Acidity Result of Clear Sodas

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Soda is consumed at a rate of 44.7 gallons per year by Americans. In clear sodas, citric acid is generally used to impart a tart flavor. We are going to explore the acid-base properties of clear sodas. Our objectives are to determine the acid content of the soda and to analyze some of the information contained in the titration curves, including the pH and Ka, and to utilize equations and theory to find these values.

Titration curves are plots of pH versus volume of titrant added to the unknown solution. Citric acid is a triprotic acid, so therefore we could write three separate equilibrium equations:
C6H8O7(aq) + H2O(l)   C6H7O7- + H3O+
C6H7O7- + H2O(l)  C6H6O72- + H3O+
C6H6O72- + H2O(l)  C6H5O73- + H3O+
Since this is a weak acid and we will be using a strong base as the titrant, the overall reaction will be:
C6H8O7(aq) + 3NaOH(aq)   Na3C6H5O73- + 3H2O(l)
When developing the titration curve, we will only see one equivalence point and not the three you would expect from citric acid being a triprotic acid. This is due to the strong base, NaOH, being added to the weak acid, citric acid, which effectively forms a buffer so that the change in pH in the first two equivalence points is not as apparent as one might expect. As the third equivalence point is reached, the buffer breaks down since there is no longer enough acid present to effectively buffer the solution. Therefore, we will see a sharp increase in the pH where we find the equivalence point, which is the mid-point of this sharply increasing area of the graph. The equivalence point is a single point defined by the reaction stoichiometry as the point at which the base (or acid) added exactly neutralizes the acid (or base) being titrated. Since their technically should be three equivalence points due to this being a triprotic acid, the first and second equivalence points will be equal to 1/3 and 2/3 of the equivalence point’s volume. When we look at a weak acid, we get:

HA(aq) + H2O(l)  A- + H3O+
The equilibrium expression for this reaction would be:
Ka = [A-] [H3O+] / [HA]
When we add hydroxide to the acid from NaOH:
HA(aq) + OH-(aq)  A- + H2O(l)
At the midpoint of this reaction, half of the acid in our solution will have been consumed and it will have produced an equal amount of A-. Therefore:
[HA] / [A-] = 1
Substitute that into the Ka equation:
[H3O+] = Ka
Taking the [HA] / [A-] = 1 further:
pH = pKa + log [HA] / [A-]
pH = pKa
Now this is only true at the midpoint of the reaction, where half of the acid will have been consumed by an equal amount of base. Since we have three different equivalence points from our triprotic acid that occur at 1/3, 2/3, and 3/3 of the final equivalence point, we can estimate Ka values for each equivalence point by multiplying it by the midpoint, or ½. Therefore, Ka for the first, second, and final equivalence points at 1/6, 3/6, and 5/6 of the final equivalence point (the midpoints of each of the three separate equilibria).

Experimental Plan:
In the initial stages of the experiment, while setting up our equipment, we will calibrate our drop counter to determine the volume per drop released from the burettes. Since our graphs will be plotting pH versus actual number of drops of NaOH used, it is important for us to have an accurate measurement of the volume per drop released. After that is completed, we can begin our experiment. First, our plan will be to make a standardized solution of NaOH of known molarity. This will help to establish our values of the unknown acid (soda). We will take a solution of HCl of a known molarity, 0.197M in this case, and titrate it with your NaOH solution. When the endpoint is reached, the phenolphthalein indicator will turn a light shade of pink to indicate that equilibrium has been reached. Molarity of our NaOH solution can now be calculated.

Next, we need to prepare the soda by slowly...
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