Will I get bromine by electrolysis of the brine from the Dead Sea?
The short answer is probably a bit, depending on the potential you apply.

There are at least a few factors involved:


How easily are $\ce{Cl-}$ and $\ce{Br-}$ oxidized?

$$\begin{align*}\ce{2Cl^{-}_{(aq)} -&gt; Cl_{2(g)} +2e-}\; &amp;E°_{\mathrm{ox}}=-1.36\ V\\\ce{2Br^{-}_{(aq)} -&gt; Br_{2(aq)} +2e-}\; &amp;E°_{\mathrm{ox}}=-1.09\ V\end{align*}$$
At standard activities, the two ions are pretty similar in oxidation potentials, so there is probably a range of potentials where both reactions occur to a similar degree or it might be possible to achieve some partial selectivity for bromine formation. The Nernst equation can be used to calculate equilibrium concentrations for a given potential, but so long as the potential applied is well over the standard oxidation potential, the exact values don't really matter.
What difference do the concentrations make?

In most cases, what determines how much of either reaction occurs is mass transport. For a redox reaction to occur, the reacting molecule must be very close to the electrode surface (&lt;10 nm). For a planar electrode at a single potential in a standing solution, mass transport occurs by diffusion and the current that flows should be directly proportional to concentration in the bulk. In principle, the Cl to Br ratio should be the same as their activities in solution, though in some situations, other factors like the speed of the electron transfer can be limiting, so this may not be the case, especially since there is so much chloride compared to bromide.
What about the electrodes?

As electrolysis is a surface phenomenon, the electrode and its interactions with the reactants can be important. Assuming you pick an electrode which doesn't itself react with the chloride or bromide, the exact material can affect the behaviour of the cell. Even though the Nernst equation may predict a certain oxidation potential, interactions of the reactants and the electrode may result in varying amounts of additional potential (overpotential) needed to cause the reaction.
What happens to the bromine?

A certain amount of bromine can dissolve in water, but depending on the pH, it can rapidly disproportionate back to bromate and hypobromate: $\ce{Br2 + 2OH- → Br- + OBr- + H2O}$ Also, the chlorine gas can react with the bromide to make bromine and bromine is also known to react with metals (use carbon electrodes?). In short, you can probably create an electrolytic cell that produces some bromine, but it's difficult to say in what ratio with chlorine and what its exact fate would be.