Reaction energy

As we have learned in the last chapter, the temperature dependence of the chemical equilibrium depends on the reaction enthalpy. To measure this reaction enthalpy, one can simply determine the change in temperature if the reaction is carried out at isobar conditions and 100% conversion, i.e. ο_ܴܪ כൌ ܿ_݌ή οܶ

However, if it is not possible to monitor the reaction itself directly, one can apply the principle of Hess, which is based on the fact that the reaction enthalpy or the reaction energy both are quantities of state, that are independent of the process itself. Consider, for illustration, the reaction enthalpy of the hydration of ethylene to ethane. Instead of observing this process, one could measure the heat of burning of ethylene and hydrogen as the educts, or pure ethane as the product, respectively, with pure oxygen (see fig. 2.33):

Q$R[LGHP%R[LGH

Q$R[LGHP%R[LGH

Fig. 2.33: The principle of Hess – conservation of energy/enthalpy for chemical reactions irrespective of the reaction pathway

The hydration enthalpy is then simply the difference between the two heats of burning οܪ ൌ ܳͳെ

ܳ_ʹ Note that in this way any reaction energy or enthalpy can be determined, taking into account also that the enthalpy of a pure element in its stable modification at standard conditions (T = 298 K, p = 1 bar) is defined as zero. For illustration, consider the burning of hydrogen with oxygen to water at standard conditions _{ܪʹ൅ ͳ ʹൗ ܱʹ՜ ܪʹܱ} The heat of burning in this case is directly the reaction enthalpy

ο_ܴܪ כൌ ܪ_ܪʹܱെ ܪ_ܪʹͳ

ൗ ܪʹ _ܱʹ

According to the convention, we can also write ο_ܴܪ כൌ ܪ_ܪʹܱ In this way, one can determine, based on some simple model reactions, a whole set of reaction enthalpies mainly on calculations. More importantly, one can also determine the enthalpy of individual chemical groups like CH₂ or COOH, leading to the total enthalpy of more complicated organic molecules without the necessity of more experiments.

To complete this puzzle, we need to know how to transfer our reaction enthalpy from standard temperature to any reaction temperature. Again, we utilize the fact that the enthalpy is a quantity of state irrespective of the process itself. Consider two possibilities for the reaction from A(T) to B(T+ΔT): either you can first heat the educt A and then carry out the reaction at temperature T+ΔT, or you can carry out the reaction first at T and then change the temperature of the product to T+ΔT. Either way, the overall change in enthalpy should be the same. This leads us to the important Kirchhoff law:

σ …_’ሺሻ ή ο ൅ ο_൅ο ൌ ο൅ σ …_’ሺሻ ή ο (Eq.2.150) ο_൅οെ ο ൌ ൫σ …_’ሺሻ െ σ …_’ሺሻ൯ ή ο (Eq.2.151)

†ሺοሻ ൌ ൫σ …_’ሺሻ െ σ …_’ሺሻ൯ ή † (Eq.2.152)

ቀ^μሺο_μ^ሻቁ ൌ σ …_’ሺሻ െ σ …’ሺሻ (Eq.2.153)

ቀ^μሺο_μ^ሻቁ ൌ σ ɋ‹…’‹ (Eq.2.154)

That is, the change in reaction enthalpy with temperature is simply given by the difference in isobar heat capacities of products and educts.

ܣ ՜ ܤ

Fig. 2.34: Kirchhoff law, two different routes from educt A(T) to product B(T+λT) with identical overall reaction enthalpy

Basic Physical Chemistry

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Kinetics

3 Kinetics

The velocity of a chemical reaction is defined as the change in concentration (for gas reactions: partial pressure) with time, taking into account the stoichiometric coefficients of the respective components.

In experimental practice, this concentration can be quantified in various ways, for example: photometry (measurement of absorbed light at specific wave length following the law of Lambert-Beer), conductometry (measurement of electric conductance, in case either ions are formed or consumed during the chemical reaction), or polarimetry (measurement of the rotational angle of polarized light in case optically active components are involved).

In the simple case of elementary reactions, that is, reactions with one single reaction step from educt to product (involving an excited state, see also figure 3.3 at the end of this chapter!), the decrease in concentration of component A with time for the reaction

݊ܣܣ ൅ ݊ܤܤ ՜ ݊ܥܥ (Eq.3.1)

is given as:

െ^݀ܿ_݀ݐ^ܣ ൌ ݇ ή ܿ_ܣ^݊ܣ ή ܿ_ܤ^݊ܤ (Eq.3.2)

More general, the reaction velocity for this reaction is given as:

ݒ ൌ െ_݊^ͳ

ܣ

݀ܿܣ

݀ݐ ൌ െ_݊^ͳ

ܤ

݀ܿܤ

݀ݐ ൌ_݊^ͳ

ܥ

݀ܿܥ

݀ݐ (Eq.3.3)

The velocity constant k is dependent on temperature, and may be increased by adding a catalyst, as we will see when we introduce the Arrhenius equation below. The total order of the reaction is given by the sum of all stoichiometric coefficients of the educts, i.e. ݊ ൌ ݊_ܣ൅ ݊_ܤ Here, it should be stressed again that this reaction order is only identical with the molecularity of the reaction, i.e. the total number of molecules reacting, if the whole process consists of a single reaction step!

Importantly, for more complex reactions which usually consist of multiple reaction steps, one has to distinguish clearly between the order of the reaction and the molecularity of the individual reaction steps: the order corresponds to a macroscopic experimental quantity, namely the exponent with which the reactions velocity scales with the respective concentration (see Eq.3.3). On the other hand, the molecularity of a single reaction step corresponds to the microscopic mechanism of this reaction step. As a consequence, a chemical reaction which is experimentally found to be of 2^nd order must not necessarily be a bimolecular reaction, since a combination of several reaction steps of different molecularities can lead to an overall reaction order of 2. Actually, a variety of possible combinations of elementary reaction steps (= proposed mechanisms of a chemical reaction) may lead to the same experimental result concerning the order of a chemical reaction!

In the first section of this chapter about chemical kinetics, we will mathematically treat the kinetics of the simplest case possible, elementary reactions with only a single educt species (section 3.1.1), or bimolecular reactions with two different educt species A, B (section 3.1.2.).

Basic Physical Chemistry

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Kinetics