Question #8fccb

1 Answer
Apr 13, 2015

!! LONG ANSWER !!

So, you're dealing with a buffer that contains monosodium phosphate, NaH_2PO_4, and disodium phosphate, Na_2HPO_4.

In aquous solution, the species that are of interest for your buffer are dihydrogen phosphate, H_2PO_4^(-), which will act as a weak acid, and hydrogen phosphate, HPO_4^(2-), which will act as the conjugate base.

Since nothing is actually added to the buffer, you have no net ionic equation to write. Now, because phosphoric acid is a triprotic acid, it will dissociate in three steps according to the following equilibrium reactions

H_3PO_(4(aq)) + H_2O_((l)) rightleftharpoons H_2PO_(4(aq))^(-) + H_3O_((aq))^(+), " "pK_(a1)

H_2PO_(4(aq))^(-) + H_2O_((l)) rightleftharpoons HPO_(4(aq))^(2-) + H_3O_((aq))^(+), " "pK_(a2)

HPO_(4(aq))^(2-) + H_2O_((l)) rightleftharpoons PO_(4(aq))^(3-) + H_3O_((aq))^(+), " "pK_(a3)

Notice that your buffer contains H_2PO_4^(-) and HPO_4^(2-), which means that the second equilibrium reaction will be established.

As a result, K_(a2) will be the more important acid dissociation constant for your buffer.

Notice that the concentration of HPO_4^(2-) is 2 times bigger than the concentration of H_2PO_4^(-); this means that the dominant form of the acid will be HPO_4^(2-) and that the solution's pH will be bigger than pK_(a2).

Moreover, because the difference between K_(a2) and K_(a3) is so significant, the concentration of PO_4^(3-) can be neglected.

So, since this is a buffer, you can use the Henderson-Hasselbalch equation to solve for the pH. Since the second equilibrium is set, you'll use pK_(a2), which is equal to

pK_(a2) = -log(K_(a2)) = -log(6.3 * 10^(-8)) = 7.20

Therefore,

pH_"sol" = pK_(a2) + log(([HPO_4^(2-)])/([H_2PO_4^(-)]))

pH_"sol" = 7.20 + log((0.29cancel("M"))/(0.13cancel("M"))) = 7.20 + 0.35 = color(green)(7.55)