300 K holds if the activation energies of reactions are in the range of 50-100
kJ/mol.
The Arrhenius equation describes the temperature dependence not only for
simple chemical processes. Psychological studies of people with different
body temperatures (from 36.4 to 39 °C) showed that the subjective sense of time
(the rate of counting beats) and the rate of forgetting random sequences of characters
are described by the Arrhenius equation with an activation energy of 190 kJ/mol [26].
A positive value of the activation energy shows that on the way from
the starting substances to the products there is an energy barrier that does not allow
all thermodynamically possible reactions would have to proceed immediately.
There are reactions that slow down on heating; their effective
activation energy (obtained by measuring the rate of the process as a whole)
25. Gubanov B. "Energia"-"Buran": a step into the future. Nauka i zhizn, 1989, No. 4, pp. 2-9;
Patrunov F.G. Below 120 degrees Kelvin. Moscow: Znanie, 1989. 176 pp., pp. 97-99
26. Leenson I.A. Why and how chemical reactions proceed. Moscow: MIROS, 1994. 176 pp., pp. 116-117
13
is negative. In such cases the stoichiometric equation describes a complex
multistep process.
For example, the reaction 2 NO + O2 = 2 NO2
proceeds in two steps, the first of which is reversible:
2 NO ↔ (NO)2; (NO)2 + O2 = 2 NO2
The rate constant of the second reaction increases with temperature. But the
concentration of the dimer (NO)2 falls on heating, and it falls faster than the
rate constant of the second reaction grows. As a result, the overall rate of the process
decreases on heating.
For many biologically important reactions, the process speeds up
(negative activation energy) when aqueous solutions of the reagents are frozen.
This is explained by the increase in the concentration of the reagents in the liquid microinclusions
that form during slow freezing [27]. As a result, cycles of temperature change
of frozen foods from -5oC to -18oC ("defrosting a refrigerator without thawing")
can cause them to spoil quickly.
In the 1960s, polymerization reactions were discovered at low (liquid nitrogen, 77
K) and ultralow temperatures (liquid helium, 4.2 K). The polymerization of formaldehyde
under the action of ionizing radiation proved especially interesting. The rate of the
conversion:
n CH2O = (-CH2O)n-
decreased steadily as the temperature was lowered, in accordance with the
Arrhenius equation, with an activation energy of 8 kJ/mol at temperatures of 150-80 K. But then the
polymerization rate ceased to depend on temperature – the reaction continued
even at 4.2 K. To explain this unusual reactivity near
absolute zero, it was necessary to use the methods of quantum mechanics. Such processes are now
explained by quantum tunneling (i.e., wave-like
displacement) of an entire formaldehyde molecule over a distance of about 0.5 angstrom [28].
27. Smirnov V.V. Chemical reactions at low temperatures. Modern Natural Science:
Encyclopedia in 10 vols. Moscow: Flinta: Nauka, 1999-2000, vol. 1. Physical Chemistry. 328 pp., p. 111
28. Sergeev G.B., Batyuk V.A. Cryochemistry. Moscow: "Khimiya", 1978. 296 pp., pp. 81-84
14
Supplement 1 to Lecture 3
Examples of practically important thermochemical calculations
For decomposition reactions of solids accompanied by the formation of
gases (an increase in entropy), calculating the enthalpy can serve as a criterion for
predicting whether the process can occur spontaneously. Such calculations are important for
assessing the hazards of some oxidizers used in pyrotechnics [29].
Let us consider such calculations using ammonium nitrate as an example.
Standard enthalpy of formation for the conventional process:
(1) 2 H2 + N2 + 1.5 O2 = NH4NO3 ΔH0
298 = -365 kJ/mol
It might seem that the reverse process, the decomposition of ammonium nitrate, is endothermic. But on
decomposition of this salt, the products are not a mixture of hydrogen and oxygen but water, the formation
of which releases energy. The most probable reaction is:
(2) NH4NO3 = N2 + 2 H2O + 0.5 O2 ΔH0
298 = -119 kJ/mol
Reactions leading to the formation of endothermic nitrogen oxides are also possible:
(3) NH4NO3 = N2O + 2 H2O ΔH0
298 = -37 kJ/mol
(4) NH4NO3 = 0.5 NO2 + 0.75 N2 + 2 H2O ΔH0
298 = -102 kJ/mol
Required tabulated data:
ΔH0
298, kJ/mol
H2O(g) -242
N2O +82
NO2(g) +34
From the thermochemical equations above it is clear that spontaneous
decomposition of ammonium nitrate (saltpeter) with the release of
energy is possible. If you try to heat a small amount of ammonium nitrate,
the spontaneous reaction does not start. However, this salt will begin to decompose on
heating if a catalyst is added to it – 5-8% by mass of potassium dichromate.
Spontaneous decomposition by another mechanism is also possible. The first
widely known case of such decomposition occurred at a chemical plant warehouse
in Oppau (Germany, 1921). When attempts were made to break up a caked mass of a mixture of
ammonium nitrate and ammonium sulfate with small charges of dynamite, the mass exploded
(detonated); about 1000 people were killed and hundreds of
buildings were destroyed.
Since then, more than 40 major accidents involving the detonation of ammonium nitrate
have been described in the literature.
The enthalpy of reaction (2) corresponds precisely to the empirical criterion for
the possibility of spontaneous self-sustaining combustion: the reaction should release
about 1.5 kJ per gram of starting materials.
Let us carry out a similar calculation for potassium chlorate:
(5) KClO3 = KCl + 1.5 O2 ΔHo
298 = -48 kJ/mol
Pure potassium chlorate does not decompose spontaneously, but a mixture of this salt
even with a small amount of combustible substances (phosphorus, sulfur) is sensitive to
friction and impact. For this reason, this salt is now almost never used in pyrotechnics, except for
the manufacture of matches.
29. Zagorsky V.V. Fireworks (Fireworks: history, theory, practice). Moscow: "Khimiya i zhizn - XXI
vek" 1997, 64 pp., illus.; Reprint: Moscow: A.N. Kolmogorov School "Samoobrazovanie", 2000, 64
pp.; Internet: http://www.divicon.ru/~vova/rdtt.html http://pyrotechnic.narod.ru/zanatie/zanatie.html
15
Supplement 2 to Lecture 3
Oscillating reactions
The Landolt reaction
(German physical chemist Hans Heinrich Landolt (1831-1910)
Na2SO3 + H2SO4 = H2SO3 + Na2SO4
HIO3 + 3 H2SO3 = 3 H2SO4 + HI
5 HI + HIO3 = 3 I2 + 3 H2O
I2 + H2SO3 + H2O = H2SO4 + 2 HI
The Belousov-Zhabotinsky reaction
B.P. Belousov (1893-1970) (1951), A.M. Zhabotinsky
BrO3
- + Br- + 2 H+ = HBrO2 + HOBr
HBrO2 + Br- + H+ = 2 HOBr
HOBr + Br- + H+ = Br2 + H2O
Br2 + CH2(COOH)2 = BrCH(COOH)2 + Br- + H+
Overall process of bromination of malonic acid:
BrO3
- + 2 Br- + 3 CH2(COOH)2 + 3 H+ = 3 BrCH(COOH)2 + 3 H2O
At a low concentration of bromide ion:
BrO3
- + HBrO2 + H+ = 2 BrO2
. + H2O
BrO2
. + Ce3+ + H+ = HBrO2 + Ce4+
2 HBrO2 = BrO3
- + HOBr + H+
HOBr + CH2(COOH)2 = BrCH(COOH)2 + H2O
Overall process of oxidative bromination:
BrO3
- + 4 Ce3+ + CH2(COOH)2 + 5 H+ = BrCH(COOH)2 + 4 Ce4+ + 3 H2O
Reduction of cerium to Ce3+ :
6 Ce4+ + CH2(COOH)2 + 2 H2O = 6 Ce3+ + HCOOH + 2 CO2 + 6 H+
4 Ce4+ + BrCH(COOH)2 + 2 H2O = Br- + 4 Ce3+ + HCOOH + 2 CO2 + 5 H+
Source: Aliev R., Shnol S.E. Oscillating chemical reactions
In: Modern Natural Science: Encyclopedia in 10 vols. Moscow: Flinta: Nauka, 1999-2000, vol. 1. Physical
Chemistry. 328 pp., pp. 130-133
You can also read about the Belousov-Zhabotinsky reaction and oscillating reactions in general:
1. Vertigel A. A story of oscillations, "Khimiya i zhizn - XXI vek", No. 2, 1998,
pp. 34-35
2. Shnol S.E. "Znanie - Sila", 1994, No. 3, pp. 62-71 or on the Internet:
http://www.znanie-sila.ru/projects/issue_87.html
16
Supplement 3 to Lecture 3
History of thermodynamics and kinetics
In 1660 the Englishman Robert Boyle (1627-1691) discovered the dependence of the volume of air on
pressure; independently, in 1676, the same results were obtained by the Frenchman Edme Mariotte (1620-
1684), a physicist, abbot of a monastery, and one of the founders of the Paris Academy of Sciences.
In 1760-1762 the Scotsman Joseph Black (1728-1799) introduced the distinction between
the quantity of heat and temperature, measured the heat of fusion of ice, and introduced the concept of
"heat capacity." In 1848 W. Thomson introduced the absolute temperature scale.
In 1787 the Frenchman Jacques Alexandre Cesar Charles (1746-1823) established the dependence of
gas pressure on temperature at constant volume.
In 1802 the Frenchman Joseph Louis Gay-Lussac (1778-1850) established the relationship of the pressure and
volume of a gas to temperature.
In 1824 the Frenchman Nicolas Leonard Sadi Carnot (1796-1832) published the work
"Reflections on the Motive Power of Fire and on Machines Fitted to Develop That Power."
He proved that the efficiency of a heat engine is determined by the difference between the temperatures of the heater and
the cooler: efficiency = (T1 - T2)/T1. He introduced the concepts of the cyclic and reversible processes, and of the
ideal cycle of heat engines. His ideas were popularized in 1834 by the Frenchman Benoit Paul
Emile Clapeyron (1799-1864), who depicted them as diagrams in P-V coordinates.
In 1840 the Russian Germain Henri Hess (German Ivanovich Hess) (1802-1850) discovered the basic law of
thermochemistry (the independence of ΔQ from the path). He established the constancy of the heat of the
neutralization reaction.
In 1840 the German physician Julius Robert Mayer (1814-1878) worked as a ship's doctor
on a voyage from Europe to Java. He noticed that venous blood in the tropics is
lighter than in Germany, and concluded that in the tropics less oxygen is needed to maintain the same
body temperature. Consequently, heat and work can be
converted into each other. In 1842 Mayer theoretically estimated the mechanical equivalent of
heat at 365 kgm (modern value 427 kgm) [30].
In 1841-1843 the English brewery owner James Prescott Joule
(1818-1889) determined the thermal equivalents of electric current and mechanical
work.
Until the mid-19th century, thermodynamic concepts developed within the framework of the
idea of a carrier of heat, caloric (the hypothesis was authored by Galileo – 1613).
In 1798 experimental data were obtained against the material theory of
heat (caloric) – the American-born Englishman Benjamin Rumford (Thompson) (1753-1814)
observed the boring of cannons in the Munich arsenal and estimated the quantity of
heat released in the process.
In 1880-1884 the Dutchman Jacobus Henricus van 't Hoff (1852-1911) studied the dependence of the
rate of chemical reactions on temperature.
In 1889 the Swede Svante August Arrhenius (1859-1927) introduced the concept of
activation energy.
In 1931 the Englishman Ralph Howard Fowler (1889-1944) formulated the zeroth law of
thermodynamics.
30. "The idea of the law of conservation of energy became for him something like a religious revelation, and he devoted his whole life to developing and
defending his idea, investing so much spiritual and physical strength in it that it
led him to a psychiatric hospital," wrote the historian of physics Mario Liozzi. Encyclopedia for
Children. Vol. 17. Chemistry. Moscow: Avanta+, 2000. 640 pp., p. 106
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