A mouthwash contains 22% alcohol by volume. How many milliliters of alcohol are in a 1.05-pint bottle of mouthwash? (2 pints – 1 quart)
The correct answer and explanation is :
To calculate the amount of alcohol in a 1.05-pint bottle of mouthwash containing 22% alcohol by volume, we can follow a step-by-step process.
Step 1: Convert Pints to Milliliters
The first step is to convert 1.05 pints to milliliters, because the final answer needs to be in milliliters. We know that 1 pint is approximately equal to 473.176 milliliters. Therefore:
[
1.05 \text{ pints} \times 473.176 \text{ milliliters per pint} = 497.8348 \text{ milliliters}
]
So, the total volume of the mouthwash is 497.8348 milliliters.
Step 2: Calculate the Volume of Alcohol
Next, we calculate the volume of alcohol in the mouthwash. Since the mouthwash contains 22% alcohol by volume, we can find the volume of alcohol by multiplying the total volume of the mouthwash by 22% (or 0.22):
[
497.8348 \text{ milliliters} \times 0.22 = 109.52 \text{ milliliters}
]
Thus, the volume of alcohol in the 1.05-pint bottle of mouthwash is approximately 109.52 milliliters.
Explanation:
This problem requires the application of unit conversion and percentage calculation. Initially, we converted pints into milliliters using the conversion factor ( 1 \text{ pint} = 473.176 \text{ milliliters} ), as many liquid measurements are typically given in milliliters in scientific and medical contexts. After determining the total volume of mouthwash in milliliters, we used the percentage of alcohol content (22%) to find the volume of alcohol. By multiplying the total volume of the mouthwash by 0.22, we obtained the volume of alcohol in the mouthwash, which is the desired quantity.
This kind of problem is common in fields that deal with concentrations and volumes, such as nursing, pharmacy, and other health sciences. It’s essential to be able to accurately convert between units and apply percentage-based calculations to ensure correct dosing or understanding of substance concentrations.