[Saged]

I've actually been working on this for the past few hours trying to figure out how to go about solving this. I'm pretty confused. Here's the question:

"An aromatic molecule was observed to give a colorless solution at neutral pH and a yellow solution in 0.1M sodium hydroxide. In order to determine pKa of the ionization involved, the absorbance at 420nm was determined for several solutions in a 1cm cuvette at 25 Celsius degree. All solutions contained the same total concentration of the aromatic molecule, but differed in their pH. Predict the pKa for the ionization."

Below is the given data, (in the table) in which I plotted pH vs. Absorbance.



Any have any ideas?

[Arkcon]

Are you aware of how the pKa can be experimentally determined?  http://en.wikipedia.org/wiki/Acid_dissociation_constant#Experimental_determination

[Saged]

Oh yes, I'm well aware. That's all Quantitative Analysis at my university. However, this is just an addon question on an absorbance lab; it's not really necessary to titrate it.

[Borek]

What is the logic behind determining pKa from the titration curve? Is there some specific point with a specific properties? Is it possible to apply similar logic here?

[Saged]

To determine pKa from a titration curve you need to have the half and full equivalence points. At the half equivalence is when [HA] = [A-], therefore pH = pKa. However, what I'm confused on is where the absorbance values come into play. I suppose I could use the Henderson-Hasselbalch equation.



Which is possible, but I don't have [HA], nor do I have the Ka to solve for it.

[Borek]

You have a curve showing absorbance as a function of pH. Can you try to use it to to estimate ratio of concentrations of HA and A^-?

For example - at pH 1, what percentage of the substance is in the HA form? And at pH 13? What about A^- form at these pH?

[Babcock_Hall]

The numbers in your data spreadsheet do not seem to correspond to the graph.  It looks as if things have gotten shifted by about 2 pH units.  This discrepancy would have to be fixed to get a good numerical answer for pK_a.  Nevertheless, the principle of getting a decent estimate of pK_a is not affected.  What is true of the ratio of HA to A^- when pH = pK_a?

[Saged]

I suppose I could estimate it. However, I wanted to get an accurate value.

@Bab, Ha and A- are equivalent species @ pH = pKa.

Thanks for all your replies, btw.

[Borek]

I suppose I could estimate it. However, I wanted to get an accurate value.

Best value you can get is the one using the estimate.

You know enough to solve the problem, start estimating and see where your estimates meet with what you wrote answering Babcock_Hall's post.

[Babcock_Hall]

I suppose I could estimate it. However, I wanted to get an accurate value.

@Bab, Ha and A- are equivalent species @ pH = pKa.

At pH 1 is the compound  > 99% in the form of HA or A^-?  How much does this absorb?
At ph 13 is the compound > 99% in the form of HA or A^-?  How much does this absorb?

I give my students an exercise that is similar to this.  We use nonlinear regression, and we first estimate pKa much as you are doing (nonlinear regression requires initial estimates of parameters).  Then from the regression exercise what we obtain is an estimate of pKa ± error.  One does not obtain a single number without an error bar, if that is what you mean by an accurate answer.