Ionic force

The ionic force , often noted I (or F_I so as to distinguish it from the intensity), is one of the independent factors influencing the Activité Ion S in aqueous solution. It is expressed in mol. L^-1 and is calculated in the following way:

$I=\; \backslash \; frac\; \{1\}\; \{2\}\; \backslash \; sum\_\; \{I\}\; C\_i\; z\_i^2\; \backslash ,\; \backslash !$ where C_i represents the concentration ion I and z_i its number of load

Measure ionic force

The best solution to determine the ionic force consists in determining the respective concentrations of the various ions in solution and using the preceding formula. However one can be also satisfied with an estimate of the ionic force knowing the total concentration in solids dissolved (noted TDS and expressed out of Mg. L^-1) or the electric Conductivity (noted SpC and expressed in 10^-6 S.cm ^-1) of the solution. These estimates use the following empirical formulas:

• I = 2.5 X 10^-5 TDS
• I= 1.7 X 10^-5 SpC

Ionic force and chemical activity

Several semi-empirical relations make it possible to obtain the average Coefficient of activity of an electrolyte (ex: NaCl, MgSO₄…) or the coefficient of activity of an ion (ex: Na⁺, Cl^-,…) in solution starting from the value of the ionic force I.

The three most current formulas are below detailed ( $\backslash \; gamma\_i\; \backslash ,\; \backslash !$ is the coefficient of activity of ion I, $z\_i\; \backslash ,\; \backslash !$ its number of loads and $a$ a homogeneous parameter with a length ):

• Formule of Debye-Hückel limits (DHL) : $log\; (\backslash \; gamma\_i)\; =\; -\; 0.5\; z\_i^2\; \backslash \; sqrt\; \{I\}\; \backslash ,\; \backslash !$
• wide Formula of Debye-Hückel (DHE) : $log\; (\backslash \; gamma\_i)\; =\; -\; 0.5\; z\_i^2\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; sqrt\; \{I\}\}\; \{1\; +\; 0.33\; has\; \backslash \; sqrt\; \{I\}\}\; \backslash \; right)\; \backslash ,\; \backslash !$
• Approximation of Güntleberg (AG) : $log\; (\backslash \; gamma\_i)\; =\; -\; 0.5\; z\_i^2\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; sqrt\; \{I\}\}\; \{1\; +\; \backslash \; sqrt\; \{I\}\}\; \backslash \; right)\; \backslash ,\; \backslash !$

formula (DHL) is valid only if the ionic force I is lower than 10^-2.3 mol. L^-1 because it regards each ion as a concentrated loading. This approximation cannot be made for a concentrated solution any more. formulas (DHE) and (AG) are as for them valid only if I is lower than 0.1 mol. L^-1.

Other more complex formulas or theories were thus developed to connect the coefficient of activity and the ionic force when I is higher than 0.1 mol. L^-1. It is in particular the case of the equation of Davies, the Modèle of Pitzer or the Théorie SIT.

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