Rubbing alcohol is 70% (m/v) isopropyl alcohol by volume. How
many mL of isopropyl alcohol are in a 500 mL container
The Correct Answer and Explanation is :
To calculate the volume of isopropyl alcohol in a 500 mL container of 70% (m/v) isopropyl alcohol, we can use the given concentration. The “70% (m/v)” means that there are 70 mL of isopropyl alcohol for every 100 mL of solution.
Step-by-Step Calculation:
- Determine the volume of isopropyl alcohol in 100 mL of solution:
[
\text{70%} = \frac{70 \, \text{mL of isopropyl alcohol}}{100 \, \text{mL of solution}}
] - Set up a ratio to find the volume of isopropyl alcohol in 500 mL of solution:
[
\frac{70 \, \text{mL of isopropyl alcohol}}{100 \, \text{mL of solution}} = \frac{x \, \text{mL of isopropyl alcohol}}{500 \, \text{mL of solution}}
]
Where (x) is the amount of isopropyl alcohol in the 500 mL container. - Solve for (x):
[
x = \frac{70 \times 500}{100} = 350 \, \text{mL}
]
Final Answer:
In a 500 mL container of 70% (m/v) isopropyl alcohol, there are 350 mL of isopropyl alcohol.
Explanation:
The concentration of rubbing alcohol is often expressed as a percentage, which indicates how much of the active ingredient (in this case, isopropyl alcohol) is present per volume of the total solution. For rubbing alcohol labeled “70% (m/v),” it means 70% of the solution is isopropyl alcohol, and the remaining 30% is water or another solvent.
To calculate the amount of isopropyl alcohol in a larger volume, such as a 500 mL container, you can use simple proportional math. Since 70% of any amount of solution is the volume of the isopropyl alcohol, you multiply the total volume (500 mL) by 0.70 (70%) to get 350 mL of isopropyl alcohol. This method is applicable to any solution where the concentration is given as a percentage.