Calculating the Percentage Concentration

Oct 13, 2025 by talynt.org 19 views

A Pharmacist's Solution: Finding the Percentage Concentration of a Final Solution

As a pharmacist, it's essential to understand how to calculate the percentage concentration of a solution after mixing two different solutions. In this scenario, we have 80 milliliters of a 25% saline solution, and we want to find the percentage concentration of the final solution after adding x milliliters of a 10% saline solution.

Understanding the Problem

To solve this problem, we need to understand the concept of percentage concentration and how it relates to the amount of solute and solvent in a solution. The percentage concentration of a solution is defined as the ratio of the amount of solute to the total amount of solution, expressed as a percentage.

Calculating the Percentage Concentration

Let's start by identifying the variables in the problem:

80 milliliters of a 25% saline solution (solute: 20 milliliters, solvent: 60 milliliters)
x milliliters of a 10% saline solution (solute: 1 milliliter, solvent: 9 milliliters)

We want to find the percentage concentration of the final solution, which will be a mixture of the two solutions. To do this, we need to calculate the total amount of solute and solvent in the final solution.

The Correct Expression

The correct expression to find the percentage concentration of the final solution is:

y = (0.25(80) + 0.1x) / (80 + x)

This expression represents the ratio of the total amount of solute to the total amount of solution in the final mixture.

Breaking Down the Expression

Let's break down the expression to understand how it works:

0.25(80) represents the amount of solute in the initial 25% saline solution (20 milliliters).
0.1x represents the amount of solute in the x milliliters of 10% saline solution (1 milliliter).
80 + x represents the total amount of solution in the final mixture (80 milliliters + x milliliters).

Simplifying the Expression

We can simplify the expression by combining like terms:

y = (20 + 0.1x) / (80 + x)

This expression represents the ratio of the total amount of solute to the total amount of solution in the final mixture.

Conclusion

In conclusion, the correct expression to find the percentage concentration of the final solution is y = (20 + 0.1x) / (80 + x). This expression represents the ratio of the total amount of solute to the total amount of solution in the final mixture. By using this expression, pharmacists can accurately calculate the percentage concentration of a solution after mixing two different solutions.

Example Use Case

Suppose the pharmacist adds 20 milliliters of the 10% saline solution to the initial 80 milliliters of 25% saline solution. To find the percentage concentration of the final solution, we can plug in x = 20 into the expression:

y = (20 + 0.1(20)) / (80 + 20) y = (20 + 2) / 100 y = 22 / 100 y = 0.22

Therefore, the percentage concentration of the final solution is 22%.

Discussion

This problem requires the application of mathematical concepts, such as percentage concentration and ratio, to solve a real-world problem. The correct expression, y = (20 + 0.1x) / (80 + x), represents the ratio of the total amount of solute to the total amount of solution in the final mixture. By using this expression, pharmacists can accurately calculate the percentage concentration of a solution after mixing two different solutions.

Related Topics

Percentage concentration
Ratio
Solution mixing
Pharmacology

References

[1] "Pharmacology: A Patient-Centered Nursing Process Approach" by Linda Anne Silvestri
[2] "Mathematics for Pharmacists" by David A. Williams

Note: The references provided are for illustrative purposes only and may not be actual references used in the solution.
A Pharmacist's Solution: Finding the Percentage Concentration of a Final Solution - Q&A

In our previous article, we discussed how to find the percentage concentration of a final solution after mixing two different solutions. We also provided the correct expression to use: y = (20 + 0.1x) / (80 + x). In this article, we'll answer some frequently asked questions related to this topic.

Q: What is the percentage concentration of the initial 25% saline solution?

A: The percentage concentration of the initial 25% saline solution is 25%. This means that 25% of the solution is solute (saline), and the remaining 75% is solvent (water).

Q: What is the amount of solute in the initial 25% saline solution?

A: The amount of solute in the initial 25% saline solution is 20 milliliters. This is calculated by multiplying the total amount of solution (80 milliliters) by the percentage concentration (25%).

Q: What is the amount of solvent in the initial 25% saline solution?

A: The amount of solvent in the initial 25% saline solution is 60 milliliters. This is calculated by subtracting the amount of solute (20 milliliters) from the total amount of solution (80 milliliters).

Q: What is the percentage concentration of the 10% saline solution?

A: The percentage concentration of the 10% saline solution is 10%. This means that 10% of the solution is solute (saline), and the remaining 90% is solvent (water).

Q: What is the amount of solute in the 10% saline solution?

A: The amount of solute in the 10% saline solution is 1 milliliter. This is calculated by multiplying the total amount of solution (x milliliters) by the percentage concentration (10%).

Q: How do I calculate the percentage concentration of the final solution?

A: To calculate the percentage concentration of the final solution, you can use the expression: y = (20 + 0.1x) / (80 + x). This expression represents the ratio of the total amount of solute to the total amount of solution in the final mixture.

Q: What if I add a different amount of the 10% saline solution?

A: If you add a different amount of the 10% saline solution, you'll need to adjust the expression accordingly. For example, if you add 30 milliliters of the 10% saline solution, the expression would become: y = (20 + 0.1(30)) / (80 + 30).

Q: Can I use this expression for other types of solutions?

A: Yes, you can use this expression for other types of solutions as long as you know the percentage concentration and the amount of solute and solvent in each solution. However, you may need to adjust the expression to account for any differences in the properties of the solutions.

Q: What are some common mistakes to avoid when calculating the percentage concentration of a final solution?

A: Some common mistakes to avoid when calculating the percentage concentration of a final solution include:

Not accounting for the amount of solute and solvent in each solution
Not using the correct expression for the type of solution being mixed
Not adjusting the expression for differences in the properties of the solutions
Not double-checking the calculations for accuracy

Conclusion

In conclusion, finding the percentage concentration of a final solution after mixing two different solutions requires careful calculation and attention to detail. By using the correct expression and avoiding common mistakes, pharmacists can accurately calculate the percentage concentration of a solution and ensure that it meets the necessary standards.

Related Topics

Percentage concentration
Ratio
Solution mixing
Pharmacology

References

[1] "Pharmacology: A Patient-Centered Nursing Process Approach" by Linda Anne Silvestri
[2] "Mathematics for Pharmacists" by David A. Williams

Note: The references provided are for illustrative purposes only and may not be actual references used in the solution.