An 80-proof brandy is a 40.% (v/v) ethanol solution. The "proof" is twice the percent concentration of alcohol in the beverage. How many milliliters of alcohol are present in 750 mL of brandy?

Verified step by step guidance

1. Understand the relationship between proof and percent concentration: Proof is defined as twice the percent concentration of alcohol. For an 80-proof brandy, the percent concentration of ethanol is 40.0% (v/v). This means 40.0 mL of ethanol is present in every 100 mL of brandy.
2. Identify the total volume of the brandy given in the problem: The total volume of the brandy is 750 mL.
3. Set up the calculation to determine the volume of ethanol: Use the percent concentration (v/v) as a conversion factor. Multiply the total volume of the brandy by the percent concentration expressed as a decimal (40.0% = 0.400). The formula is: $\mathrm{Volume} \mathrm{of} \mathrm{ethanol}=\mathrm{Total} \mathrm{volume} \mathrm{of} \mathrm{brandy} \times 0.400$
4. Substitute the given values into the formula: Replace the total volume of brandy with 750 mL. The equation becomes: $\mathrm{Volume} \mathrm{of} \mathrm{ethanol}=750 \times 0.400$
5. Perform the multiplication to find the volume of ethanol in milliliters. Ensure the final answer is reported with the correct number of significant figures based on the given data (3 significant figures for 750 mL and 40.0%).

Key Concepts

Proof and Alcohol Concentration

Proof is a measure of the strength of an alcoholic beverage, defined as twice the percentage of alcohol by volume (ABV). For example, an 80-proof beverage contains 40% ethanol, meaning that in every 100 mL of the beverage, there are 40 mL of pure alcohol. Understanding this relationship is crucial for calculating the amount of alcohol in a given volume of the beverage.

Volume and Concentration Calculations

To determine the amount of alcohol in a solution, one can use the formula: Volume of alcohol = Total volume × (Alcohol concentration/100). In this case, knowing the total volume of the brandy (750 mL) and its alcohol concentration (40% v/v) allows for straightforward calculations to find the volume of pure alcohol present.

Milliliters to Liters Conversion

Understanding the conversion between milliliters (mL) and liters (L) is essential in volume calculations. Since 1 L equals 1000 mL, this conversion is often necessary when dealing with larger volumes or when results need to be expressed in different units. However, in this specific problem, the calculations remain in milliliters, simplifying the process.