Mistake in EOC problem 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^3 has a larger numerical value than s^2.  That's true if
s is greater than 1.  But s is given in the questions 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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