[crroth]

In class we did a lab trying to determine the concentration of caffeine and benzoic acid in diet mountain dew, using UV spec. This mtn. dew was diluted 1:25, and we prepared a few other solutions of caffeine and benzoic acid to get some absorbance data.

Below is the key and their values.

AB = absorbance of unknown @ λmax benzoic acid
AC = absorbance of unknown @ λmax caffeine
Ecc = molar absorptivity coefficient for caffeine @ λmax caffeine
Ecb = molar absorptivity coefficient for caffeine @ λmax benzoic acid
Ebc = molar absorptivity coefficient for benzoic acid @ λmax caffeine
Ebb = molar absorptivity coeff. for benzoic acid @ λmax benzoic acid
[benz] = unknown concentration of benzoic acid
[caffeine] = unknown concentration of caffeine

To simplify future equations, I assigned variables to these.

AB = q = 1.6765
AC = x = 1.4968
Ecc =y = 0.06954**
Ecb =r = 0.02765**
Ebc =a = 0.03462**
Ebb =s = 0.08736**

**(y,r,a,s) were calculated from the slopes of my absorbance vs concentration data.

[benz] = b
[Caffeine] = z

b = (x-yz) / a

z = (q-sb) / r

I have calculated my [caffeine] to be ~59ppm. (59mg/L ---> 1.7mg/oz) 1.7mg * 12 oz = 20.4 g per can. (this is not including the 1:25 dilution, which would put it at 510mg caffeine per can!!) 

I used these equations:

z = [caffeine]

z =  (1.6765 - 0.08736((1.4968 - (0.06954z)/0.03462))/0.02765

b = [benz]

b = (1.4968 - 0.06954((1.6765 - (0.08736b)/0.02765))/0.03462

I plugged these into wolfram alpha:

b :  http://www.wolframalpha.com/input/?i=b+%3D+%281.4968+-+0.06954%28%281.6765+-+%280.08736b%29%2F0.02765%29%29%2F0.03462

z : http://www.wolframalpha.com/input/?i=z+%3D++%281.6765+-+0.08736%28%281.4968+-+%280.06954z%29%2F0.03462%29%29%2F0.02765

I just solve for one, let's say [benz], and get b = 0.3516

If this is plugged into the equation for [z], (1.6765-(0.08736*0.3516))/0.02765 = [z] = 59.522

Now I go back to the equations above, but this time solve for [z]; z = 0.5710

Plugging this into the equation for [benz], (1.4968-(0.06954*0.571))/0.03462 = [benz] = 42.088


    These last two equations give me [caffeine] = 59.522, [benz] = 42.088

    I am assuming that these numbers are PPM (mg/L), and when converting them to mg/oz I get [caffeine] = 1.76 mg/oz, and [benz] = 1.25 mg/oz.

    When I take into account 12 oz per can, these numbers are in the teens... definitely not high enough. So then I remember that it was a 1:25 dilution, so I multiply by 25. Wayyyy to high.

Any help or guidance you could offer would be awesome!

Thank you.

[JGK]

check the units of all of your data to make sure they are correct.


Purely on a scientific note, most official UV spectrophotometry methods would require the unknown absorbance to be in the 0.2 - 0.8 AU. Reproducibility of results is much better at these absorbance levels

At 1 AU only 10% of the light reaches the detector at 2 AU it is 1%.

[Babcock_Hall]

I cannot convince myself that you have used the correct equations, but I am not sure they are wrong, either.  Suppose I asked, what is equation that governs the absorbance (AC, which is equal to 1.497) at λ_max of caffeine in this example.  What would you write?

[Yggdrasil]

Your calculations would seem to be ok for solutions containing only caffeine and benzoic acid, but there are likely other compounds in the soda that absorb at the wavelengths you measured.  Unless you can show that everything else in the soda (esp. the artificial coloring) does not absorb at the wavelenghts you're looking at, I don't know how much faith I would put in your measurements.