Is there any theoretical way to estimate the activity of $\ce{NaCl}$ at high ionic strengths in water and that in $\pu{7 M}$ $\ce{NaCl}$ solution? This question is based on whether solubility of $\ce{NaCl}$ in $\pu{7 M}$ $\ce{LiCl}$ solution should decrease. Solubility of $\ce{Na+}$ in $\ce{LiCl}$ solution can be approximated to

$$ [\ce{Na+}]=\frac{(K_\mathrm{sp})_{\ce{NaCl}}}{m_{\ce{LiCl}}} $$

We have, however, assumed that both $\ce{NaCl}$ (and $\ce{LiCl}$) are in their unit activities, which is not true. How to get conservative estimates for $a_{\ce{LiCl}}$ and $a_{\ce{NaCl}}$ at high ionic strengths, say $\pu{7 M}$?

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    $\begingroup$ Mathematical modeling has progressed greatly since I was a student, but I believe that such activities would rely on experimental measurements rather than theory. $\endgroup$ – MaxW Sep 19 '19 at 23:43

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