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? (9.4)

Verified step by step guidance

1. Identify the given information: The brandy is 80-proof, which means it is a 40% (v/v) ethanol solution.
2. Understand that '40% (v/v)' means there are 40 mL of ethanol in every 100 mL of brandy.
3. Set up a proportion to find the volume of ethanol in 750 mL of brandy: $\frac{40\text{ mL ethanol}}{100\text{ mL brandy}}=\frac{x\text{ mL ethanol}}{750\text{ mL brandy}}$.
4. Solve the proportion for $x$ by cross-multiplying and dividing: $x=\frac{40\times 750}{100}$.
5. Calculate the value of $x$ to find the volume of ethanol in 750 mL of brandy.

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 of solution × (Concentration of alcohol / 100). This formula allows for the calculation of the volume of pure alcohol present in any given volume of a solution, which is essential for solving problems related to alcoholic beverages.

Ethanol as a Component of Beverages

Ethanol, or ethyl alcohol, is the primary type of alcohol found in alcoholic beverages. It is important to recognize that the concentration of ethanol directly affects the beverage's proof and overall effects on the body. In the context of the question, knowing that the brandy is a 40% ethanol solution helps in accurately calculating the amount of ethanol in the specified volume.