Mistake in EOC exercise 17.50(a) solution (section 17.4)

[Zellmer, Robert]

The answer in the solutions manual for 17.50(a) end-of-chapter problem is
incorrect.  The Ksp for MZ2 is smaller than the Ksp for MA. The manual does
this in terms of "s" (the solubility) and has the wrong formula for the Ksp for MZ2.

Ksp (for MA) = [M][A] = s^2

Ksp (for MZ2) = [M][Z]^2 = 4 s^3

The solutions manual states the later is 4s^2 (which is wrong).  It then proceeds
to say essentially that 4s^2 has a larger numerical value than s^2.  That's
certainly true if it were actually 4s^2 compared to s^2.  However, it should be
4s^3 compared to s^2.  In this case 4s^3 is not necessarily greater than s^2.
That's true if "s" is greater than 1.  But "s" is given in the question as 4 x 10^-4 M.
When you raise a number less than one to a power the result actually gets smaller
as the power gets larger.

Ksp (for MA) = [M][A] = s^2 = (4 x 10^-4)^2 = 1.6 x 10^-7

Ksp (for MZ2) = [M][Z]^2 = 4 s^3= 4*(4 x 10^-4)^3 = 2.6 x 10^-10

So Ksp (for MZ2) is smaller than Ksp (for MA).

Dr. Zellmer
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