Problem 47 - Introductory Algebra for College Students

Question

Must the concentration of a mixture always be greater than the concentration of an ingredient in one of the solutions and less than the concentration of the ingredient in the other solution being mixed? Explain your answer.

Step-by-Step Solution

Answer

No, the concentration of a mixture is not necessarily always greater than the concentration of an ingredient in one of the solutions and less than the concentration of the ingredient in the other solution being mixed. It rather depends on the initial concentrations and the volumes of the solutions being mixed.

Step 1: Understand Concentration of Mixtures

In chemistry, concentration is a measure of how much solute is dissolved in a specific amount of solvent or solution. When two solutions are mixed, the final concentration of the resulting solution will depend on the initial concentrations and the volumes of the two solutions. The concentration of the mixture could be more, less or the same as the concentrations of the individual solutions.

Step 2: Give An Example To Illustrate The Change In Concentration

For instance, if equal volumes of two solutions A and B are mixed with A having a higher concentration than B, the final concentration of the mixture will be somewhere between the concentration of A and B. On the other hand, if the volume of solution B is much higher than the solution A even though A has a higher concentration, the final concentration could be less than both solutions as solution B dilutes the overall concentration.

Step 3: Conclusion

Therefore, the concentration of a mixture does not always have to be greater than the concentration of an ingredient in one of the solutions and less than the concentration of the ingredient in the other solution being mixed. It all depends on the initial concentrations of the solutions and their volumes.