Solution Mixing is the process of combining two or more solutions to create a new, final solution. In chemistry, this most often involves calculating the final concentration of a solute after mixing solutions of different concentrations.

The fundamental principle behind all mixing calculations is the conservation of moles. The total amount of solute (in moles) in the final mixture is simply the sum of the amounts of solute contributed by each of the initial solutions.

Similarly, the final volume of the mixture is assumed to be the sum of the individual volumes of the solutions being mixed (unless stated otherwise).

The process of calculating the final concentration is governed by a straightforward formula derived from the principle of mole conservation.

Since Moles = Molarity × Volume (M * V), the total moles are M₁V₁ + M₂V₂. The total volume is V₁ + V₂.

The final molarity (M_f) is the total moles divided by the total volume:

M_f = (M₁V₁ + M₂V₂) / (V₁ + V₂)

Each part of the mixing formula represents a specific quantity:

M₁ and V₁: The Molarity and Volume of the first solution.

M₂ and V₂: The Molarity and Volume of the second solution.

M_f: The final Molarity of the resulting mixture.

It is crucial that the units for volume (e.g., mL or L) are consistent for all terms in the calculation.

Solution mixing is one of the most common procedures in any laboratory or medical setting.

Laboratory Research: Scientists constantly need to prepare solutions of a specific concentration for experiments. They often do this by mixing a concentrated stock solution with a diluent (like water) or another solution.

Pharmaceutical Compounding: Pharmacists use these principles to prepare custom medications, such as IV drips or liquid medicines, by mixing different stock drug solutions to achieve the exact concentration prescribed by a doctor.

Industrial Processes: In manufacturing, large vats of chemical solutions are often adjusted by mixing in other solutions to maintain optimal concentrations for a chemical process.