How to Achieve Specific Alcohol Concentrations Through Water Addition

When dealing with solutions of alcohol, it's important to understand how to manipulate their concentration by adding water. This article covers the steps and calculations needed to achieve a specific alcohol concentration, specifically focusing on the 30% to 10% alcohol solution.

Understanding the Problem

The question at hand is: How many liters of water must be added to 30 liters of alcohol to produce 50 liters of a 10% alcohol solution? It's essential to break down the problem into clear steps to get an accurate answer.

Given Information

Starting volume (V1): 30 liters Starting alcohol concentration (C1): 30% Desired final volume (V2): 50 liters Desired final alcohol concentration (C2): 10%

Step-by-Step Calculation

To solve this, we use the dilution formula:

V1C1 V2C2

Where

V1 Starting volume (30 liters) C1 Starting concentration (30%) V2 Desired final volume (50 liters) C2 Desired final concentration (10%)

Calculation

First, we need to calculate the volume of alcohol in the starting solution:

Volume of pure alcohol in 30 liters of 30% solution:

0.30 x 30 9 liters of pure alcohol

Now, let's apply the dilution formula to find the starting volume (V1) that would give 50 liters of a 10% solution:

0.30 x V1 50 x 0.1

V1 (50 x 0.1) / 0.30

V1 16.67 liters

Volume of Water to be Added

To achieve the desired solution, we need to calculate how much water to add:

Volume of water to be added Desired final volume - Starting volume

Volume of water to be added: 50 - 16.67 33.33 liters

Therefore, to convert 16.67 liters of 30% alcohol to 50 liters of 10% alcohol, you need to add 33.33 liters of water.

Explanation of Results

The calculated result shows that adding 33.33 liters of water to 16.67 liters of 30% alcohol yields 50 liters of a 10% alcohol solution.

Conclusion

Based on these calculations, the problem can be accurately solved using the dilution formula. The key is in understanding the initial and final volumes and concentrations.

Common Mistakes

Common mistakes in similar problems include

Misinterpreting the given information Omitting necessary steps in the calculation process Not checking the feasibility of the final solution

It's always a good practice to verify whether the solution makes sense in terms of its total volume and alcohol content.

For more detailed information and advanced problems, refer to the alcohol dilution calculations resources available online.