activity and activity coeff2

8/6/2019 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.

activity and activity coeff2

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