 of our models computed with both $\alpha_\mathrm{PMS}=1.0$ and $\alpha_\mathrm{PMS}=\alpha_\mathrm{MS}=1.68$ are in good agreement with data for the primary components (1.0 M$_\odot\la$ M$_1$ $\la 1.4$ M$_\odot$), within the uncertainties, since lithium depletion is almost negligible for such masses. Therefore, the primary components belonging to our sample do not allow further constraints on the $\alpha_\mathrm{PMS}$ value. In contrast, the impact of $\alpha_\mathrm{PMS}$ gets stronger and stronger as the mass decreases below about 1 M$_\odot$. The secondary of EK Cep and RXJ 0529.4+0041 A might thus give useful constraints[^5]. Unfortunately, among the selected systems, the lithium data for the secondary components are quite uncertain, with errors as large as 0.5 dex (see Table \[tab:binarie\]), avoiding a robust comparison. The model with a low-convection efficiency is fully compatible with the data for the secondary component of EK Cep, although we cannot exclude $\alpha_\mathrm{PMS} =1.68$, while in the case of RXJ 0529.4+0041 A, nothing can be concluded owing to extremely uncertain lithium abundance determination, which is only a lower limit [see also the discussion in, @alcala00; @covino01; @dantona03]. From this analysis it is evident that an effort to improve the measurements of the main parameters of binary systems, lithium abundance included, is required, in order to better constrain the super-adiabatic efficiency of theoretical models. Moreover, we emphasize that EBs are extremely useful tools for testing the validity of stellar models, and consequently, precise data about such systems would be required.

Conclusions
===========

We have discussed in detail the uncertainties on theoretical models by evaluating the effect of the errors affecting the initial chemical composition and the up-to-date physical inputs (i.e. opacity, reaction rates, EOS), for several ages, masses, and chemical compositions. From these computations, we obtained a quantitative estimation of the error bar associated to the $^7$