How to Dilute Acids to Achieve a Specific Mixture: A Detailed Guide

Understanding how to dilute acids to achieve a specific concentration is a crucial skill in many scientific and industrial applications. In this article, we will guide you through the process of determining how many quarts of a highly concentrated acid must be added to a lower concentration acid to achieve a desired mixture. This is an essential concept in fields such as chemistry, pharmacology, and environmental science. Let's dive into the step-by-step process using the example of diluting a 10% acid solution to achieve a 25% acid concentration.

Problem Statement

The problem at hand involves starting with 10 quarts of a 10% acid solution (10 acid) and determining how many quarts of a 100% acid solution (100 acid) need to be added to achieve a 25% acid mixture.

Step-by-Step Solution

We can solve this problem using algebra. Let's define the unknown quantity:

Definitions

Initial Calculations

Firstly, calculate the amount of acid in the initial 10 quarts of 10 acid:

Amount of acid in the 10 acid solution:

10 quarts × 0.10 1 quart

Next, calculate the total volume of the mixture after adding x quarts of 100 acid:

Total volume after adding x quarts of 100 acid:

10 quarts x quarts

Calculate the total amount of acid in the mixture after adding x quarts of 100 acid:

Total acid in the mixture:

1 quart x quarts

Setting up the Equation

Set up the equation for the desired concentration of 25% (0.25), since 25% acid means 25 parts acid per 100 parts solution:

Equation based on the desired concentration:

(frac{Total text{ acid}}{Total text{ volume}} 0.25)

Substitute the expressions we have found:

(frac{1 x}{10 x} 0.25)

Solving the Equation

Cross-multiply to solve for x:

1 x 0.25(10 x)

Simplify:

1 x 2.5 0.25x

Rearrange the equation to isolate x:

x - 0.25x 2.5 - 1

0.75x 1.5

Solve for x:

x (frac{1.5}{0.75} 2)

Therefore, 2 quarts of 100 acid must be added to the 10 quarts of 10 acid to obtain a mixture of 25 acid.

Additional Thoughts on Unit Consistency

Using quarts as the unit for volume is common in some regions, especially in the United States. However, it is beneficial to be aware that the value of a quart can differ slightly between the US and UK systems (approximately 0.946 liters for a UK quart versus 1.137 liters for a US quart). For this reason, it is essential to specify the system when using quarts to avoid confusion.

Conclusion

Understanding how to dilute acids to achieve a specific concentration is critical for various applications. This example demonstrates the step-by-step process of adding a highly concentrated acid to a less concentrated one to achieve a desired mixture. Always double-check your calculations, especially when dealing with units like liters and quarts, to ensure accuracy.

Additional Resources

For further reading and practical applications, you might want to explore articles and resources on chemistry, acid dilution, and unit conversions. Many scientific journals and online platforms offer comprehensive guides and useful tips for these topics.