Page:Text-book of Electrochemistry.djvu/185

 170 THE DISSOCIATION THEORY. chap.

If, now, the specific gravity of solutions of a substance, A, can be found from —

S = 1 + an,

and that of solutions of another substance, B, from —

S=l + fin,

then for solutions containing both substances, 7i-normal with respect to A, and iii normal with respect to B, we have —

/S* = 1 + a>i +/3711.

If we take the case of a highly dissociated salt, c.ff. sodium chloride, we may for the present purpose assimie that it is completely dissociated in dilute solution. The solution con- tains in unit volume a certain number (n) of sodium ions, and the same number of chlorine ions. Let us now set the coefficient of the chlorine ions = a, of the sodium ions = /3, and, further, the coefficients for bromine ions = 7, and for ammonium ions = S, then we obtain for 0'1-normal solutions of the salts sodium chloride (a), sodium bromide (b), ammonium chloride (c), and, ammonium bromide (d) the equations —

.S: = 1 + 0-l(« + /3),

S, = l + O'lQi + y), 5. = 1 + 0-l(a + 8), .S:, = 1 + 0-1(7 + ^)-

Consequently —

This illustrates a typical additive property. If we have numerical data of a property for equally concentrated solu- tions of four salts, AiKi, A1K2, A2K1, and A2Ka, which are formed from a pair of positive ions, K, and a pair of negative ions. A, then the diflFerence in the value of this property for the salts AiKi and A1K2 is the same as the difference between the salts A2K1 and A2K2. We may put this in the form —

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