First we need to know what vitamin(s) your tablet contains, B-6, B-12, etc., and what amount per tablet. It looks like you are making standard solutions based on the amount given for each tablet instead of using pure known samples for this purpose.
Let's assume that your tablet contains 100 mg of Vitamin B (one or more of the eight B-vitamins). The tablet was dissolved in 50 mL of buffer solution and sonicated. Then 20 mL of this solution was diluted to a final volume of 250 mL, to make "Solution B."
Initially, the solution concentration was 100 mg (assumed) of vitamin B / 50 mL = 2.0 mg/mL. You can then use the dilution formula to calculate the concentration of Solution B:
C1V1 = C2V2
C1 = 2.0 mg/mL
V1 = 20 mL
C2 = ?
V2 = 250 mL
Plugging in gives C2 = 0.16 mg/mL for Solution B (assuming the tablet had 100 mg of vitamin B in it).
Then you made another dilution of Solution B. 100 mL of Solution B was diluted to a final volume of 250 mL to give Solution C. Using the dilution formula again gives the concentration of Solution C to be 0.064 mg/mL.
The absorbance (wavelength = ?) of Solution C is called A1.
Then 20 mL of buffer was added to 20 mL of Solution C. The absorbance of this solution = A2.
For the concentration, use the dilution formula again. V1 = 20 mL, C1 = 0.064 mg/mL, V2 = 40 mL and C2 = ?. C2 come out to be 0.032 mg/mL.
I think you then take 20 mL of this last solution and add 20 mL of buffer to it. In other words, double the volume and halve the concentration again. If that is the case, the next and succeeding concentrations would be 0.016 mg/mL, 0.0080 mg/mL, 0.0040 mg/mL, 0.0020 mg/mL, etc. The procedure does not say so specifically, so you'll want to check this.
You will have to correct these concentrations, depending on the mg of vitamin B that was in your tablet.
Well, once you get all your concentrations and absorbances, you make a Beer's law plot, absorbance vs. concentration. If you have a TI 8x calculator, you can have it do a best line fit with the linear regression function, or you can use an online calculator such as this one at http://www.easycalculation.com/statistics/regression.php. The correlation coefficient takes more work to calculate. It is described at http://richardbowles.tripod.com/maths/correlation/corr.htm. I haven't checked to see if the TI calculators will calculate this for you automatically, but it might.
As far as using a buffer solution instead of water, if the absorbance of vitamin B changes with pH, which is the case with many molecules, then you would want to keep the pH constant to avoid incorrect absorbance readings if the pH is allowed to vary.
Sonication is used to aid in the breakdown of tablet particles so that the vitamin B is extracted as completely as possible from other substances in the tablet, such as a binder.
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