(Solved): Solubility with activity. Find the concentrations of the major species in a saturated aqueous solut ...

Solubility with activity. Find the concentrations of the major species in a saturated aqueous solution of LiF, Consider the following reactions. \[ \begin{array}{ll} \mathrm{LiF}(\mathrm{s}) \rightleftharpoons \mathrm{Li}^{+}+\mathrm{F}^{-} & K_{\mathrm{sp}}=\left[\mathrm{Li}^{+}\right] \gamma_{\mathrm{Li}^{+}}\left[\mathrm{F}^{-}\right] \gamma_{\mathrm{F}} \\ \mathrm{LiF}(\mathrm{s}) \rightleftharpoons \mathrm{LiF}(\mathrm{aq}) & K_{\text {ion pair }}=[\mathrm{LiF}(\mathrm{aq})] \gamma_{\mathrm{LiF}(\mathrm{aq})} \\ \mathrm{F}^{-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{HF}+\mathrm{OH}^{-} & \left.K_{\mathrm{b}}=K_{\mathrm{w}} / K_{\mathrm{a}} \text { (for } \mathrm{HF}\right) \\ \mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}^{+}+\mathrm{OH}^{-} & K_{\mathrm{w}}=\left[\mathrm{H}^{+}\right] \gamma_{\mathrm{H}^{+}}\left[\mathrm{OH}^{-}\right] \gamma_{\mathrm{OH}^{-}} \end{array} \] Look up the equilibrium constants and report their \( \mathrm{p} K \) values. The ion pair reaction is the sum of \( \mathrm{LiF}^{2}(\mathrm{~s}) \rightleftharpoons \mathrm{Li}^{+}+\mathrm{F}^{-} \)and \( \mathrm{Li}^{+}+\mathrm{F}^{-} \rightleftharpoons \mathrm{LiF}(\mathrm{aq}) \) \[ \mathrm{p} K_{s \mathrm{p}}= \] \[ \mathrm{p} K_{\text {ion pair }}= \] \[ \mathrm{p} K_{\mathrm{b}}= \] Write the equilibrium constant expresions and the charge and mass balances. charge balance: mass balance: \( = \) Create a spreadsheet that uses activities to find the concentrations of all species and the ionic strength. Use \( \mathrm{pF}^{-} \)and \( \mathrm{pOH}^{-} \)as independent variables to estimate. It does not work to choose \( \mathrm{pF}^{-} \)and \( \mathrm{pLi}^{+} \)because either concentration fixes that of the other through the relation \( K_{\mathrm{sp}}=\left[\mathrm{Li}^{+}\right] \gamma_{\mathrm{Li}}+\left[\mathrm{F}^{-}\right] \gamma_{\mathrm{F}} \). \[ \left[\mathrm{F}^{-}\right]= \] \[ \text { M }\left[\mathrm{OH}^{-}\right]= \] \[ \left[\mathrm{Li}_{\mathrm{I}}^{+}\right]= \] \[ \text { M }[\operatorname{LiF}(a q)]= \] \[ [\mathrm{HF}]= \] \[ \text { M }\left[\mathrm{H}^{+}\right]= \] \[ \mu= \]