${\mathbf{K}}_{\mathbf{d}}\mathbf{}\mathbf{=}\frac{\left[{\mathrm{Co}}^{3+}\right]{\left[{\mathrm{NH}}_{3}\right]}^{\mathbf{6}}}{\left[\mathrm{Co}{{\left({\mathrm{NH}}_{3}\right)}_{6}}^{3+}\right]}\phantom{\rule{0ex}{0ex}}\mathbf{2}\mathbf{.}\mathbf{2}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{34}}\mathbf{}\mathbf{=}\frac{\left(x\right){\left(6x\right)}^{\mathbf{6}}}{(0.500-x)}$

$\frac{\left[\mathrm{Co}{{\left({\mathrm{NH}}_{3}\right)}_{6}}^{3+}\right]}{{\mathbf{K}}_{\mathbf{d}}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{0}\mathbf{.}\mathbf{500}}{\mathbf{2}\mathbf{.}\mathbf{2}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{34}}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{500}$

Using the dissociation constant, K_{d} = 2.2 × 10^{–34}, calculate the equilibrium concentrations of Co^{3+} and NH3 in a 0.500-M solution of Co(NH_{3})_{6}^{3+}.

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