Solve each of the following problems using one or more conversion factors:
a. Wine is 12% alcohol by volume. How many milliliters of alcohol are in a 0.750-L bottle of wine?

검증된 단계별 안내

Step 1: Understand the problem. The wine is 12% alcohol by volume, meaning 12 mL of alcohol is present in every 100 mL of wine. You are tasked with finding the volume of alcohol in a 0.750-L bottle of wine.

Step 2: Convert the volume of wine from liters to milliliters. Use the conversion factor: 1 L = 1000 mL. Multiply 0.750 L by 1000 mL/L to express the wine volume in milliliters.

Step 3: Set up the proportion to calculate the volume of alcohol. Use the given percentage (12% alcohol by volume) as a conversion factor: 12 mL alcohol / 100 mL wine. Multiply the total volume of wine (from Step 2) by this conversion factor.

Step 4: Perform dimensional analysis to ensure units cancel appropriately. The milliliters of wine will cancel, leaving milliliters of alcohol as the final unit.

Step 5: Write the final expression for calculation: (Volume of wine in mL) × (12 mL alcohol / 100 mL wine). This will give the volume of alcohol in milliliters.

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주요 개념

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Alcohol by Volume (ABV)

Alcohol by Volume (ABV) is a standard measure used worldwide to quantify the amount of alcohol (ethanol) contained in an alcoholic beverage. It is expressed as a percentage, indicating the volume of alcohol per 100 milliliters of the beverage. For example, a wine with 12% ABV contains 12 milliliters of alcohol in every 100 milliliters of wine.

Volume Conversion

Volume conversion involves changing a measurement from one unit to another, such as liters to milliliters. In this context, it is essential to know that 1 liter equals 1,000 milliliters. This conversion is crucial for accurately calculating the amount of alcohol in a given volume of wine, as the problem specifies the wine's volume in liters.

Calculation of Alcohol Content

To calculate the alcohol content in a beverage, you multiply the total volume of the beverage by the percentage of alcohol by volume (ABV). In this case, to find the milliliters of alcohol in a 0.750-L bottle of wine with 12% ABV, you would convert the volume to milliliters and then apply the formula: (total volume in mL) x (ABV) = volume of alcohol in mL.

Solve each of the following problems using one or more conversion factors:a. Wine is 12% alcohol by volume. How many milliliters of alcohol are in a 0.750-L bottle of wine?