How many grams of pure medication are in 500 milliliters of a 1:250 solution?
The correct answer and explanation is:
Correct Answer: 2 grams
To find out how many grams of pure medication are in 500 milliliters of a 1:250 solution, start by understanding what the ratio means. A 1:250 solution means there is 1 part of solute (in this case, pure medication) in 250 parts of total solution. This can also be interpreted as 1 gram of medication in every 250 milliliters of solution, assuming the solution is measured in grams per milliliter.
To calculate the amount of pure medication in 500 milliliters, use the following proportion: 1 gram250 mL=x grams500 mL\frac{1 \text{ gram}}{250 \text{ mL}} = \frac{x \text{ grams}}{500 \text{ mL}}
Now solve for xx by cross-multiplying: 250x=500⋅1250x = 500 \cdot 1 250x=500250x = 500 x=500250=2x = \frac{500}{250} = 2
So, there are 2 grams of pure medication in 500 milliliters of a 1:250 solution.
This method uses proportional reasoning. Since the concentration remains consistent throughout the solution, scaling the volume by a factor of 2 (from 250 mL to 500 mL) also scales the amount of solute by the same factor. That is why 1 gram in 250 mL becomes 2 grams in 500 mL.
The ratio 1:250 is a common way to express concentration in pharmacy and chemistry. It helps standardize how much of a substance is present in a solution and supports accurate dosing and preparation. Using this approach ensures correct calculations when converting between different volumes of the same solution concentration. The process is based entirely on proportion and unit analysis, which are fundamental principles in solving concentration problems.