Understanding Final Concentration After Mixing Solutions

In chemistry, calculating the final concentration of a solution after mixing is essential for various applications, including laboratory experiments, pharmaceuticals, and industrial processes. This process typically involves knowing the concentrations and volumes of the solutions being mixed. In this article, we will explore three practical examples of finding the final concentration after mixing solutions to illustrate these concepts clearly.

Example 1: Mixing Salt Solutions

Context

A laboratory technician needs to prepare a salt solution for an experiment. They have two solutions: one is a 2 M sodium chloride (NaCl) solution, and the other is a 4 M sodium chloride solution. The technician wants to know the final concentration after mixing 100 mL of each solution.

To find the final concentration, we can use the formula:

[ C_f = \frac{C_1V_1 + C_2V_2}{V_1 + V_2} ]

Where:

• ( C_f ) = final concentration
• ( C_1 ) = concentration of the first solution (2 M)
• ( V_1 ) = volume of the first solution (100 mL)
• ( C_2 ) = concentration of the second solution (4 M)
• ( V_2 ) = volume of the second solution (100 mL)

Calculation

Substituting the values into the formula, we get:

[ C_f = \frac{(2 \text{ M} \times 100 \text{ mL}) + (4 \text{ M} \times 100 \text{ mL})}{100 \text{ mL} + 100 \text{ mL}} ] [ C_f = \frac{200 + 400}{200} = \frac{600}{200} = 3 \text{ M} ]

The final concentration of the mixed solution is 3 M sodium chloride.

Notes

• If the volumes or concentrations change, simply adjust the values in the formula.
• This method can be applied to any solute and solvent mixture as long as the units are consistent.

Example 2: Diluting Acid Solutions

Context

A chemistry student needs to dilute a concentrated hydrochloric acid (HCl) solution for a titration experiment. They have a 6 M HCl solution and wish to dilute it to a final volume of 500 mL at a concentration of 2 M. The student wants to determine how much of the concentrated solution they need to mix with water.

The formula for dilution is:

[ C_1V_1 = C_2V_2 ]

Where:

• ( C_1 ) = initial concentration (6 M)
• ( V_1 ) = volume of the concentrated solution to find
• ( C_2 ) = final concentration (2 M)
• ( V_2 ) = final volume (500 mL)

Calculation

Rearranging the formula to solve for ( V_1 ):

[ V_1 = \frac{C_2V_2}{C_1} ]

Substituting the values:

[ V_1 = \frac{2 \text{ M} \times 500 \text{ mL}}{6 \text{ M}} = \frac{1000}{6} \approx 166.67 \text{ mL} ]

The student needs to use approximately 166.67 mL of the 6 M HCl solution and dilute it with water to reach a total volume of 500 mL.

Notes

• Always add acid to water, not water to acid, to ensure safety and proper mixing.
• This example illustrates how dilution is a specific case of mixing solutions.

Example 3: Combining Solutions with Different Concentrations

Context

In a pharmaceutical setting, a pharmacist needs to combine two different concentrations of a medication to create a specific dosage for a patient. They have a 1.5 mg/mL solution and a 0.5 mg/mL solution. The pharmacist decides to mix 50 mL of the 1.5 mg/mL solution with 150 mL of the 0.5 mg/mL solution. They wish to calculate the final concentration of the combined solution.

Using the mixing formula:

[ C_f = \frac{C_1V_1 + C_2V_2}{V_1 + V_2} ]

Where:

• ( C_1 ) = concentration of the first solution (1.5 mg/mL)
• ( V_1 ) = volume of the first solution (50 mL)
• ( C_2 ) = concentration of the second solution (0.5 mg/mL)
• ( V_2 ) = volume of the second solution (150 mL)

Calculation

Substituting the values into the formula:

[ C_f = \frac{(1.5 \text{ mg/mL} \times 50 \text{ mL}) + (0.5 \text{ mg/mL} \times 150 \text{ mL})}{50 \text{ mL} + 150 \text{ mL}} ] [ C_f = \frac{75 + 75}{200} = \frac{150}{200} = 0.75 \text{ mg/mL} ]

The final concentration of the mixed medication solution is 0.75 mg/mL.

Notes

• This example shows how to handle solutions with differing concentrations effectively.
• Pharmacists often use these calculations to ensure accurate dosing for patients.

These examples of finding final concentration after mixing solutions illustrate the importance of understanding concentration calculations in various fields. By applying the formulas accurately, you can confidently determine the concentrations of mixed solutions in practical scenarios.