Final answer:
To find the mass of the entire pill with a 2.53% concentration of active ingredient, rearrange the mass percent formula to solve for the mass of the entire pill, then convert the result from milligrams to grams.
Step-by-step explanation:
To calculate the mass of the entire pill when the medication contains 50.0 mg of active ingredient and this represents 2.53% by mass of the pill, we use the concept of percentage by mass. Percentage by mass (mass percent) is a way of expressing the concentration of an ingredient in a mixture or solution.
The percentage by mass (mass percent) formula is:
Mass percent = (mass of solute / mass of solution) x 100%
Here, the 'mass of solute' refers to the mass of the active ingredient in the pill, and the 'mass of solution' is the mass of the entire pill, including the active ingredient and any inactive ingredients.
To find the mass of the pill, we rearrange the formula to solve for the mass of solution (mass of the entire pill):
Mass of solution = (mass of solite) / (Mass percent / 100%)
Substituting the given values, we get:
Mass of the entire pill = (50.0 mg) / (2.53 / 100)
By performing the calculation, we can determine the mass of the entire pill in milligrams. It is important to then convert this value to grams since the mass of medicinal pills is commonly expressed in grams.
To convert milligrams to grams, remember that there are 1000 milligrams in a gram. The calculation will thus require dividing the mass of the pill in milligrams by 1000.