Which Of The Following Would Form An Electrolyte Solution

Ionic Solutions

To express the chemical potential of an electrolyte in solution in terms of molality, let us use the example of a dissolved salt such as magnesium chloride, (MgCl_{2}).

[MgCl_{2}rightleftharpoons Mg^{2+}+2Cl^{-} label{1}]

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We can now write a more general equation for a dissociated salt:

[M_{nu+}X_{nu-}rightleftharpoonsnu_{+}M^{z+}+nu_{-}X^{z-} label{2} ]

where (nu_{pm}) represents the stoichiometric coefficient of the cation or anion and (z_pm) represents the charge, and M and X are the metal and halide, respectively.

The total chemical potential for these anion-cation pair would be the sum of their individual potentials multiplied by their stoichiometric coefficients:

[mu=nu_{+}mu_{+}+nu_{-}mu_{-} label{3} ]

The chemical potentials of the individual ions are:

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[mu_{+} = mu_+^{circ}+RTln m_+ label{4} ]

[mu_{-} = mu_-^{circ}+RTln m_- label{5} ]

And the molalities of the individual ions are related to the original molality of the salt m by their stoichiometric coefficients

[m_{+}=nu_{+}m]

Substituting Equations (ref{4}) and (ref{5}) into Equation (ref{3}),

[ mu=left( nu_+mu_+^{circ}+nu_- mu_-^{circ}right)+RTlnleft(m_+^{nu+}m_-^{nu-}right) label{6} ]

since the total number of moles (nu=nu_{+}+nu_{-}), we can define the mean ionic molality as the geometric average of the molarity of the two ions:

[ m_{pm}=(m_+^{nu+}m_-^{nu-})^{frac{1}{nu}}]

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then Equation (ref{6}) becomes

[mu=(nu_{+}mu_{+}^{circ}+nu_{-}mu_{-}^{circ})+nu RTln m_{pm} label{7} ]

We have derived this equation for a ideal solution, but ions in solution exert electrostatic forces on one another to deviate from ideal behavior, so instead of molarities we must use the activity a to represent how the ion is behaving in solution. Therefore the mean ionic activity is defined as

[a_{pm}=(a_{+}^{nu+}+a_{-}^{nu-})^{frac{1}{nu}}]

where

[a_{pm}=gamma m_{pm} label{mean}]

and (gamma_{pm}) is the mean ionic activity coefficient, which is dependent on the substance. Substituting the mean ionic activity of Equation (ref{mean}) into Equation (ref{7}),

[mu=(nu_{+}mu_{+}^{circ}+nu_{-}mu_{-}^{circ})+nu RTln a_{pm}=(nu_{+}mu_{+}^{circ}+nu_{-}mu_{-}^{circ})+RTln a_{pm}^{nu}=(nu_{+}mu_{+}^{circ}+nu_{-}mu_{-}^{circ})+RT ln a label{11}]

when (a=a_{pm}^{nu}). Equation (ref{11}) then represents the chemical potential of a nonideal electrolyte solutions. To calculate the mean ionic activity coefficient requires the use of the Debye-Hückel limiting law, part of the Debye-Hückel theory of electrolytes .

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