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If there is a ketone and ester functional group in the same compound and I want to protonate with $\ce{HCl}$, which one will protonate first? Is it the carbonyl group in the ketone or the carbonyl group in the ester and why? Is it related to the $\mathrm{p}K_\mathrm{a}$ of the functional group?

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    $\begingroup$ The $\mathrm{p}K_\mathrm{a}$ values of protonated esters, protonated ketones and hydrochloric acid are close to each other (-7 to -6 according to www2.onu.edu/~b-myers/organic/2511_Files/pKa%20table.pdf), so $\ce{HCl}$ will protonate both groups, perhaps with a slight preference for the ketone. $\endgroup$ – Jannis Andreska Jun 2 '15 at 17:36
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As was mentioned in the comments, with reference to the Myers $\mathrm{p}K_{\mathrm{a}}$ table, the $\mathrm{p}K_{\mathrm{a}}$ values of a protonated ester and a protonated ketone are largely similar (in the region of $-7$ to $-6$).

Therefore, it will likely depend on external factors, which group is protonated first. Are there electron withdrawing or electron donating groups in the vicinity of either? Can the proton on either maybe intramolecularly hydrogen bond to something?

All these effects will also slightly modify the $\mathrm{p}K_{\mathrm{a}}$ of the functional group you’re observing. The one with the higher $\mathrm{p}K_{\mathrm{a}}$ will be protonated first. Thus, it is impossible to give a general answer here, it depends on which molecule you have and which groups are where.

Side fact: $\ce{HCl}$ has almost the same $\mathrm{p}K_{\mathrm{a}}$, so the protonation will be very close to equilibrated between all three components.

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