What is the percentage strength (v / v) of alcohol in a mixture of 12 mL of 17 % v / v alcohol,

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What is the percentage strength (v / v) of alcohol in a...

What is the percentage strength $(\mathrm{v} / \mathrm{v})$ of alcohol in a mixture of $12 \mathrm{~mL}$ of $17 \% \mathrm{v} / \mathrm{v}$ alcohol, $10 \mathrm{~mL}$ of $50 \% \mathrm{v} / \mathrm{v}$ alcohol, and $500 \mathrm{~mL}$ of $33 \% \mathrm{v} / \mathrm{v}$ alcohol?

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Key Concepts

Weighted Average in Mixtures

The weighted average is a fundamental concept in mixture problems whereby the overall concentration of a mixture is calculated as the total amount of the pure solute divided by the total volume of the mixture. Each component’s contribution is 'weighted' by its volume, ensuring that larger volumes have a correspondingly greater impact on the final concentration.

Percentage Strength (v/v)

This concept refers to the ratio of the volume of a solute to the total volume of a solution, expressed as a percentage. It is a common way to describe the concentration of a liquid in mixtures, particularly in solutions like alcoholic beverages where the solute is alcohol.

Volume Calculation of Pure Solute

When working with solutions of known percentage strength, the actual volume of the pure solute in each component of the mixture is determined by multiplying the total volume of the component by its percentage strength (expressed as a decimal). This step is critical in mixture problems as it allows you to quantify the amount of the key substance (e.g., alcohol) in each part of the solution.

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