[cvc121]

For an experiment I am trying to calculate the reducing sugar content as a percentage of the original weight of a sample of ripe bananas and am having some difficulty doing so.

Some background info:

First, I prepared a calibration curve of the reduction of DNS reagent by the reducing sugar glucose (absorbance vs. concentration of glucose in µg/mL) and obtained the equation y = 0.0025x - 0.0322. This equation will later be used to solve for the concentration of reducing sugar in the supernatant.

The mass of the sample of ripe banana, 1 g, was immersed in distilled water and following centrifugation, the sample was decanted. The total supernatant volume was 10 mL. Next, I prepared a test tube containing 0.2 mL of supernatant, 0.8 mL water, and 2.0 mL DNS reagent. The absorbance of the banana sample was measured to be 0.706 via spectrophotometry.

Here is my attempt at the calculation:
 
First, plugging the absorbance into the equation y = 0.0025x - 0.0322 to solve for the concentration of reducing sugar in the supernatant, the x value. The result is 295.28 µg/mL.

To account for the dilution and solving for the concentration of reducing sugar in the test tube used to measure absorbance:
(295.28 µg/mL)(0.2 mL) = (C₂)(0.2 + 0.8 + 2.0 = 3.0 mL)
C₂ = 19.68 µg/mL

Next, multiplying this concentration by the total supernatant volume:
19.68 µg/mL x 10 mL = 196.8 µg = 1.968 x 10^-4 g

Finally, calculating the % of reducing sugar content in ripe banana sample as follows:
(grams of reducing sugar in banana / grams of banana)(100) = (1.968 x 10^-4 g / 1 g)(100) = 0.01968 %.

According to literature values, the reducing sugar content in ripe bananas is usually around 10-15% on average. Thus, my answer does not seem accurate which is why I am questioning if my method for solving the problem is correct. Is there anything in my attempt at the solution that seems incorrect? 

All guidance is very much appreciated. Thank you.

[Babcock_Hall]

Which should be higher, the concentration of sugar in the supernatant or in the test tube used to make the absorbance measurement?

[Arkcon]

There is lots of math here, and when I have a couple of hours free, I will work fgdogh it, because I, personally, love these sorts of problems.  No sarcasm.  I mean really.

Now, to help yourself with these sorts of problems, assume 100% extraction from sample (you already have, but maybe you shouldn't) -- what OD level do you calculate for 10 and 15%?  Is that level even covered by your cal curve?  You can apply thus trick to any such problem, even on an exam.

[cvc121]

Thank you for the responses. The concentration of reducing sugar should be higher in the supernatant since only 0.2 mL was extracted to make the measurement in the test tube. Based on this reasoning, I accounted for the dilution and calculated the reducing sugar content in the test tube used to measure absorbance, 19.68 µg/mL. Then multiplying this value by the total supernatant volume to obtain the total mass of reducing sugar, 196.8 µg. Did something go wrong in one of these steps? Does a dilution factor come into play here (dilution factor = final dilution volume / original volume of substance being diluted = 3 mL / 0.2 mL = 15)? Multiply 295.28 µg/mL by 15 to get concentration in supernatant sample?

[cvc121]

Here is another attempt at the solution:

y = 0.0025x - 0.0322
0.706 = 0.0025x - 0.0322
x = 295.28 µg/mL

dilution factor = final dilution volume / original volume of substance being diluted = 3 mL / 0.2 mL = 15
(295.28 µg/mL)(15) = 4429.2 µg/mL = concentration of reducing sugar in supernatant

(4429.2 µg/mL)(10 mL) = 44292 µg = 0.044292 g

(grams of reducing sugar in banana / grams of banana)(100) = (0.044292 g / 1 g)(100) = 4.43%

Does this attempt at the solution seem more accurate?

[Babcock_Hall]

You have corrected the error that I suspected was in your original solution, and the answer is close to your expected range, but a little bit low.  It might be that your assay is not linear in this region as Arkcon suggested, but I don't see enough evidence to draw a conclusion, one way or another.