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Applied Chemistery-I
Session 2009-10 , UET Lahore
Activity (chemistry)
In chemical thermodynamics activity (symbol: a) is a measure of the “effective concentration” of a
species in a mixture. By convention, it is a dimensionless quantity. The activity of pure substances in
condensed phases (solid or liquids) is normally taken as unity. Activity depends on temperature,
pressure and composition of the mixture, among other things. For gases, the effective partial pressure is
usually referred to as fugacity.
The difference between activity and other measures of composition arises because molecules in nonideal gases or solutions interact with each other, either to attract or to repel each other. The activity of
an ion is particularly influenced by its surroundings.
Activities should be used to define equilibrium constants but, in practice, concentrations are often used
instead. The same is often true of equations for reaction rates. However, there are circumstances where
the activity and the concentration are significantly different and, as such, it is not valid to approximate
with concentrations where activities are required. Two examples serve to illustrate this point:


In a solution of potassium hydrogen iodate at 0.02 M the activity is 40% lower than the
calculated hydrogen ion concentration, resulting in a much higher pH than expected.
When a 0.1 M hydrochloric acid solution containing methyl green indicator is added to a 5 M
solution of magnesium chloride, the color of the indicator changes from green to yellow—
indicating increasing acidity—when in fact the acid has been diluted. Although at low ionic
strength (<0.1 M) the activity coefficient decreases with increasing ionic strength, this
coefficient can actually increase with ionic strength in a high ionic strength regime. For
hydrochloric acid solutions, the minimum is around 0.4 M.[1]
Definition
The activity of a species i, denoted ai, is defined[2][3] as:
where μi is the chemical potential of the species under the conditions of interest, μoi is the chemical
potential of that species in the chosen standard state, R is the gas constant and T is the thermodynamic
temperature. This definition can also be written in terms of the chemical potential:
Hence the activity will depend on any factor that alters the chemical potential. These include
temperature, pressure, chemical environment etc. In specialised cases, other factors may have to be
considered, such as the presence of an electric or magnetic field or the position in a gravitational field.
However the most common use of activity is to describe the variation in chemical potential with the
composition of a mixture.
The activity also depends on the choice of standard state, as it describes the difference between an
actual chemical potential and a standard chemical potential. In principle, the choice of standard state is
arbitrary, although there are certain conventional standard states which are usually used in different
situations.
Activity coefficient
Main article: Activity coefficient
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
The activity coefficient γ relates the activity to a measured amount fraction xi, molality
mi or amount concentration ci:
The division by the standard molality mo or the standard amount concentration co is necessary to ensure
that both the activity and the activity coefficient are dimensionless, as is conventional.
When the activity coefficient is close to one, the substance shows almost ideal behaviour according to
Henry's law. In these cases, the activity can be substituted with the appropriate dimensionless measure
of composition xi, mi/mo or ci/co. It is also possible to define an activity coefficient in terms of Raoult's
law: the International Union of Pure and Applied Chemistry (IUPAC) recommends the symbol ƒ for
this activity coefficient,[3] although this should not be confused with fugacity.
Standard states
Gases
In most laboratory situations, the difference in behaviour between a real gas and an ideal gas is
dependent only on the pressure and the temperature, not on the presence of any other gases. At a given
temperature, the "effective" pressure of a gas i is given by its fugacity ƒi: this may be higher or lower
than its mechanical pressure. By historical convention, fugacities have the dimension of pressure, so
the dimensionless activity is given by:
where φi is the dimensionless fugacity coefficient of the species, xi is its fraction in the gaseous mixture
(x = 1 for a pure gas) and p is the total pressure. The value po is the standard pressure: it may be equal
to 1 atm (101.325 kPa) or 1 bar (100 kPa) depending on the source of data, and should always be
quoted.
Mixtures in general
The most convenient way of expressing the composition of a generic mixture is by using the amount
fractions x of the different components, where
The standard state of each component in the mixture is taken to be the pure substance, i.e. the pure
substance has an activity of one. When activity coefficients are used, they are usually defined in terms
of Raoult's law,
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
where ƒi is the Raoult's law activity coefficient: an activity coefficient of one indicates
ideal behaviour according to Raoult's law.
Dilute solutions (non-ionic)
A solute in dilute solution usually follows Henry's law rather than Raoult's law, and it is more usual to
express the composition of the solution in terms of the amount concentration c (in mol/L) or the
molality m (in mol/kg) of the solute rather than in amount fractions. The standard state of a dilute
solution is a hypothetical solution of concentration co = 1 mol/L (or molality mo = 1 mol/kg) which
shows ideal behaviour (also referred to as "infinite-dilution" behaviour). The standard state, and hence
the activity, depends on which measure of composition is used. Molalities are often preferred as the
volumes of non-ideal mixtures are not strictly additive and are also temperature-dependent: molalities
do not depend on volume, whereas amount concentrations do. [4]
The activity of the solute is given by:
Ionic solutions
When the solute undergoes ionic dissociation in solution (a salt e.g.), the system becomes decidedly
non-ideal and we need to take the dissociation process into consideration. We can define activities for
the cations and anions separately (a+ and a–).
It should be noted however that in a liquid solution the activity coefficient of a given ion (e.g. Ca2+)
isn't measurable because it is experimentally impossible to independently measure the electrochemical
potential of an ion in solution. (We cannot add cations without putting in anions at the same time).
Therefore one introduces the notions of
mean ionic activity
a±ν = a+ν+a–ν–
mean ionic molality
m±ν = m+ν+m–ν–
mean ionic activity coefficient
γ±ν = γ+ν+γ–ν–
where ν = ν+ + ν– represent the stoichiometric coefficients involved in the ionic dissociation process
Even though γ+ and γ– cannot be determined separately, γ± is a measureable quantity that can also be
predicted for sufficiently dilute systems using Debye–Hückel theory. For the activity of a strong ionic
solute (complete dissociation) we can write:
a 2 = a ± ν = γ ± νm ± ν
Measurement
The most direct way of measuring an activity of a species is to measure its partial vapor pressure in
equilibrium with a number of solutions of different strength. For some solutes this is not practical, say
sucrose or salt (NaCl) do not have a measurable vapor pressure at ordinary temperatures. However, in
such cases it is possible to measure the vapor pressure of the solvent instead. Using the Gibbs–Duhem
relation it is possible to translate the change in solvent vapor pressures with concentration into
activities for the solute.
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
Another way to determine the activity of a species is through the manipulation of
colligative properties, specifically freezing point depression. Using freezing point
depression techniques, it is possible to calculate the activity of a weak acid from the relation,
where m' is the total molal equilibrium concentration of solute determined by any colligative property
measurement(in this case ΔTfus, m is the nominal molality obtained from titration and a is the activity of
the species.
There are also electrochemical methods that allow the determination of activity and its coefficient.
The value of the mean ionic activity coefficient γ± of ions in solution can also be estimated with the
Debye–Hückel equation, the Davies equation or the Pitzer equation.
Use
Chemical activities should be used to define chemical potentials, where the chemical potential depends
on the temperature T, pressure p and the activity ai according to the formula:
where R is the gas constant and µio is the value of µi under standard conditions.
Formulae involving activities can be simplified by considering that:

For a chemical solution:
o the solvent has an activity of unity
o At a low concentration, the activity of a solute can be approximated to the ratio of its
concentration over the standard concentration:
Therefore, it is approximately equal to its concentration.

For a mix of gas at low pressure, the activity is equal to the ratio of the partial pressure of the
gas over the standard pressure:
Therefore, it is equal to the partial pressure in bars (compared to a standard pressure of 1 bar).

For a solid body, a uniform, single species solid at one bar has an activity of unity. The same
thing holds for a pure liquid.
The latter follows from any definition based on Raoult's law, because if we let the solute concentration
x1 go to zero, the vapor pressure of the solvent p will go to p*. Thus its activity a = p/p* will go to
unity. This means that if during a reaction in dilute solution more solvent is generated (the reaction
produces water e.g.) we can typically set its activity to unity.
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
Solid and liquid activities do not depend very strongly on pressure because their molar
volumes are typically small. Graphite at 100 bars has an activity of only 1.01 if we
choose po = 1 bar as standard state. Only at very high pressures do we need to worry about such
changes.
Example values
Example values of activity coefficients of sodium chloride in aqueous solution are given in the table. In
an ideal solution, these values would all be unity. The deviations tend to become larger with increasing
molality and temperature, but with some exceptions.
Molality
(mol/kg)
25
°C
50
°C
0.05
0.820
0.814
0.794
0.725
0.592
0.473
0.50
0.680
0.675
0.644
0.619
0.322
0.182
2.00
0.669
0.675
0.641
0.450
0.212
0.074
5.00
0.873
0.886
0.803
0.466
0.167
0.044
5
100
°C
200
°C
300
°C
Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
350
°C