1.10.15: Gibbs Energies- Salt Solutions- Electric Neutrality
- Page ID
- 384696
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The solid crystalline salt \(\mathrm{NaCl}\) comprises a lattice of sodium \(\mathrm{Na}^{+}\) and chloride \(\mathrm{Cl}^{-}\) ions. The charge number on each sodium ion, \(\mathrm{z}_{+}\), is \(+ 1\); the charge number on each chloride ion, \(\mathrm{z}_{-}\), is \(- 1\). The amount of sodium ions \(\mathrm{ν}_{+}\) produced by one mole of sodium chloride is 1 mol. The amount of chloride ions \(\mathrm{ν}_{-}\) produced by one mole of sodium chloride is 1 mol. The electric charge on the sodium ions in one mole of sodium chloride is \(\left(\mathrm{v}_{+} \, \mathrm{z}_{+} \, \mathrm{N}_{\mathrm{A}} \, \mathrm{e} \right) \mathrm{~C}\) where \(\mathrm{e}\) is the unit charge and \(\mathrm{N}_{\mathrm{A}}\) is the Avogadro constant. The product \(\left(\mathrm{N}_{\mathrm{A}} \, \mathrm{e}\right) \quad\left\{=[\mathrm{C}] .[\mathrm{mol}]^{-1}\right\}\) is the Faraday constant \(\left{=\left[\mathrm{C} \mathrm{mol}^{-1}\right]\right\}\). Similarly the electric charge on the chloride ions in 1 mol of sodium chloride equals, \(\left(\mathrm{v}_{-} \, \mathrm{z}_{-} \, \mathrm{N}_{\mathrm{A}} \, \mathrm{e} \right) \mathrm{~C}\). The total electric charge on one mole of solid sodium chloride equals \(\left[\left(\mathrm{v}_{+} \, \mathrm{z}_{+} \, \mathrm{N}_{\mathrm{A}} \, \mathrm{e}\right)+\left(\mathrm{v}_{-} \, \mathrm{z}_{-} \, \mathrm{N}_{\mathrm{A}} \, \mathrm{e}\right)\right] C\) which equals zero.
We make these points in order to highlight the fact that the total electric charge on 1 mol of sodium cations (in for example 53 g of common salt) is enormous, being 96 500 C. Very few laboratories can handle such enormous electric charges. Chemists cope because the electric neutrality condition always operates [1]. When we set down equations describing the properties of salt solutions we ensure that the electric neutrality condition is not violated. However when we turn to the task of developing molecular models for these systems we recognize the magnitude of the forces involved.
Footnotes
[1] One model of Utopia is a society when there are equal number of men and women. It is interesting to note that from the perspective of each male, the Utopian society has a majority of women. Similarly each woman lives in a male dominated society. Life is the same for ions.