Solubility with Activity: Find the concentration of the major species in a saturated aqueous solution of $\mathrm{LiF}$. Consider these reactions:

$$\begin{gathered} \mathrm{LiF}\left(\mathrm{s}\right)\mathrm{֏}{\mathrm{Li}}^{+}+{\mathrm{F}}^{-}{\mathrm{K}}_{\mathrm{sp}}=\left[{\mathrm{Li}}^{+}\right]{\mathrm{\gamma }}_{{\mathrm{Li}}^{+}}\left[{\mathrm{F}}^{-}\right]{\mathrm{\gamma }}_{{\mathrm{F}}^{-}} \\ \mathrm{LiF}\left(\mathrm{s}\right)\mathrm{֏}\mathrm{LiF}\left(\mathrm{aq}\right){\mathrm{K}}_{\mathrm{ionpair}}=\left[\mathrm{LiF}\left(\mathrm{aq}\right)\right]\mathrm{\gamma LiF}\left(\mathrm{aq}\right) \\ {\mathrm{F}}^{-}+{\mathrm{H}}_2\mathrm{O}\mathrm{֏}\mathrm{HF}+{\mathrm{OH}}^{-}{\mathrm{K}}_{\mathrm{b}}=\raisebox{1ex}{${\mathrm{K}}_{\mathrm{w}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{K}}_{\mathrm{a}}$}\right.\left(\mathrm{forHF}\right) \\ {\mathrm{H}}_2\mathrm{O}\stackrel{{\mathrm{K}}_{\mathrm{w}}}{\mathrm{֏}}{\mathrm{H}}^{+}+{\mathrm{OH}}^{-}{\mathrm{K}}_{\mathrm{w}}=\left[{\mathrm{H}}^{+}\right]{\mathrm{\gamma }}_{{\mathrm{H}}^{+}}\left[{\mathrm{OH}}^{-}\right]{\mathrm{\gamma }}_{{\mathrm{OH}}^{-}} \end{gathered}$$

1. Look up the equilibrium constants in the appendixes and write their pK values. The ion pair reaction is the sum of localid="1654945209684" $\mathrm{LiF}\left(\mathrm{s}\right)\mathrm{֏}{\mathrm{Li}}^{+}+{\mathrm{F}}^{-}$from the Appendix ${\mathrm{FandLi}}^{+}\mathrm{֏}\mathrm{LiF}\left(\mathrm{aq}\right)$from Appendix J. write the equilibrium constant expressions and the charge and mass balance.
2. Create a spreadsheet that uses activities to find the concentration of all species and the ionic strength. Use pH and pOH as independent variables to estimate. It does not work to choose pH and pLi because their concentration fixes that of the other through the relation ${\mathrm{K}}_{\mathrm{sp}}=\left[{\mathrm{Li}}^{+}\right]{\mathrm{\gamma }}_{{\mathrm{Li}}^{+}}\left[{\mathrm{F}}^{-}\right]{\mathrm{\gamma }}_{{\mathrm{F}}^{-}}$

Step by step solution

01

Step 1:Finding the equation for the Charge Balance and Mass Balance.

In this task, we need to find the concentration of the species in a saturated aqueous solution of LiF along with considering the reactions given in the task.

First, let us consider the following,

$$\begin{gathered} {\mathrm{K}}_{\mathrm{sp}}=\left[{\mathrm{Li}}^{+}\right]\mathrm{\gamma }\left({\mathrm{Li}}^{+}\right)\left[{\mathrm{F}}^{-}\right]\mathrm{\gamma }\left({\mathrm{F}}^{-}\right)=0.0017 \\ {\mathrm{K}}_{\mathrm{ionpair}}=\left[\mathrm{LiF}\right]\mathrm{\gamma }\left(\mathrm{LiF}\right)=0.0029 \\ {\mathrm{K}}_{\mathrm{w}}=\left[{\mathrm{H}}^{+}\right]\mathrm{\gamma }\left({\mathrm{H}}^{+}\right)\left[{\mathrm{OH}}^{-}\right]\mathrm{\gamma }\left({\mathrm{OH}}^{-}\right)=1\times {10}^{-14} \end{gathered}$$

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