Titrations and Buffers
A titration is an analytic method used by chemists to determine the concentration of a known reactant in solution.
Setting Up A Titration
When we set up a titration we start by adding our unknown solution called the analyte to a beaker. For example, we might place 1 mole of HCl into our beaker, to begin with. From there we add our titrant to the solution little by little. When performing a titration we always add the opposite of what we started with. In this example, we started with acid so we will titrate the solution with a base. If we had started with a base then we would have added acid to carry out the titration.
As we add more and more of the titrant whatever we start with is slowly neutralized. In this diagram below we can see how this proceeds.
Since HCl is a strong acid it completely dissociates so we will start with 1 mol of H+ ions. From there we add NaOH which reacts with the H+ ions to form water. Since the NaOH is the limiting reactant plenty of H+ ions will remain in the solution.
When the number of moles of H+ from the HCl and the number of moles of OH– from the NaOH is equal the titration is said to be complete. This point is also called the equivalence point because both the moles of the titrant and analyte are now equal or equivalent to one another. Furthermore, the equivalence point is marked by a rapid pH change since all of our HCl will be neutralized into water.
Titration Plots
When titration is plotted the equivalence point corresponds to the very center of the vertical portion on the titration curve. This portion of the graph represents a rapid and sudden pH change as the H+ concentration rapidly drops as the remaining H+ ions are neutralized at the equivalence point.
Since scientists don’t know the number of moles at the start of the titration they need a way of knowing when they have reached the equivalence point. To do this they add an indicator.
The indicator will change color on the basis of the pH solution. This means that for each titration we need to estimate what the equivalence point pH will be. When we react equal strength acids and bases this will lie around a pH of 7. As seen in the two examples above and the one below.
However, when the titration is carried out between acids and bases of unequal strength the equivalence point pH lies closer to the stronger species.
This means that different titrations will require different indicators whose color change corresponds to the different equivalence points.
Titration Calculation
In the first example, I specified how many moles of HCl were present in the solution. However, we are often asked to determine this information so how can we calculate this on the basis of a titration plot. First, we have to remember that at the equivalence point the number of moles of acid will be equal to the number of moles of base.
[latexpage]
\[ Mols\; Acid = Mols\;Base\]
Since we picked our titrant and carefully measure how much we added throughout the experiment we should be able to determine how many moles of base were present at the equivalence point from the plot below.
Here we can see that the equivalence point corresponds to the addition of 10 mL of 2M NaOH. From this information, we can calculate the moles of base present. Since the moles of acid and base are equivalent we have also determined the number of moles of HCl present at the beginning of the experiment.
So in this scenario, we started with 0.02 moles of HCl or 0.02 moles of H+ since HCl is a strong acid and will completely dissociate into its ionic components.
Buffering Regions
So far we have learned about the basics of titrations and the vertical portion of a titration plot or the equivalence point. What about the horizontal aspect of the plots? If we trace this portion of the plot out we can see that as we increase the titrant the pH doesn’t move much at all.
We call this region the buffering region because it represents an area that buffers or resists pH change even as we add more base to the solution. Right at the middle of the buffering region the pH = pKa. Why? we can imagine each end of the buffering region as representing the percentage of neutralized acid or base. On the far left of this region, the titration hasn’t begun so 0% of the analyte has been neutralized. On the right side of the buffering region, the titration is nearing the equivalence point and 100% of the analyte has been neutralized.
Directly in between these two points, the analyte is 50% neutralized. Since the pKa and the pH are equal when a chemical species is split between its conjugate acid-base pair this 50% mark corresponds to the pKa of the acidic or basic spot in question.
Buffers
While all titrations will have buffering regions not all acid and bases make great buffers. What is a buffer then? A buffer is a solution of a weak acid-base conjugate pair that resists changes in pH when small quantities of strong acid are added to it. Why a weak acid-base pair though? In short they don’t fully dissociate but their equilibrium shifts according to the external pH.
You can think of this portion as the median between a two-way highway. The median prevents head-on car crashes from occurring in the same way the buffer prevents wild swing in pH.
In biological organisms, this is extremely important because enzymes that catalyze vital reactions fall apart outside their specific pH ranges. Furthermore, other reactions biochemical reactions require are negatively affected by even small changes in pH.
Polyvalent Titrations
In the above example, we focused on a titration between HCl and NaOH which only has one H+ ion or is a monoprotic acid. What happens when we carry out a titration with a polyvalent acid or base? The same thing except multiple times for each acidic or basic spot on the acid or base. So a titration of a triprotic acid would have three separate equivalence points and three buffering regions.
Amino Acid Titrations
