To measure the phosphoric acid content of a common cola, a solution is prepared

Question

To measure the phosphoric acid content of a common cola, a solution is prepared of Cherry Coke and 0.10M NaOH is added incrementally and the pH is tested each addition. The experimental equivalence point occurs at 5.50mL NaOH with a pH of 4.25. The neutralization of phosphoric acid occurs according to the following reaction:H3PO4 + OH- -> H2PO4- + H2O   H2PO4- + OH -> HPO4(2-) + H2O. The dissociation constant for the third proton of phosphoric acid, Ka3=4.7*10^-13.

Calculate the theoretical value for [H+] concentration and pH at the first equivalence point.

What I have: 0.10M NaOH*0.0055L = 0.00055mol NaOH Kb=(1*10^-14) / (4.7*10^-13)=0.0213

Help! I don;t understand how I'm supposed to calculate the theoretical pH

Explanation / Answer

The dissociation of H3PO4 will be

H3PO4 --> H+ + H2PO4-     Ka1    = 7.5 x 10^-3

H2PO4- --> H+   + HPO4-2    Ka2   =6.2 X10^-8

HPO4-2 --> H+   + PO4-3    Ka3 =4.7*10^-13 (very low)

At first equivalence point

Ka1 = [H+] [ H2PO4-] / [H3PO4]

For weak triportic acid the first eqivalence point is when

pH = [Pka1 + pKa2]/2 = [2.12 + 7.21 ] /2 = 4.67   [these are established formulae]

Similarly , second equivalence point will be at pH

pH = (pka2 + pka3) /2

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