Solution Mixing — New Concentration Calculator Tutorial

What Is Solution Mixing?

Solution mixing is the process of combining two or more solutions that contain the same solute (for example NaCl, HCl or NaOH) to produce a new solution. This operation is very common in chemistry, especially during concentration adjustment, dilution and stock solution preparation.

The key idea here is: Solute is neither created nor destroyed. During mixing, only the total volume over which the solute is distributed changes.

Core Chemical Principle: Conservation of Moles

At the heart of all solution mixing problems lies one powerful principle:

n_total = n₁ + n₂

The total moles of solute equals the sum of the moles from each solution.

This principle is the application of the law of conservation of mass and matter to solutions. It is assumed that the solute does not evaporate, does not react and does not leave the system.

The Concept of Concentration (Molarity)

One of the most commonly used concentration measures in chemistry is molarity (M):

M = n / V

n: moles of solute, V: volume of solution (L)

Therefore, the moles of solute in a solution are found as:

n = C · V

The Logic Behind the Mixing Formula

Consider two solutions:

Solution 1: concentration C₁, volume V₁
Solution 2: concentration C₂, volume V₂

The moles of solute in each:

n₁ = C₁ · V₁
n₂ = C₂ · V₂

After mixing:

Total moles: n_total = C₁·V₁ + C₂·V₂
Total volume: V_total = V₁ + V₂

The new concentration is found by dividing total moles by total volume:

C_new = (C₁·V₁ + C₂·V₂) / (V₁ + V₂)

Step-by-Step Example

0.5 M, 100 mL NaCl solution
1.0 M, 200 mL NaCl solution

n₁ = 0.5 × 100 = 50 (M·mL)
n₂ = 1.0 × 200 = 200 (M·mL)
Total moles = 250
Total volume = 300 mL
C_new = 250 / 300 ≈ 0.83 M

Result: The concentration of the mixture is approximately 0.83 M.

Important Considerations

This method is only valid for the same solute in both solutions.
If a chemical reaction occurs (e.g. acid + base), this formula cannot be applied directly.
Volume units must be consistent (mL–mL or L–L).
Results are based on idealised assumptions.

Note: Solution mixing problems in chemistry are among the cleanest and most reliable calculations for those who grasp the logic of "find the moles first, then divide by volume".