Understanding the Calculation of Final Concentration after Mixing Two Solutions

Calculating the final concentration after mixing two solutions is essential in chemistry and industry. It determines the resulting solute concentration when combining different volumes and concentrations.

This article explores detailed formulas, common values, and real-world applications for accurately computing final concentrations. You will find comprehensive tables, step-by-step examples, and expert insights.

• Calculate the final concentration when mixing 100 mL of 0.5 M NaCl with 200 mL of 1.0 M NaCl.
• Determine the concentration after mixing 50 mL of 2 M HCl with 150 mL of 0.5 M HCl.
• Find the final molarity when 250 mL of 0.1 M glucose solution is mixed with 250 mL of 0.3 M glucose solution.
• Calculate the concentration after mixing 300 mL of 0.2 M KOH with 100 mL of 0.8 M KOH.

Comprehensive Tables of Common Values for Mixing Solutions

Fundamental Formulas for Calculating Final Concentration

The calculation of the final concentration after mixing two solutions relies on the principle of conservation of moles of solute. The total moles of solute before mixing equals the total moles after mixing, assuming no chemical reaction occurs.

The primary formula used is:

• C_f: Final concentration of the mixed solution (mol/L or Molarity)
• C₁: Concentration of solution 1 before mixing (mol/L)
• V₁: Volume of solution 1 before mixing (L or mL)
• C₂: Concentration of solution 2 before mixing (mol/L)
• V₂: Volume of solution 2 before mixing (L or mL)

Note: Volumes must be in the same units (commonly liters or milliliters) for the formula to be valid.

Explanation of Variables and Common Values

• Concentration (C): Typically expressed in molarity (M), which is moles of solute per liter of solution. Common values range from dilute solutions (0.01 M) to concentrated solutions (up to 10 M or more depending on solute solubility).
• Volume (V): The amount of solution, usually measured in milliliters (mL) or liters (L). Volumes can vary widely depending on the application, from microliters in laboratory settings to liters in industrial processes.

Additional Formulas for Related Calculations

In some cases, you may need to calculate the amount of solute (in moles) before or after mixing:

Where:

• n: Number of moles of solute (mol)
• C: Concentration (mol/L)
• V: Volume (L)

Using this, the total moles after mixing is:

Then, the final concentration is:

This approach is particularly useful when dealing with solutions of different units or when calculating the amount of solute required to achieve a target concentration.

Real-World Applications and Detailed Examples

Example 1: Preparing a Diluted Sodium Chloride Solution in a Laboratory

A chemist needs to prepare 300 mL of a 0.833 M NaCl solution by mixing 100 mL of 0.5 M NaCl with 200 mL of 1.0 M NaCl. The goal is to verify the final concentration after mixing.

Step 1: Identify known values

• C₁ = 0.5 M
• V₁ = 100 mL
• C₂ = 1.0 M
• V₂ = 200 mL

Step 2: Calculate total moles of NaCl

Step 3: Calculate total volume

Step 4: Calculate final concentration

The final concentration matches the target, confirming the calculation’s accuracy.

Example 2: Industrial Mixing of Acid Solutions for pH Adjustment

An industrial process requires mixing 50 L of 2 M hydrochloric acid (HCl) with 150 L of 0.5 M HCl to achieve a specific concentration for a neutralization reaction.

Step 1: Known values

• C₁ = 2 M
• V₁ = 50 L
• C₂ = 0.5 M
• V₂ = 150 L

Step 2: Calculate moles of HCl

Step 3: Calculate total volume

Step 4: Calculate final concentration

This final concentration is critical for ensuring the neutralization reaction proceeds with the desired efficiency and safety.

Additional Considerations and Advanced Topics

While the basic formula assumes ideal mixing and no volume change upon mixing, in some cases, volume contraction or expansion can occur, especially with concentrated solutions or different solvents. This can affect the accuracy of the final concentration calculation.

For highly precise applications, consider:

• Volume contraction: Some mixtures exhibit volume changes due to molecular interactions. This requires experimental data or correction factors.
• Temperature effects: Concentration and volume can vary with temperature; temperature control or compensation may be necessary.
• Non-ideal solutions: Activity coefficients may be needed for ionic strength or non-ideal behavior.

For further reading on solution mixing and concentration calculations, authoritative sources include:

• American Chemical Society: Principles of Solution Chemistry
• Chemguide: Mixing Solutions and Concentrations
• NIST Chemical Measurements and Standards

Summary of Key Points

• The final concentration after mixing two solutions is calculated by the weighted average of moles over total volume.
• Ensure volumes are in consistent units and concentrations are expressed in molarity.
• Use the formula: C_f = (C₁ × V₁ + C₂ × V₂) / (V₁ + V₂) for straightforward calculations.
• Consider real-world factors such as volume changes, temperature, and solution non-ideality for precise applications.
• Tables of common values assist in quick reference and validation of calculations.

Mastering these calculations is fundamental for chemists, chemical engineers, and laboratory technicians to ensure accurate solution preparation and process control.