Thermodynamic activity

The activity is a thermodynamic quantity which is used in the physical chemistry in place of the substance concentration. With it apply to real mixtures, the same laws (regarding physical measurement parameters such as freezing, boiling point, conductivity of electrolyte solutions, electrical voltage, vapor pressures of solvents), such as the concentration for ideal mixtures.

The dimensionless activity coefficient is the ratio of the activity to the concentration. It is to the ideal behavior that is observed at infinite dilution at 1 and differs with increasing concentration.

• 5.1 the field of engineering
• 5.2 Electrochemistry

Introduction

With activities electrolyte solutions ( conductivity ), vapor pressure of a solvent system, amounts of gas in liquids, freezing point, boiling point changes, osmotic pressures and changes in the amount of volume, the temperature change of solvent mixtures are described accurately. The actual concentration of the added substance results in a non-proportional change in the physical variable ( eg conductivity ), so that the product of the activity coefficient and concentration indicates the measured value on the observed proper concentration ( activity ). The variations in the measured values ​​are based on Coulomb interactions of salt ions, hydrogen bonds or van der Waals interactions in solvent systems. The word activity coefficient was first proposed by Svante Arrhenius for the exact description of the dissociation (chemistry) needed.

In electrolyte systems, the respective activity coefficient can be calculated based on the charges of individual ions or be quickly determined by conductivity measurements. The activity coefficient is in electrolyte solutions is almost always less than 1, and is converged at very high dilution to 1 for very concentrated electrolyte solutions, the activity coefficient can be greater than 1. The determination of an activity coefficient for a specific ion species is not possible, because the cations and anions in the electrolyte are present together. Electrolyte solutions are added, therefore, to have an average activity coefficients, which indicates the physical deviations of both ions. Ions in water and other solvents attach themselves to other ions of opposite charge. Wherein the ions are shielded, there is interaction, namely the stronger the higher the concentration and the higher the charge of the respective ion. In very high dilution ( 0.00001 molar) these interactions disappear. For determination of the equivalent conductivity of the conductivity limit of salts, acids and bases, however, the activity coefficients of the Debye- Huckel theory may not be used. The latter coefficients apply to the law of mass action and for the solubility product, the dependencies of the conductivity can be described by the carbon intoxication law.

Even with mixtures of several solvents may lead to interactions that are manifested in volume, temperature or steam pressure changes. For a pure solvent of vapor pressure at a given temperature can be determined accurately. Therefore, should in an ideal behavior in a solvent mixture in the vapor phase mole fractions of the respective amounts of gas after their interests in the solvent mixture find ( Dalton 's law). In many real solvent mixtures, however, one observes a non-ideal behavior. There interactions may occur higher or lower vapor pressures of the individual components by van der Waals. Also in this case is used for describing the activity coefficient of the real situation. In this case, the activity coefficient can be greater than 1. In the fractional distillation of mixtures of substances, therefore, the knowledge of the activity coefficients, or fugacity coefficient ( at pressures ) is particularly important because the gas phase enriched in the component can be determined exactly so.

Also in the reverse case, the solution of a gas in a liquid, the gas solubility is often approximately proportional to the gas pressure ( Henry 's law). Also in this case there are deviations from the ideal behavior, so that the activity coefficient is used. Further, volume, temperature changes may occur during the mixing of solvent or in a paste of salts in solvents which are not also in proportion to the concentration of the added material.

Ideal mixtures are characterized in that no mixing effects occur, that is, that the volume on mixing the pure components does not change (at constant pressure ) and the temperature and thermodynamically important quantities such as enthalpy or heat capacity multiplied additively from the values ​​of the individual components with the respective mole fractions ( mole fractions ) put together. This is only the case when the components are chemically very similar, so that the interactions between particles of different varieties is the same as the interactions between identical particles. In general, this is not the case, so you have it with real rather than to do with ideal mixtures. In real mixtures, the thermodynamic quantities volume, internal energy and enthalpy are not additive composed of the weighted with the mole fraction values ​​of the individual components. To the equations for ideal mixtures to be able to apply them to real mixtures, the activity is introduced, which is defined such that in the exchange of mole fractions by the activities of the additive context of the thermodynamic quantities for the mixture of the corresponding quantities for the individual components is also given for real mixtures. In ideal mixtures, the activity of a component corresponds to exactly the mole fraction of the component in real mixtures of the two variables in the rule will differ.

Definition

The (relative) activity is defined by:

Here represents the activity for the absolute temperature, for the chemical potential and the chemical potential under standard conditions. is the universal gas constant.

In an ideal mixture results in the chemical potential of the components from the equation

Where the mole fraction ( mole fraction ) is the component i.

For a real mixture, a correction must be made:

The activity is associated with the amount of substance by the following relationship:

The dimensionless factor is called the activity coefficient. While no intermolecular interactions are present in an ideal mix, and thus the chemical potentials and all associated values ​​are due to the mole fractions of the components are present in a real mixing interaction between the particles. These interactions may e.g. be electrostatically. The activity coefficient accurately describes these deviations from the ideal behavior of the mixture. He was introduced by Gilbert Newton Lewis in 1907 as a purely empirical size for strong electrolytes. Svante Arrhenius and Jacobus Henricus van't Hoff used the expression activity coefficient bit earlier for the degree of dissociation at the freezing point depression by salts.

One approach is that one chooses a very small quantities of material. This leads (of course only in theory ) to the following considerations / results:

• Few particles to a large distance of the particles and thus no interactions
• It can be neglected interactions with the vessel walls

In solutions is still assumed that no significant interaction between the solvent and solute are present. Mathematically, the approximations expressed as follows:

The approximation for solutions at concentration ranging from about relatively well (of course it also depends on the measurement method used to ). The divisor follows from the dimension of the chemical potential: Should be a dimensionless, one must divide the corresponding concentration by any concentration. By definition, the standard concentration used. To return now to go the step to real mixtures, the required terms are simply multiplied by the activity coefficient.

Activity of a solvent

In solutions, the activity of a substance defined by

The vapor pressure of the pure solvent is (to be chosen as Standardfugazität ), the vapor pressure of the solvent in the solution (actually the fugacity ). a is seen in this case analogous to the mole fraction: This is the mole fraction, which is crucial in considerations of the system. The Raoult's law applies to the more solvent, the closer is the mole fraction approaches 1, ie the purer the solvent. In order to describe the behavior clearly, a correction factor was also introduced here, which is now defined as follows:

With for

This relationship can be derived from the chemical potential and the Raoult's law.

Border activity coefficient

Activity coefficient of the boundary is the activity coefficient at infinite dilution of a component () in a solvent or a solvent mixture.

Type of ions and the electrolyte

The determination of the activities based on the dissociation of electrolytes. Van't Hoff certain lowering of vapor pressure, osmotic pressure, boiling point elevation, freezing point depression of electrolyte solutions and could see significant deviations from the molecular weight determination in very dilute salt solutions. By conductivity measurements almost identical variations as the freezing point depression were observed. Later activity coefficients were also determined by potential measurements. Between the different methods, there are slight variations between the determined activity coefficients, so that an indication of the type of design should not be missed. Thanks very inexpensive electronic instruments, the determination of activity coefficients in aqueous solutions has become very simple and straightforward.

By 1920, however, it was a very arduous task for chemists from electrolyte solutions to determine the activity coefficients. Debye and Huckel ( Debye- Hückel theory ) were able to provide a very nice theory on the behavior of electrolyte in the electrolyte solution in 1923.

For dilute electrolytes can be the activity coefficient from the Debye- Hückel theory to calculate. However, this purely mathematical method is reasonably accurate only at solutions to 0.01 mol / l. It should be noted that the above defining equation is valid only for each individual ion species

However, since any solution must be electrically neutral, that is, must have equal number of positive and negative charges, individual activities can be calculated, although useful, but not measured. For according to the equation

Completely dissociated electrolyte is true if we the indices for the cations and - use of the anions,

In order to simplify

The mean activity

And the average activity coefficient

Defined. can be measured, for example in galvanic cells. Then apply to the average activity of the electrolyte

Examples:

Activity coefficient

Field of engineering

In the technical field are used for the assessment of the activity coefficient known models such as NRTL ( non -random two- liquid), UNIQUAC (Universal Quasi Chemical) and UNIFAC (Universal Quasi Chemical Functional Group Activity Coefficients ) are used.

Electrochemistry

According to the interpretation of Debye and Hückel is the electrostatic potential energy which arises when one mole of the ion type A is charged from the discharged state to its fictive real amount of charge within its oppositely charged ion cloud. This potential energy is thus negative ( "You have to put in energy to remove the ion species A from its ion cloud ").

Debye- Hückel:

Therein is the universal gas constant and temperature. W is negative; thus lies between 0 and 1 requires the theory of Debye- Hückel a strong dilution of A.

Experimental measurements showed a dependence between the ion concentration of A and its activity coefficient. For large concentrations of A is greater than one ( "I win energy when I remove A "). Large ion concentrations of A are not considered by the Debye- Hückel theory.

Example: For a 1-molar acetic acid = 0.8 and 0.1 M acetic acid 0.96.

A method for the estimation of activity coefficients is the regular solution theory. The activity coefficient is written a = f × c. C is the concentration, and f is the activity coefficient of the A type.