Problem 3 - Introductory Chemistry Atoms First

Question

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.

Step-by-Step Solution

Answer

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 1: 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%.

Step 2: 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%

Step 3: 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.

Key Concepts

Proof of alcohol

Alcohol "proof" is a term used to measure the alcohol content in beverages. It is an indicator of the strength of the alcohol. Typically, proof is numerically double the percentage of the alcohol by volume. This means if you know the proof of a beverage, you can easily find out the percentage of alcohol it contains by dividing the proof number by two.

For example:

• A 100-proof beverage contains 50% alcohol by volume.
• Similarly, a 135-proof drink contains 67.5% alcohol by volume.

This system provides an easy way to understand and compare the alcohol content of different beverages.

Solvent and solute

In chemistry, a solution is made up of two main components: the solvent and the solute.

The **solvent** is the component that is present in the greater amount and typically dissolves the solute. In practical terms, the solvent is what does the dissolving.

The **solute** is the component that is present in a smaller amount and is dissolved by the solvent.

To apply this to a high-proof alcohol like our 135-proof vodka:

• The alcohol content is 67.5%, and the water content is 32.5%.
• Since the alcohol content is greater, alcohol acts as the solvent.
• Since water is less in comparison, it acts as the solute.

This distinction shifts depending on the composition of the solution and can provide insight into the nature of a mixture.

Percentage calculations

Calculating percentages is a vital skill in solution chemistry, especially when dealing with proofs and determining concentration. Here’s a basic way to understand percentage calculations using our example.

The total percentage of different components within a solution always adds up to 100%. Therefore, if you have one known percentage, you can easily find the other unknown percentage by subtracting the known from 100.

For example, in a 135-proof vodka:

• It contains 67.5% alcohol.
• Thus, the percentage of water will be: 100% - 67.5% = 32.5%.

These calculations help clearly determine the concentrations of each component, helping to accurately define the solvent and solute.

Alcohol content in beverages

Understanding alcohol content is crucial, especially for labeling and consumption purposes. The alcohol content influences the strength, taste, and even the legal classification of beverages.

Here are some things to keep in mind:

• A beverage with higher alcohol content is "stronger" and will have more pronounced effects when consumed.
• Alcohol content is key in determining proof, which impacts labeling regulations and consumer information.

For example, the 135-proof vodka we discussed is quite strong because of its high alcohol percentage of 67.5%. Such knowledge helps consumers make informed choices about what they consume and assists manufacturers with proper labeling.