Citric acid polyprotic acid equilibria

In summary, the conversation discusses the use of different equilibria to determine the concentration of H+ and pH in a solution. The first equilibrium, H3A <-> H2A- + H+, is used to find a concentration of 0.01165 M for H+. The second equilibrium, H2A- <-> HA2- + H+, is found to have a negligible effect on the overall H+ concentration. The question asks why it wouldn't be more accurate to add the two concentrations together and continue with the third equilibrium. The answer given is that for most practical applications, if the difference between two calculations is less than 0.1 pH unit, it is considered negligible. However, there is personal choice involved in determining
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i_love_science
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Homework Statement
Citric acid (H3C6H5O7) is a triprotic acid with Ka1 = 8.4*10^-4, Ka2 = 1.8*10^-5, and Ka3 = 4.0*10^-6. Calculate the pH of 0.15 M citric acid.
Relevant Equations
polyprotic acid equations (below)
Using the first equilibrium, H3A <-> H2A- + H+, the [H+] is solved to be 0.01165 M ~ 1.1 * 10^-2 M.

Using the second equilibrium, H2A- <-> HA2- + H+, the additional change in H+ is found to be 1.8 * 10^-5 M. The solution says that this second equilibrium is negligible, because 1.1 * 10^-2 M + 1.8 * 10^-5 M ~ 1.1 * 10^-2.

The question asks to find the pH though, not specifically the concentration [H+]. I don't understand why it would not be better to add 0.01165 M + 1.8 * 10^-5 M = 0.011668 M, and continue with this type of calculation with the third equilibrium as well? Would it make the answer more precise? I got pH 1.93 using this method, but the solution gives 1.96.

Could anyone explain why, or whether my reasoning is right? Thanks.
 
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It is always a matter of deciding "which answer is already good enough".

For most practical applications if the difference between two ways of calculating pH is below 0.1 pH unit it doesn't matter, as there are other sources of error, typically larger (or at least comparable). But it is not like it is an approach set in stone, there is a lot of personal choice in whether the difference of 0.05, 0.1 or 0.2 can be considered to be negligible.

I have no idea how you calculated the value of 0.01165, assuming a monoprotic acid with Ka=8.4e-4 I got pH of 1.97 ([H+ = 0.01081M). I would understand the value of 0.01122 as that's what you can get from approximated calculations, but 0.01165 seems like some kind of error to me.

Using pH calculator and your set of Ka values (they are often listed as slightly different, that's one of these error sources I mentioned earlier) I got an 'exact' pH of 1.97 using all three Ka for calculations, and NO difference between pH values (slight difference in calculated H+ concentration was too low) no matter whether I did calculations using one, two or three Ka values/dissociation steps.
 
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Related to Citric acid polyprotic acid equilibria

1. What is citric acid and how is it used?

Citric acid is a weak organic acid found in citrus fruits, such as lemons and limes. It is commonly used as a food additive to add a sour or acidic taste to foods and drinks, as well as a preservative to prevent spoilage.

2. What is the structure of citric acid?

Citric acid has a chemical formula of C6H8O7 and a molecular weight of 192.12 g/mol. It has three carboxylic acid functional groups, making it a polyprotic acid. The three carboxylic acid groups are connected by a central carbon atom, giving citric acid a three-dimensional structure.

3. How does citric acid act as a polyprotic acid?

As a polyprotic acid, citric acid can donate more than one proton (H+) in a solution. It has three dissociation constants, meaning it can lose one, two, or all three protons in a solution, depending on the pH. This allows citric acid to act as a buffer, maintaining a stable pH in a solution.

4. What is the equilibrium constant for citric acid polyprotic acid equilibria?

The equilibrium constant for citric acid polyprotic acid equilibria depends on the specific dissociation reaction being considered. For the first dissociation (loss of one proton), the equilibrium constant is Ka1 = 7.4 x 10^-4. For the second dissociation (loss of two protons), the equilibrium constant is Ka2 = 1.7 x 10^-5. And for the third dissociation (loss of all three protons), the equilibrium constant is Ka3 = 4.0 x 10^-6.

5. How does temperature and concentration affect citric acid polyprotic acid equilibria?

Temperature and concentration can both affect the equilibrium of citric acid polyprotic acid equilibria. As temperature increases, the equilibrium constants for dissociation may change, leading to a shift in the equilibrium position. Additionally, as the concentration of citric acid increases, the amount of protons available for dissociation also increases, leading to a higher concentration of the conjugate base and a lower pH.

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