🤓 Based on our data, we think this question is relevant for Professor Phillips' class at VANDERBILT.

Mg(OH)_{2} + NH_{4}Cl → MgCl_{2} + 2 NH_{3} + 2 H_{2}O

Step 1

Step 2

$\overline{){\mathbf{K}}_{\mathbf{a}}\mathbf{}\mathbf{=}\mathbf{}\frac{\left[{\mathrm{NH}}_{3}\right]\left[{H}^{+}\right]}{\left[{{\mathrm{NH}}_{4}}^{+}\right]}}\phantom{\rule{0ex}{0ex}}\mathbf{5}\mathbf{.}\mathbf{6}\mathbf{}\mathbf{\times}\mathbf{}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{=}\frac{\left(x\right)\left(x\right)}{\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{-}\mathbf{}\mathbf{x}}\phantom{\rule{0ex}{0ex}}(5.6\times {10}^{-10})(1.3-x)\mathbf{}\mathbf{=}\mathbf{}{\mathbf{x}}^{\mathbf{2}}\phantom{\rule{0ex}{0ex}}{\mathbf{x}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{5}\mathbf{.}\mathbf{6}\mathbf{}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{x}\mathbf{}\mathbf{-}\mathbf{}\mathbf{7}\mathbf{.}\mathbf{28}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$

When excess solid Mg(OH)_{2} is shaken with 1.00 L of 1.3 M NH_{4}Cl solution, the resulting saturated solution has pH = 9.10. Calculate the K_{sp} of Mg(OH)_{2}.

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Based on our data, we think this problem is relevant for Professor Phillips' class at VANDERBILT.