# A student wishes to reduce the zinc ion concentration in a saturated zinc iodate solution to 1 xx 10^-6 M. How many moles of solid KIO_3 must be added to 1.00 L of solution? [K_(sp) Zn(IO_3)_2 = 4 xx 10^-6 at 25°C)?

Jun 1, 2018

So this is a ${K}_{\text{sp}}$ problem, for which you have provided the relevant data...

#### Explanation:

$Z n {\left(I {O}_{3}\right)}_{2} \left(s\right) r i g h t \le f t h a r p \infty n s Z {n}^{2 +} + 2 I {O}_{3}^{-}$...
for which ${K}_{\text{sp}} = \left[Z {n}^{2 +}\right] {\left[I {O}_{3}^{-}\right]}^{2} \equiv 4.0 \times {10}^{-} 6$...
We will be requiring that $Z {n}^{2 +} \equiv 1.0 \times {10}^{-} 6 \cdot m o l \cdot {L}^{-} 1$ by the terms of the question...and thus we solve for $\left[I {O}_{3}^{-}\right]$ in the given equation.....
$\left[I {O}_{3}^{-}\right] = \sqrt{{K}_{\text{sp}} / \left[\left[Z {n}^{2 +}\right]\right]} = \sqrt{\frac{4.0 \times {10}^{-} 6 \cdot m o l \cdot {L}^{-} 1}{1.0 \times {10}^{-} 6 \cdot m o l \cdot {L}^{-} 1}}$
$\sqrt{4} = 2 \cdot m o l$...I must be clever cos I did this all in my nut!