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Transcript of Activity and Activity Coeff2
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Activity and Activity Coefficients
The chemical potential of a real or ideal solvent is given by the
following equation.
For an ideal solution the solvent obeys Raoults law at all
conditions and we write
The above form of the equation can be retained when the
solution does not obey Raoults law by writing
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The quantity aA
is the activity of a, a kind of effective mole
fraction just like the fugacity is an effective pressure. Because
(1) is true for both real and ideal solutions (the only
approximation being the use of pressures rather than
fugacities), we can conclude by comparing it with equation( 3)
and get,
[There is nothing mysterious about the activity of a solvent.
It can be determined experimentally simply by measuringthe vapor pressure and then using equation (4)]
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Because all solvents obey Raoults law
increasingly closely as the concentration of the solute
approaches zero, the activity of the solvent
approaches the mole fraction as
As in the case of real gases, a convenient way of
expressing this convergence is to introduce theactivity coefficient , by the definition
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Mean Activity Coefficients
In the chemical potential of a univalent cation M+ is denoted as
the Q+ and that of a univalent anion X-
as Q- , the total molarGibbs energy of the ions in the electrically neutral solution is the
sum of these partial molar quantities. The molar Gibbs energy of
an ideal solution is
All the deviation from ideality are contained in the last term.
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There is no experimental way of separating the product into
contributions from the cations and anions. The best way wecan do experimentally is to assign responsibility for the non-
ideality equally to both kinds of ions. Therefore for a 1,1
electrolyte, we introduce the mean activity coefficient as the
geometric mean of the individual coefficients
And express the individual chemical potentials of the ions as
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The sum of these two chemical potentials is the same as
before, in (6) but now the non ideality is shared equally.
In general
s = p+q
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Methods of Determining Activity Coefficients
1.E M F METHOD
This method may be illustrated by taking a specific case of
silver-silver chloride electrode. The half electrode is combined
with a hydrogen electrode to yield a cell
The electrode reactions of this cell are
Left electrode:
:
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Right electrode:
Overall reaction:
The emf of the cell is
E=ER-EL
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In terms of , the mean activity of hydrochloric acid
, equation 4 can be written as
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At 298 K,
From Debye Huckel limiting law,
for a 1:1 electrolyte and therefore equation 7 becomes
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By measuring emf of the cell at different
molalities of hydrochloric acid, the quantity on
the left is calculated and then plotted as a
function of m and extrapolated to m=0. The
intercept on the y axis gives the value of thestandard potential of silver-silver chloride
electrode
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Measurement of cell emf is a powerfultechnique in the evaluation of activities and
activity coefficients. E0 value for the cell is first
accurately obtained by extrapolation as was
done in the previous section. The mean activity
( a
) or the mean activity coefficient (K
) at
any other concentration of the electrolyte can
then be calculated by measuring of the emf ofthe cell at that concentration.
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2.SOLUBILITY METHOD
If one molecule of the substance dissociates intopositive and negative ions, thus,
Since and are constant at a given temperature, and is a
constant as long as the solution is saturated, if follows
that
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The constant Ks is the activity solubility product, and equation
(11a) expresses the solubility product principle. The activitiesmay be written as the product of the respective
concentrations and activity coefficients, so that
for a saturated solution. If S is the solubility of the salt in moles
per liter is equal to and to and hence (12)
becomes
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Where is equal to the total number of ions, i.e., + produced from
one molecule upon ionization and is the mean activity coefficient. It
follows therefore, from (13), since and are constants for the given
electrolyte, that
If two solutions, which may contain added salts, are designated I and
II it follows from (14) that,
a result which may be employed to determine the mean activity
coefficient of a sparingly soluble salt. This is done by making solubility
measurements in the presence of added salts at various ionic
strengths, and extrapolating to infinite dilution. Since is then unity,
the extrapolated solubility gives the constant of (15) ; once this is
known the mean activity coefficient can be evaluated from solubility
measurements in any solution.