I was planning to extract citric acid from lemon juice by reacting the lemon juice with calcium chloride hoping it would react to form calcium citrate and precipitate according to the reaction $$\ce{2 C6H8O7(aq) + 3 CaCl2(aq) -> Ca3(C6H5O7)2(s) + 6 HCl(aq)}$$ However I was not sure that the reaction would occur. I know that the calcium citrate should precipitate out and drive the reaction forward, however it seems that the $\ce{HCl}$ generated reaction would then react with any calcium citrate bringing back to calcium chloride and citric acid. Which reaction would move to completion or would the two reactions reach an equilibrium. If this will not work I plan to just use calcium hydroxide instead by reacting calcium chloride with sodium hydroxide.
Answer
How do you know that calcium citrate will precipitate out and drive the reaction forward? In fact, it will not. Why in the world would it? Because calcium citrate is poorly soluble (which is true)? Well, that's not enough. Calcium carbonate or calcium phosphate are even more insoluble, yet even they will not precipitate in similar conditions (i.e., in acidic media). That's the problem with the salts of weak acids. (Yes, we may consider phosphoric acid weak, if we are talking of its third proton.) You have a solution with plenty of calcium and citrate (or phosphate, or carbonate), but most of that citrate (or phosphate, or carbonate) is not in the fully deprotonated form, so the solubility limit is not reached, and the precipitate can't appear.
Also, the very word "extract" does not quite apply here anyway.
Also, what was your plan to regenerate citric acid from calcium citrate afterwards?
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