Two Concept Questions for you:

1) Why is the concentration of a solution such as NaH2PO4 ignored when calculating the pH given Ka1, Ka2, and K3 values?

2) Given Pka1=3.13, Pka2=4.76, and Pka3 = 6.40, calculate the pH of lemon juice which is about 5% citric acid.
--I know I have to just go pH= (1/2) pka1,
but why is it just (1/2) of Pka1? Where did the (1/2) come from?

1. If you derive the formula for (H^+) at the (say) first equivalence point, the concn of the salt present cancels and one is left with (H^+) = sqrt(k1k2) which is 1/2(pk1 + pk2) = pH.

2. Citric acid is so highly buffered between the beginning and the final (only) practical equivalence point, that the Henderson-Hasselbalch equation of
pH = pK + log(base/acid) is essentially pK and log (base/acid) is log 1 = 0
Here is a site that talks about that but only a little.
http://www.titrations.info/acid-base-titration-polyprotics-and-mixtures

thanks. that helped!!

1) The concentration of a solution, such as NaH2PO4, is ignored when calculating the pH given Ka1, Ka2, and K3 values because the assumption is made that the solution is dilute and that the dissociation of acid or base does not significantly affect the initial concentration of the hydrogen ions (H+) or hydroxide ions (OH-). In other words, the concentration of the solution is considered to be constant and does not have a significant impact on the pH calculation.

This assumption is valid in many cases when dealing with weak acids or weak bases in dilute solutions. The concentration of the acid or base is often much higher than the concentration of the dissociated ions, so the change in concentration due to ionization is relatively small and can be neglected. However, it is important to note that this assumption may not hold true for very concentrated solutions or strong acids/bases, where the ionization can significantly affect the concentration of ions and alter the pH calculation.

2) To calculate the pH of lemon juice, which is approximately 5% citric acid, you can use the pKa values provided. The pKa values are a logarithmic form of the equilibrium constant (Ka) for acid dissociation. The pKa values represent the acidity of each dissociation step of citric acid.

The equation pH = (1/2) pKa1 is used because citric acid has three dissociation steps. The (1/2) factor accounts for the fact that each step only contributes half of the total acidity. This is because in the first step, one hydrogen ion is released, and in the second and third steps, two hydrogen ions are released.

So, when calculating the pH of a solution with citric acid, you only consider the contribution of the first dissociation step, which is represented by half of the pKa1 value. This is because the subsequent dissociation steps contribute less to the overall acidity due to the loss of one or two hydrogen ions in each step.

It's important to note that this approximation assumes that the acid is not highly concentrated and that the pH is controlled mainly by the first dissociation step. In the case of lemon juice, the concentration is relatively low, and considering only half of the pKa1 value provides a good estimate of the pH.