A scientist mixes 40 mL of a 10% saline solution with 60 mL of a 20% saline solution. What is the concentration of the resulting solution?

Title: How to Calculate the Concentration of a Mixed Saline Solution: A Scientific Approach

When mixing saline solutions of different concentrations, understanding how to compute the resulting concentration is essential in laboratory, medical, and educational settings. A common challenge is determining the final concentration when combining measured volumes of solutions with known salt (solute) percentages. In this article, we explore a precise method using a practical example: mixing 40 mL of a 10% saline solution with 60 mL of a 20% saline solution. The result? A clearer understanding of concentration calculations that combines chemistry and arithmetic.

Understanding the Context

Step-by-Step Breakdown: How to Find the Final Concentration

To find the concentration of the mixed solution, we use the principle of mass balance—the idea that the total amount of solute before mixing equals the total amount after mixing, regardless of volume or concentration.

Given:

Volume of 10% saline solution: 40 mL
Concentration of 10% solution: 10% = 0.10
Volume of 20% saline solution: 60 mL
Concentration of 20% solution: 20% = 0.20

A scientist mixes 40 mL of a 10% saline solution with 60 mL of a 20% saline solution. What is the concentration of the resulting solution?

Key Insights

Step 1: Calculate the amount of salt in each solution

For a solution, concentration (%) = (mass of solute / mass of solution) × 100, but we can also work directly with volumes and concentrations for a straightforward calculation.

Salt mass from first solution:
(10 / 100) × 40 mL = 0.10 × 40 = 4 grams of salt

Salt mass from second solution:
(20 / 100) × 60 mL = 0.20 × 60 = 12 grams of salt

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Final Thoughts

Step 2: Add the total salt and total volume

Total salt = 4 grams + 12 grams = 16 grams
Total volume = 40 mL + 60 mL = 100 mL

Step 3: Calculate the final concentration

Concentration = (Total salt mass / Total volume) × 100
= (16 g / 100 mL) × 100 = 16%

Final Answer:

The resulting solution has a 16% saline concentration.

Why This Method Matters

This calculation reflects the law of conservation of mass applied in solution chemistry. It helps scientists, medical professionals, and students accurately prepare and verify saline solutions for experiments, medical treatments, or educational demonstrations. Understanding concentration mixing is foundational in fields such as biology, pharmacy, and chemical engineering.