Answer

(a) Ephedrine sulfate is a 1:2 electrolyte and hence the ionic strength is given by equation (3.37) as

I = ±[(0.002 x 2 x 12) + (0.002 x 22)] = 0.006 mol kg-1

From the Debye-Huckel equation (equation 3.36),

- log y± = 0.509 x 1 x 2 x V0.006 log y± = -0.0789 Y& = 0.834

The mean ionic activity may be calculated from equation (3.35):

(b) Ionic strength of 0.01 mol kg 1 NaCl = 2 (0.01 X 12) + (0.01 X 12) = 0.01 mol kg-1.

Total ionic strength = 0.006 + 0.01 = 0.016 -log y& = 0.509 x 2 x V0.016 log y& =-0.1288 Y & = 0.743

Box 3.4 Mean ionic parameters

In general, we will consider a strong electrolyte which dissociates according to

Cv+Av-2v+Cz+ + v_Az-where v+ is the number of cations, Cz+, of valence z+, and v_ is the number of anions, Az-, of valence z-. The activity, a, of the electrolyte is then a = a++a-- = av± (3.26)

In the simple case of a solution of the 1:1 electrolyte sodium chloride, the activity will be a = aNa x aCi = a± whereas for morphine sulfate, which is a 1:2 electrolyte,

Similarly, we may also define a mean ion activity coefficient, y±, in terms of the individual ionic activity coefficients y+ and y 0:

For a 1 : 1 electrolyte equation (3.28) reduces to

Finally, we define a mean ionic molality, m±, as mv± = m++m-- (3.30)

For a 1 : 1 electrolyte, equation (3.31) reduces to that is, mean ionic molality may be equated with the molality of the solution.

The activity of each ion is the product of its activity coefficient and its concentration a+= y+m+ and a_ = y_m_ so that y+=— and y_ = —

Expressed as the mean ionic parameters, we have a&

Substituting for m& from equation (3.31) gives a&

This equation applies in any solution, whether the ions are added together, as a single salt, or separately as a mixture of salts. For a solution of a single salt of molality m:

Equation (3.34) reduces to a±

For example, for morphine sulfate, v+ = 2, v_ = 1, and thus a& a&

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