Calculate the pH of the buffer system of 0.20M K2HPO4/0.25M KH2PO4
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To calculate the pH of a buffer solution, you need to use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
In this case, K2HPO4 is the salt and KH2PO4 is the acid. K2HPO4 dissociates to release HPO4^2- ions, and KH2PO4 dissociates to release H2PO4^- ions. HPO4^2- (conjugate base) and H2PO4^- (acid) make up the acid-base pair in this buffer system.
First, we need to determine the pKa of the phosphoric acid (H3PO4) system because the pKa value is not given. The pKa can be estimated by calculating the average of the pKa values for the two acidic hydrogens of phosphoric acid:
pKa = (pKa1 + pKa2) / 2
The pKa1 of phosphoric acid (H3PO4) is 2.15, and the pKa2 is 7.20.
pKa = (2.15 + 7.20) / 2 = 4.675
Now we can substitute the given concentrations and pKa value into the Henderson-Hasselbalch equation:
pH = 4.675 + log ([HPO4^2-] / [H2PO4^-])
To find the concentrations of the HPO4^2- and H2PO4^- ions, we need to consider the dissociation of the salts in water.
K2HPO4 → 2K+ + HPO4^2-
KH2PO4 → K+ + H2PO4^-
Since K2HPO4 has a concentration of 0.20 M, the HPO4^2- concentration is also 0.20 M. Similarly, since KH2PO4 has a concentration of 0.25 M, the H2PO4^- concentration is 0.25 M.
Substituting the values into the equation:
pH = 4.675 + log (0.20 / 0.25)
pH = 4.675 + log (0.8)
Calculating:
pH ≈ 4.675 + (-0.0969)
pH ≈ 4.5781
The pH of the buffer system of 0.20 M K2HPO4 / 0.25 M KH2PO4 is approximately 4.5781.