# Problem: Calculate the equilibrium concentration of Zn2+ in a 0.30-M solution of Zn(CN)42−.

###### FREE Expert Solution

The equilibrium expression, Kd for the dissociation of the complex Zn(CN)42- is:

**Exponent is equal to the stoichiometric coefficient

First, we need to construct an ICE table for the dissociation of Zn(CN)42-

Next, we calculate for x, to determine the equilibrium concentration of Zn2+ and CN-

Kd = 2.1 × 1019

${\mathbf{K}}_{\mathbf{d}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{1}\mathbf{×}{\mathbf{10}}^{\mathbf{19}}\mathbf{=}\frac{\mathbf{\left[}{\mathbf{Zn}}^{\mathbf{2}\mathbf{+}}\mathbf{\right]}{\mathbf{\left[}{\mathbf{CN}}^{\mathbf{-}}\mathbf{\right]}}^{\mathbf{4}}}{\mathbf{\left[}\mathbf{Zn}{{\mathbf{\left(}\mathbf{CN}\mathbf{\right)}}_{\mathbf{4}}}^{\mathbf{2}\mathbf{-}}\mathbf{\right]}}\phantom{\rule{0ex}{0ex}}{\mathbf{K}}_{\mathbf{d}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{1}\mathbf{×}{\mathbf{10}}^{\mathbf{19}}\mathbf{=}\frac{\mathbf{x}{\mathbf{\left(}\mathbf{4}\mathbf{x}\mathbf{\right)}}^{\mathbf{4}}}{\left(0.30-x\right)}\phantom{\rule{0ex}{0ex}}\mathbf{2}\mathbf{.}\mathbf{1}\mathbf{×}{\mathbf{10}}^{\mathbf{19}}\mathbf{=}\frac{\mathbf{256}{\mathbf{x}}^{\mathbf{5}}}{\left(0.30-x\right)}\phantom{\rule{0ex}{0ex}}$

We can ignore the term "-x" in the denominator to simplify the equation, assuming x is a small value:

$\mathbf{2}\mathbf{.}\mathbf{1}\mathbf{×}{\mathbf{10}}^{\mathbf{19}}\mathbf{=}\frac{\mathbf{256}{\mathbf{x}}^{\mathbf{5}}}{\left(0.30\overline{)-x}\right)}\phantom{\rule{0ex}{0ex}}\mathbf{2}\mathbf{.}\mathbf{1}\mathbf{×}{\mathbf{10}}^{\mathbf{19}}\left(0.30\right)\mathbf{=}\frac{\mathbf{256}{\mathbf{x}}^{\mathbf{5}}}{\overline{)\left(0.30\right)}}\overline{)\mathbf{\left(}\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{\right)}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{\mathbf{6}\mathbf{.}\mathbf{3}\mathbf{×}{\mathbf{10}}^{\mathbf{18}}}{\mathbf{256}}\mathbf{=}\frac{\overline{)\mathbf{256}}{\mathbf{x}}^{\mathbf{5}}}{\overline{)\mathbf{256}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\sqrt[\mathbf{5}]{\mathbf{2}\mathbf{.}\mathbf{461}\mathbf{×}{\mathbf{10}}^{\mathbf{16}}}\mathbf{=}\sqrt[\mathbf{5}]{{\mathbf{x}}^{\mathbf{5}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{x}\mathbf{=}\sqrt[\mathbf{5}]{\mathbf{2}\mathbf{.}\mathbf{461}\mathbf{×}{\mathbf{10}}^{\mathbf{16}}}$

###### Problem Details

Calculate the equilibrium concentration of Zn2+ in a 0.30-M solution of Zn(CN)42−.