1. The problem statement, all variables and given/known data What is the pH of a carbonate buffer solution prepared by mixing 1.500 mol Na2CO3 and 1.000 mol NaHCO3 and adding water to make a 1.000 L solution? (pKa of (HCO3)- is 10.32) A 200.00 mL sample of 1.000 M nitric acid was added to the buffered solution above. What is the resulting pH? 2. Relevant equations Henderson-Hasselbalch equation (pH = pKa + log ([A-]/[HA])) pH = -log [H+] 3. The attempt at a solution I used the equation for the first part, and I calculated a pH of 10.50 (pH = 10.32 + log (1.500/1.000)). Is this correct? I'm not sure how to include the second part though... I'm guessing I'm supposed to calculate the resulting pH when nitric acid is added to 1.000 L of water and then somehow use that pH for the second part... If that makes any sense. Any help is appreciated!
10.50 looks OK, although you added, not multiplied (I guess that's just a typo). What reaction takes place in the solution when you add strong acid? How does it change amounts of CO_{3}^{2-} and HCO_{3}^{-}?
Oops, that is a typo =P Apologies! So if I add HNO_{3}, it would dissociate, creating more H_{3}O^{+}. And the addition of hydronium ions would shift the equilibrium to increase the concentration of HCO_{3}^{-}, which decreases the concentration of CO_{3}^{2-}. Is that right?
So this is what I ended up doing: 0.200 L of 1.000 M nitric acid was added, which means that 0.200 moles of nitric acid was added. Since it's a strong acid, it fully dissociates, meaning that there are 0.200 additional moles of hydrogen ions in the solution. Since there are more protons in the solution, the equilibrium shifts to create more HCO_{3}^{-}, meaning that CO_{3}^{2-} are used. Using the ICE method, I figured that the concentration of HCO_{3}^{-} is 1.000 M and that of CO_{3}^{2-} is 1.083 M. Then I used the H-H equation and got this: pH = 10.32 + log (1.083 M / 1.000 M) = 10.35. Does that look right?
No. As told - use just the stoichiometry of the reaction. Simple check - you started with total concentration of carbonate and bicarbonate being 2.5M, now you are down to 2.083 - so there must be something wrong, carbon can't just disappear from the solution (unless it bubbles out as CO_{2}, but you are not protonating bicarbonate, so this is not the case).
Just one more question: so the volume doesn't change even after adding 0.200 L of nitric acid? Wouldn't it be different?
Changes - but it doesn't matter. You see, in the Henderson-Hasselbalch equation under log there is a ratio of two concentrations. If you add water, both concentrations change in the same way, so their ratio stays constant. In fact, it can be easily shown that volume cancels out, and it is just ratio of number of moles of acid and conjugate base that counts. Beware: there are some traps here. Please read the page about HH equation that I linked to to find out what is the problem.