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Solution Mixing Calculator

Calculate the final concentration when mixing solutions or determine volumes needed to achieve a target concentration.

Calculation Mode

C1V1 + C2V2 = CfVf
Find final concentration after mixing

Solution 1

Solution 2

Final Concentration

0.8750 M
Total Volume: 200.0 mL

Mixing Summary

Solution 1
Concentration: 2 M
Volume: 50 mL
Moles added: 100.0000 mmol
Solution 2
Concentration: 0.5 M
Volume: 150 mL
Moles added: 75.0000 mmol
Final Mixture
Total Volume: 200.0 mL
Total Moles: 175.0000 mmol

What Is Solution Mixing?

Solution mixing is the process of combining two or more solutions to create a new solution with a desired concentration. This is one of the most fundamental operations in chemistry laboratories, pharmaceutical manufacturing, food production, and industrial processes. The final concentration after mixing depends on the volumes and concentrations of the component solutions, governed by the conservation of moles.

The key principle is that the total number of moles of solute in the final mixture equals the sum of moles contributed by each component solution. When two solutions are mixed, moles from solution 1 (C₁V₁) plus moles from solution 2 (C₂V₂) equal the total moles in the mixture, which at the final concentration C_f occupies volume V_f. This gives the fundamental mixing equation: C₁V₁ + C₂V₂ = C_f × V_f.

Solution mixing differs from simple dilution in that both components may contain solute. In dilution, only one component (the solvent) contributes no solute, simplifying the calculation. In mixing, both solutions contribute solute, and the final concentration reflects the weighted average of the two inputs based on their volumes.

Understanding solution mixing is critical for preparing buffer solutions, making cell culture media, formulating pharmaceutical products, blending chemicals in industrial processes, and creating calibration standards. Accurate mixing requires precise volumetric measurements and thorough mixing to ensure homogeneity.

The Mixing Equations

The fundamental equation for mixing two solutions is derived from the conservation of moles. When mixing solution 1 (concentration C₁, volume V₁) with solution 2 (concentration C₂, volume V₂), the final concentration is: C_f = (C₁V₁ + C₂V₂) / (V₁ + V₂). This assumes volumes are additive, which is a reasonable approximation for dilute solutions.

For the special case of diluting a stock solution with pure solvent (C₂ = 0), the equation simplifies to the well-known dilution formula: C₁V₁ = C_f × V_f, or C₁V₁ = C₂V₂. This is used when preparing solutions of known concentration from a more concentrated stock.

When preparing a target concentration from a stock solution and a diluent, the required volume of stock is: V_stock = (C_target - C_diluent) × V_total / (C_stock - C_diluent). For diluting with pure solvent (C_diluent = 0), this simplifies to V_stock = C_target × V_total / C_stock.

These equations assume complete mixing and negligible volume change upon mixing. For precise work, especially with organic solvents or highly concentrated solutions, actual volumes should be verified experimentally.

Solution Mixing Equation

C₁V₁ + C₂V₂ = C_f × V_f

Where:

  • C₁= Concentration of solution 1 (M)
  • V₁= Volume of solution 1 (mL)
  • C₂= Concentration of solution 2 (M)
  • V₂= Volume of solution 2 (mL)
  • C_f= Final concentration after mixing (M)
  • V_f= Total final volume (mL) = V₁ + V₂

How to Use This Calculator

This solution mixing calculator operates in two modes to handle different laboratory scenarios. Select the mode that matches your needs:

Mix Solutions Mode: Use this when you have two solutions with known concentrations and volumes and want to find the final concentration after mixing. Enter the concentration and volume for each solution, and the calculator determines the final concentration and total volume.

Target Concentration Mode: Use this when you need to prepare a specific volume at a target concentration from a stock solution and diluent. Enter your target concentration and volume, along with the stock and diluent concentrations. The calculator determines exactly how much stock and diluent to measure.

Follow these steps for the target concentration mode:

  1. Enter Target Parameters: Specify the desired concentration and total volume of the final solution.
  2. Enter Stock Concentration: Input the concentration of your concentrated stock solution.
  3. Enter Diluent Concentration: Usually 0 for pure water or buffer. If using a second solution as diluent, enter its concentration.
  4. Review Volumes: The calculator provides the exact volumes of stock and diluent needed, along with a step-by-step procedure.
  5. Verify: The calculator confirms that the mixed solution achieves the target concentration.

Understanding the Results

In Mix Mode, the results show the final concentration, total volume, and a detailed summary of each component solution including its concentration, volume, and the moles it contributed. The final concentration is a volume-weighted average of the input concentrations.

In Target Mode, the results provide the exact volumes of stock solution and diluent needed, along with a step-by-step mixing procedure. The verification section confirms that the calculated volumes produce the correct final concentration by recalculating from the volumes and concentrations.

The mixing summary shows the contribution of each solution to the final mixture, including the moles of solute from each source. This information helps verify that the correct amount of each component was added.

When the diluent concentration is zero (pure solvent), the mixing equation reduces to the familiar dilution formula. When both solutions contain solute, the final concentration reflects the weighted contribution of each based on its volume.

Real-World Applications

Solution mixing is fundamental to countless laboratory and industrial operations. In biochemistry and cell biology, preparing culture media, buffer solutions, and reagent solutions requires precise mixing of stock solutions. The wrong concentration can affect cell growth, enzyme activity, or experimental results.

In pharmaceutical manufacturing, drug formulations are prepared by mixing concentrated active ingredients with diluents, flavoring agents, and preservatives. The final concentration must be within strict specifications for safety and efficacy. IV solutions, injectable medications, and oral formulations all require accurate mixing.

Analytical chemistry relies on solution mixing for preparing calibration standards, diluting samples to within the instrument's linear range, and creating matrix-matched standards. Serial dilution and standard addition methods both involve systematic mixing operations.

In food and beverage production, mixing determines the flavor, alcohol content, and nutritional value of products. Wine blending, soft drink formulation, and sauce preparation all involve controlled mixing of concentrated ingredients with water or other solvents.

Environmental monitoring requires mixing samples with reagents for analysis, diluting concentrated pollutants to measurable levels, and preparing standard solutions for instrument calibration.

Worked Examples

Mixing Two Salt Solutions

Problem:

What is the final concentration when mixing 50 mL of 2.0 M NaCl with 150 mL of 0.5 M NaCl?

Solution Steps:

  1. 1Solution 1: C₁ = 2.0 M, V₁ = 50 mL. Moles₁ = 2.0 × 50 = 100 mmol.
  2. 2Solution 2: C₂ = 0.5 M, V₂ = 150 mL. Moles₂ = 0.5 × 150 = 75 mmol.
  3. 3Total moles = 100 + 75 = 175 mmol.
  4. 4Total volume = 50 + 150 = 200 mL.
  5. 5Final concentration = 175 / 200 = 0.875 M.

Result:

The final concentration is 0.875 M NaCl in 200 mL total volume.

Preparing a Target Concentration from Stock

Problem:

How much 5.0 M HCl stock solution is needed to prepare 100 mL of 1.0 M HCl?

Solution Steps:

  1. 1Use the dilution equation: C₁V₁ = C₂V₂.
  2. 2C₁ = 5.0 M (stock), C₂ = 1.0 M (target), V₂ = 100 mL.
  3. 3V₁ = C₂V₂ / C₁ = (1.0 × 100) / 5.0 = 20 mL.
  4. 4Diluent volume = 100 - 20 = 80 mL of water.
  5. 5Verification: (5.0 × 20) / 100 = 1.0 M ✓

Result:

Measure 20 mL of 5.0 M HCl stock and add 80 mL of water to obtain 100 mL of 1.0 M HCl. Always add acid to water, not water to acid.

Mixing Solutions with Different Concentrations

Problem:

What volume of 0.1 M NaOH must be mixed with 200 mL of 0.3 M NaOH to obtain a 0.2 M solution?

Solution Steps:

  1. 1Let V₁ = volume of 0.1 M NaOH. C₁ = 0.1, V₂ = 200 mL, C₂ = 0.3.
  2. 2Target: C_f = 0.2 M. Total volume = V₁ + 200.
  3. 3C₁V₁ + C₂V₂ = C_f(V₁ + V₂).
  4. 40.1V₁ + 0.3(200) = 0.2(V₁ + 200).
  5. 50.1V₁ + 60 = 0.2V₁ + 40.
  6. 620 = 0.1V₁ → V₁ = 200 mL.

Result:

Mix 200 mL of 0.1 M NaOH with 200 mL of 0.3 M NaOH to obtain 400 mL of 0.2 M NaOH.

Tips & Best Practices

  • ✓Always add the more concentrated solution to the less concentrated solution (or solvent) for safety.
  • ✓Use volumetric glassware for precise measurements—graduated cylinders are less accurate.
  • ✓Mix thoroughly after combining solutions to ensure homogeneous concentration.
  • ✓For acids and bases, always add acid to water, never water to acid, to control the exothermic mixing.
  • ✓Prepare slightly more than needed to account for losses during transfer and mixing.
  • ✓Label all prepared solutions with concentration, date, and preparer's initials.
  • ✓For critical applications, verify the final concentration by analytical measurement.

Related Calculators

Dilution Calculator

Calculate dilution volumes

Molarity Calculator

Calculate molar concentration

Solution Calculator

Calculate solution properties

Buffer Calculator

Prepare buffer solutions

Frequently Asked Questions

Dilution is a special case of mixing where one component is pure solvent (concentration = 0). In dilution, the equation simplifies to C₁V₁ = C₂V₂. In mixing, both solutions contain solute, so the equation C₁V₁ + C₂V₂ = C_f × V_f must be used. Mixing produces a weighted average concentration based on the volumes and concentrations of both inputs.
Volumes are approximately additive for dilute aqueous solutions, but not perfectly. When molecules of different substances interact, the total volume may be slightly more or less than the sum of individual volumes. For most laboratory purposes with dilute solutions, assuming additive volumes introduces negligible error. For concentrated solutions or organic solvents, actual volumes should be verified.
Precision requirements depend on your application. For general laboratory work, volumetric pipettes (±0.1-0.2% accuracy) are sufficient. For analytical chemistry and pharmaceutical preparations, Class A volumetric glassware (±0.05-0.1%) is recommended. For critical applications, analytical balance mass measurements are more accurate than volumetric measurements.
Yes, the principle extends to any number of solutions. The total moles equal the sum of moles from all solutions: Σ(CᵢVᵢ) = C_f × ΣVᵢ. You can calculate the final concentration by dividing the total moles by the total volume. The calculator handles two solutions, but the principle is the same for three or more.
In most laboratory mixing operations, the diluent is pure water or buffer that contains no solute of interest. Setting C₂ = 0 simplifies the mixing equation to the dilution formula. However, when preparing buffers or complex media, the diluent may contain other solutes at known concentrations, in which case the non-zero diluent concentration must be entered.

Sources & References

Last updated: 2026-06-06

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Editorial Note

MyCalcBuddy Editorial Team

This page is maintained as an educational calculator reference.

Source

Formula Source: Chemistry: The Central Science

by Brown, LeMay, Bursten

UpdatedLast reviewed: May 2026
CheckedFormula checks are based on standard references and internal QA review.