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Is it because citrate chelates calcium and then is unable to react with other chemicals being added? If so can someone explain this reaction to me, or if not provide what the reason is? If anyone has any studies they've found on it that would be incredibly helpful! Thank you!

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"Inhibited" is not probably the right term, as there is no catalyst inhibition, affecting the reaction kinetics.

If we consider about neutral $\mathrm{pH}$ range, the citrate buffer keeps $\mathrm{pH}$ by equilibrium reactions

$$\ce{HA^2- <=> H+ + A^3-}$$ $$\ce{HA^2- + OH- <=> H2O + A^3-}$$

with $\mathrm{p}K_\mathrm{a3}=6.4 $

Carbonate as a base spends the buffer capacity

$$\ce{CO3^2- + 2 HA^2- <=> CO2(g) + H2O + 2 A^3-}$$

If it was sodium carbonate, sodium ions would be just bystander ions.

But calcium ions form chelate with citrate 3:2, decreasing concentration of free hydrogen citrate + citrate ions.

So the overall calcium carbonate effect is being base and chelating citrate.

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