phosphoric acid reaches equilibrium in water.
The error in the estimation of K
a
/pK
a
values can be associated with the fact that the
titration curve is not 100% accurate, but instead based upon the data points that we were able
to put in. For example, the first and second equivalence points were identified by the place
where the second derivative was equal to zero (or where the first derivative achieved a
maximum value). A problem with using this point as the equivalence point is that that there
may have been an even higher maximum point if we had measured the pH after adding even
smaller increments of the base. For example, a solution would be to add the base in quantities
of 0.1 mL instead of between 0.5 and 1.0 mL. Another possible source of error is the fact that
some carbon dioxide gas may have still been present in the cola sample, consuming the added
NaOH to form another type of acid (carbonic acid). No data was collected for the third K
a
value
since the titration was ended after a pH of 10 was achieved.
In conclusion, it was determined that the concentration of phosphoric acid in the cola
was 4.5 X 10
-3
moles
liter
.
Sine the cola had a pH of 2.42, phosphoric acid was determined to
have a percent dissociation of 84%. This is a relatively high value, considering phosphoric acid is
a weak acid. However, the high percent dissociation is due to phosphoric acid’s ability to donate
three hydrogen ions in solution.
Discussion Questions:
1.
The true values for the K
a
of phosphoric acid are 7.1 X 10
-3
, 6.3 X 10
-8
, and 4.5 X 10
-13
. The
values that were obtained for the first two K
a
values were 1.3 X 10
-3
and 1.0 X 10
-7
. There is a
noticeable issue when using graphical analysis to determine the K
a
/pK
a
values. In order to
determine these values we had to determine the location of the inflections points on the
titration curve, or essentially where the second derivative had a value of zero. Although the
inflections points were clearly visible on the graph of the derivative (the local maximums
and minimums), this only represents the general region around which the actual equilibrium
and half equilibrium position lie. A titration curve is based on a group of points, and the
curve is not always completely smooth. Therefore the maximums and minimums on the
derivative function can only represent the inflection points of the given data. Increasing the
accuracy of estimation with a titration curve would involve plotting a lot more points.
Adding the NaOH in 0.1 mL quantities, for example, would help achieve a far smoother
curve with more concrete points. This would reduce the amount of estimation that needs to
be done by the graphing program when developing the curve, and reduce the amount of
estimation that needs to be done when reading the graph.
2.
Degassing the cola prior to the titration was a very important step because it eliminated the
risk of a side reaction that would have altered the data. The gas in the cola is carbon dioxide.

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- Fall '12
- SOPER
- pH, Phosphoric acid