Final answer:
To calculate the 2000-fold dilution for the soft drink assay, convert the carbohydrate content to molar concentration, adjust for volume units, and apply the dilution formula C1V1 = C2V2 to find the volume of stock solution needed.
Step-by-step explanation:
To calculate the appropriate 2000-fold dilution of a soft drink for an assay using 1 ml of diluted sample, you need to take into account the initial concentration of the carbohydrate in the soft drink. According to the USDA nutrient database, there is approximately 3 g of carbohydrate per fluid ounce (fl. oz.).
Firstly, convert 3 g/fl. oz. to a molar concentration, assuming that all the carbohydrate is sucrose (C12H22O11) which has a molecular weight of about 342.3 g/mol.
- 3 g/fl. oz. x 1 mol/342.3 g = 0.00876 mol/fl. oz.
Then, convert fluid ounces to milliliters (1 fl. oz. is approximately 29.5735 mL):
- 0.00876 mol/fl. oz. x 1 fl. oz./29.5735 mL = 0.000296 mol/mL
To find out how much of the stock solution you would need for a 2000-fold dilution in 1 ml of solvent:
- 0.000296 mol/mL / 2000 = 0.000000148 mol/mL for the diluted solution
You would then use the formula for dilutions, C1V1 = C2V2, where C1 and V1 are the concentration and volume of the stock solution, and C2 and V2 are the concentration and volume of the diluted solution:
- (0.000296 mol/mL) (V1) = (0.000000148 mol/mL) (1 mL)
- V1 = (0.000000148 mol/mL) / (0.000296 mol/mL)
- V1 = 0.0005 mL of soft drink concentrate is needed to make 1 mL of a 2000-fold diluted solution.
This means that to prepare 1 mL of the diluted solution for the assay, 0.0005 mL (or 0.5 μL) of the original soft drink should be used and brought up to a total volume of 1 mL with solvent.