Question

\(\mathrm{A}\) bottle of champagne is \(11 \%(\mathrm{v} / \mathrm{v})\) alcohol. If there are \(750 \mathrm{~mL}\) of champagne in the bottle, how many milliliters of alcohol are present?

Short answer

82.5 mL of alcohol

Step-by-step solution

Identify the given data

Given that a bottle of champagne is 11% (v/v) alcohol and the total volume of champagne in the bottle is 750 mL.

Understand the percentage concept

The 11% (v/v) means that 11% of the total volume of the champagne is alcohol. This can be calculated using the formula for percentage: \[ \text{Volume of alcohol} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total volume} \]

Substitute the values into the formula

Substitute 11% for the percentage and 750 mL for the total volume into the percentage formula: \[ \text{Volume of alcohol} = \left( \frac{11}{100} \right) \times 750 \]

Calculate the result

Perform the multiplication: \[ \text{Volume of alcohol} = 0.11 \times 750 = 82.5 \text{ mL} \]

State the final answer

The volume of alcohol present in the 750 mL bottle of champagne is 82.5 mL.

Key concepts

percentage concentration

Percentage concentration is a way to express the amount of a substance in a mixture. It's often expressed as a percentage and shows how much one element is mixed with another. In our exercise, we discuss the percentage concentration of alcohol in champagne. To find out what 11% (v/v) actually means, think of it as: Out of every 100 units of champagne, 11 of those units are alcohol. This concept helps us understand and calculate the content of a specific ingredient in various mixtures such as drinks, medicines, and chemical solutions. Remember that when dealing with percentages, converting them into their decimal form is helpful for calculations. For example, 11% becomes 0.11 when converted into a decimal.

volume per volume (v/v)

Volume per volume percentage, abbreviated as (v/v), is commonly used in chemistry and biology to describe the concentration of a solution. When a solution's concentration is given as 11% (v/v), it means that there are 11 milliliters of solute in every 100 milliliters of solution. Let's be clear: the solute is the alcohol, and the solution is the champagne. By understanding the formula and units, we can calculate how much alcohol is in a given volume of champagne. It's essential to have the correct units when performing your calculations since this maintains consistency and helps you arrive at the correct answer.

alcohol content calculation

To calculate the alcohol content in the champagne, we use the percentage concentration formula: \text{Volume of alcohol} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total volume}Substituting the given values: 11% as the percentage and 750 mL as the total volume of champagne, we get:\[\text{Volume of alcohol} = \left( \frac{11}{100} \right) \times \text{750}\]Solving this we get, the volume of alcohol equals 82.5 mL. This means there are 82.5 milliliters of alcohol in the 750 mL bottle of champagne. Following this process helps ensure you make precise calculations in similar real-life scenarios.

unit conversion

Unit conversion is a key skill in many scientific calculations. Here, we work with milliliters (mL) since we're measuring volumes of liquids. It’s important to know the basic unit conversion, for instance:

• 1 liter (L) = 1000 milliliters (mL)
• 100 milliliters (mL) = 0.1 liters (L)

Understanding these conversions can help convert measurements into different units when needed. In our example, since the total volume is already in milliliters and we need the result in the same unit, no conversion is necessary. But knowing how to convert between units is vital in many cases, such as when dealing with larger or smaller quantities than those given.