Final answer:
Through a series of dilution calculations starting from the concentration of a diluted aspirin solution, it was determined that one tablet of aspirin contains approximately 2.117 mg of the substance, based on its molar mass of 180.15 g/mol.
Step-by-step explanation:
To determine the mass of aspirin present in one tablet, we can use the provided concentration of the diluted aspirin solution and work backwards through the dilutions to find the concentration of the original solution and then the mass in the tablet. The original concentration was calculated as 2.35 x 10-2 M, and the dilute solution was found to be 2.94 x 10-4 M. Since we know the molar mass of aspirin is 180.15 g/mol, we can convert moles of aspirin to mass.
The dilution steps are as follows:
- Calculate the moles in the diluted (2.50 mL) solution using the concentration of 2.94 x 10-4 M.
- Since the aliquot came from a concentrated solution diluted to 125 mL volume, calculate the moles in this 125 mL solution.
- Finally, determine the moles in the entire original 10 mL solution, and thus the one tablet.
- Convert the moles of aspirin in one tablet to mass using the molar mass 180.15 g/mol and express it in mg.
To start, the number of moles in the 200 mL diluted solution is:
n = volume x concentration = (0.00250 L) x (2.94 x 10-4 M) = 7.35 x 10-7 moles
Since this is a dilution, we can say:
(2.35 x 10-2 M)(0.125 L) = 7.35 x 10-7 moles x 200 L
This simplifies to:
Moles in 125 mL solution = (7.35 x 10-7 moles x 200) / 0.125 = 1.176 x 10-5 moles
This is the number of moles initially in the 10 mL of NaOH solution where the tablet was dissolved. Thus:
Moles in 10 mL original solution = 1.176 x 10-5 moles
Finally, convert the moles to mass:
Mass = moles x molar mass = (1.176 x 10-5 moles) x (180.15 g/mol) = 2.117 mg (rounded to three significant figures)
Therefore, there are 2.117 mg of aspirin in one tablet.