Rubbing alcohol (isopropanol) is usually sold as a 70% vol aqueous solution. If the density of isopropyl alcohol is 0.785 g/mL, how many grams of isopropyl alcohol are present in a 355 mL bottle of rubbing alcohol?
The Correct Answer and Explanation is:
To determine the mass of isopropyl alcohol present in a 355 mL bottle of a 70% (vol/vol) aqueous solution of isopropanol, we can follow these steps:
- Understand the Solution Concentration: A 70% (vol/vol) solution means that there are 70 mL of isopropyl alcohol in every 100 mL of solution.
- Calculate the Volume of Isopropanol in 355 mL:
- Since we want to find out how much isopropyl alcohol is in 355 mL of solution:
[
\text{Volume of isopropanol} = 355 \, \text{mL} \times \frac{70 \, \text{mL}}{100 \, \text{mL}} = 248.5 \, \text{mL}
]
- Use the Density to Find the Mass:
- The density of isopropyl alcohol is given as 0.785 g/mL. We can use this density to find the mass of the isopropanol:
[
\text{Mass} = \text{Volume} \times \text{Density} = 248.5 \, \text{mL} \times 0.785 \, \text{g/mL} \approx 195.3 \, \text{g}
]
Therefore, the mass of isopropyl alcohol in a 355 mL bottle of rubbing alcohol is approximately 195.3 grams.
Explanation
In a volumetric solution, the concentration indicates how much solute (in this case, isopropyl alcohol) is present relative to the total volume of the solution. A 70% vol/vol solution signifies that 70% of the volume is pure isopropanol, and the remaining 30% is water or other solvents.
To find the specific mass of the solute in a known volume of solution, we first calculate the volume of the solute based on the given concentration. By multiplying the total volume of the solution (355 mL) by the percentage of isopropanol (70%), we determine that there are 248.5 mL of isopropanol in the solution.
Next, to convert volume to mass, the density of isopropyl alcohol (0.785 g/mL) is utilized. Density is defined as mass per unit volume, so we multiply the volume of isopropanol by its density to find the total mass. The resulting mass of approximately 195.3 grams reflects the amount of isopropyl alcohol present in the 355 mL bottle, illustrating the practical applications of concentration, volume, and density in chemistry.