Activities and Activity coefficients of strong electrolytes:

    The thermodynamics and other properties of the solutions of non-electrolytes can be adequately expressed in terms of their concentrations, even at moderate concentrations. But the solutions of electrolytes exhibit marked derivation even at relatively low concentrations. Dilute ionic solutions have a concentration of 0.001 m or even less. According to Debye's huckle theory of interionic attraction, the electrostatic attractions between ions in the solution of an electrolyte have a significant influence on the mobility of ions. The ionic concentrations in case of weak electrolytes, being low don’t show applicable derivations from the ideal behavior. But in solutions of strong electrolytes, the ionic concentrations are large, so interionic forces can’t be neglected. Due to electrostatic attraction between in a fraction of cations and ions, the solutions exhibit the properties of one in which the effective or apparent concentrations of the ions are less than the theoretical concentrations depending on the relative importance of factors, such as ion-ion concentrations and ion solvent interactions, the effective concentrations of the solute dissolved in water may appear to be less than, equal to or greater than the molal concentration. This effect becomes more significant at higher concentrations and increases the valance of the ions.

    G.N Lewis suggested due to restricted, mobility of the ions in solutions of strong electrolytes the ions don’t exert their full effect for showing their behavior. He proposed the term activity in place of concentration terms (molarity, molality, mole fraction, formality). So as to explain the departure of electrolytes solution from ideal behavior. To distinguished between the molar and molal or formal of a substance in the effective concentration of an ion a solution is called its activity. It is the customer to relate the activity of a species to its concentration through the expression.

ai= Ï’imi

in which ai is the activity of the substance I, Ï’i, is the activity coefficient of the substance I, and mi is the molar concentration of the substance i. The activity coefficient(Ï’) is not a constant and its value varies with the concentration. For aqueous solutions, both activity and concentration are expressed in the same units, so that the activity coefficient is dimensionless. [For dilute solutions, the molarity is almost numerically equal to molality, which is the preferred unit for colligative properties (because then the properties of the solutions don’t depend on the identity for the solutes). Therefore, we can shift from molarity concentration units to molality concentration units].

For dilute solutions (<0.001m), the electrostatic attractions can be neglected,

ai= mi

and the value of Ï’i becomes unity, For electrolytes, such as NaCl, The activity of Na+  and Cl-  ions can be written as

a+= Ï’+ m+

and a-=Ï’- m-

    since it isn’t possible to get only positive and negative ions in the solution of an electrolyte, there is no experimental method available to determine the activity or activity coefficient of individual ionic species. The reason is the solutions are electrically neutral and we can’t increase the number of cations without an equal increase in the number of anions. Since we can’t study relatively the effects of cations and anions in the presence of each other in a neutral solution is there for, it not possible to measure the individual ion activities. Fortunately for more purposes, it is sufficient to know the means of ionic activity(a±) and the mean activity coefficient (Ï’±).

    Since it is possible to substitute concentrations for activities in ionic solutions, it is essential to consider how the ionic concentrations may be converted to the activities and how such activities can be evaluated in order to introduce some definitions commonly employed in dealing with activities of the strong electrolytes. Consider an electrolyte AxBy which ionize in the solution according to

Ax By= XAz+ + yBz-

 When Z+ and Z- are the charges on the cation and anion respectively. the activity of the electrolyte as a whole, a2, is defined in terms of the activities of the two ions, a +and a - as

                        a2=ax+ay-

If V is the total number of the ions furnished by one molecule of the electrolyte, I. e  V= x +y, then mean activity is defined as

            a±=(a2)1/v =(ax+ay-)1/v

The activities of the ions are related to their concentration through the relation.

            a+= Ï’+m+

            a.= Ï’-m.

    Where m+ and m- are the modalities of the cation and anions and y and y are the corresponding activity coefficients. These activities coefficients are appropriate factors that when multiplied by the modalities of the respective ions yield their activities. introducing Eq (09 .06) and (9.67) into Eq  (9.64) . we obtain for as

a2=(m+ Ï’ +)X (m- Ï’ -) y

   a2= (m+x my-) (Ï’ x+ Ï’ y-)

and for mean activity from Eq. (9.65)

a±=(a2)1/v = ( m+xmy-) 1/v  Ï’ x+ Ï’ y-)1/v3

the factor (mx+yy-)1/v is defined as the mean molality of the electrolyte.

m± =(m+xmy-)1/v

similarly ( Ï’ x+ Ï’ y-)1/v is known as the mean activity coefficient.

 Ï’ ±= ( Ï’ X+ Ï’ y-)1/v

in term of mean molality and mean activity coefficient, Eq (9.68) and (9.69) may be written as

a2    =ay±=m±  y±

a± = a21/v   =   (m± y± )v

                 finally since for any electrolyte of molality m,we have

m+ = xm

m-=ym

Eqs. (9.70) and (9.71) then take the form

a±(m x+m-y)1/v  Ï’±

            =[ (xm)x ( ym)y ]1/v Ï’ ±   

            = [  (xx mx) (yymy) ] 1/v  Ï’±

                                =[(xxyy)1/v (mx+y) ] 1/v Ï’±

                                =[(xxyy)1/v m Ï’±

and                           a2=(a±)v=[(xxyy)1/vm Ï’±]v

                        = (xxyy)mv Ï’v±

equation (9.72) and (9.73) are the expression needed for converting activities to modalities or vice versa .thus for 1.1 electrolyte such as KCL,of molality

m, we have x =1, y =1,v=2  and therefore.

a ±= ( 1x1) 1/2m Ï’±

a 2=a2± =m2y2±

again for an electrolyte of the 2:1 type, such as BaCl2  we have c=1,y=2 and V= 3

a±=(1x22) 1/3 m Ï’±

= (4)1/3m Ï’±

a2=a3±=4m3 Ï’3±

Example 9.5.

calculate the mean and total activity of the following electrolytes

 (Ä°) CuSO4    

  (Ä°Ä°)  Na3  PO 4

(Ä°Ä°Ä°) Ca3 (PO4 )2

Solution:

(Ä°)  CuS4 x=1,y=1,and v=1+1=2

            a± =(1x1) ½ m Ï’±

                = m Ï’±

a2= (a±)2=m2 Ï’2±

(Ä°Ä°)  Na3PO4 X=3,Y=1,V=X+Y=4

                a±= (33x11)1/4m Y ± = (27)1/4   mY±

                a2=(a±)4 27 m 4 Y4±

(Ä°Ä°Ä°) Ca3(PO4) 2X =3,Y=2,V=X+Y=3+2=5

a±=(3322)1/5 m Ï’± = (108) 1/5 m Ï’ ±

a2=108m5 Ï’5±

Example 9.6 calculate the mean activity of the ions and activity of the electrolyte in 0.1m Na Cl solution. the Ï’± is 0.778

solution:

                        m=0.1 and Ï’±= 0.778

                        a±=m Ï’±=0.1 x0.778=0.0778

                        a2=(a±)2=(0.0778)2=6.05x103



By: Muzalim Kahlid 

The writer is a post-graduate student from the Chemistry Department University of Turbat 

Kech Balochistan