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Chapter 12: Problem 3

The "proof" value of any liquor is equal to twice the percentage of alcohol; for example, a 50-proof liquor is \(25 \%\) alcohol in water. Vodka is normally sold between 80 and 100 proof, but suppose you came across a bottle of 135 -proof vodka. Would you be justified in calling the alcohol the solvent and the water the solute? Explain.

Short Answer

Expert verified
Yes, you would be justified in calling the alcohol the solvent and the water the solute in a 135-proof vodka. This is because the percentage of alcohol in 135-proof vodka is 67.5%, which is greater than the water percentage of 32.5%. Therefore, alcohol, being the component in a larger amount, can be considered the solvent, while water is the solute.

Step by step solution

01

Find the percentage of alcohol in a 135-proof vodka

Half the proof value gives us the alcohol percentage in the vodka. So, we'll divide 135 by 2. \(Percentage \thinspace of \thinspace Alcohol = \frac{135}{2} \) Now, calculate the quotient. \(Percentage \thinspace of \thinspace Alcohol = 67.5 \% \) The alcohol content in the 135-proof vodka is 67.5%.
02

Compare the percentages of alcohol and water

Now, we need to find the percentage of water in the vodka and compare it with the alcohol percentage. Since the vodka consists of only alcohol and water, their percentages must add up to 100%. \(Percentage \thinspace of \thinspace Water = 100 - Percentage \thinspace of \thinspace Alcohol \) Substitute the alcohol percentage we calculated in Step 1. \(Percentage \thinspace of \thinspace Water = 100 - 67.5 = 32.5 \% \) Now, let's compare: Alcohol: 67.5% Water: 32.5%
03

Determine the solvent and solute

In a solution, the component present in the larger amount is considered the solvent, while the component in the smaller amount is considered the solute. In this case, alcohol is present in a larger amount (67.5%) than water (32.5%). Therefore, alcohol can be considered the solvent, and water can be considered the solute. In conclusion, yes, you would be justified in calling the alcohol the solvent and the water the solute in this 135-proof vodka.

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