Solution Mixing

Biology • Solutions Concentrations, and Dilutions

Written by STEM Calculators Team Published January 3, 2026 Updated February 24, 2026

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Solution mixing (final concentration after mixing)

Mix 2–5 solutions with concentrations \(C_i\) and volumes \(V_i\). The final concentration (compatible units only) is:

\[ \begin{aligned} C_f &= \frac{\sum_{i=1}^{k} C_i V_i}{\sum_{i=1}^{k} V_i} \end{aligned} \]

Special case: pure solvent is simply a component with \(C=0\).

Inputs

Add/remove rows, or paste/upload CSV. Units must be compatible (molar family vs mg/mL).

Output concentration unit

Auto-limited by unit family.

Output volume unit

Actions

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CSV / paste mode

Columns: name, C, Cu, V, Vu. Header is optional. You can paste comma-separated or tab-separated.

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Tip: keep \(C_i\) units all molar (M/mM/µM) or all mg/mL. Solvent can be \(C=0\) in the same family.

Stacked volume share

Hover for values • drag to pan • wheel to zoom

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Solute contribution \(C_iV_i\)

Shows which component contributes most to total solute

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Mixing beaker

Segments show volume portions; hover to inspect

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Solution Mixing: Final Concentration

When multiple solutions of the same solute are combined, the final concentration is determined by conservation of solute across the total mixed volume. This solution mixing calculator computes the final (post-mix) concentration as a volume-weighted average.

Core definitions and formulas

Mixing is modeled by adding each component’s solute contribution and dividing by the total volume (pure solvent is a valid component with C = 0).

\[ \begin{aligned} V_{\text{tot}} &= \sum_{i=1}^{k} V_i \\ S &= \sum_{i=1}^{k} C_i \cdot V_i \\ C_f &= \frac{S}{V_{\text{tot}}} \end{aligned} \]

Symbols: k is the number of components; C_i is the concentration of component i; V_i is its volume; V_tot is total mixed volume; S is total solute contribution. Concentration units must be compatible (molar units such as M/mM/µM are inter-convertible, while mg/mL is a different concentration scale that requires a molar-mass conversion before mixing with molarity).

Interpreting outputs and avoiding mistakes

A larger C_i \cdot V_i means that component contributes more to the total solute; a larger V_i (especially with lower C_i or with C = 0) increases dilution and lowers C_f. Typical volume units are µL, mL, or L; typical concentration units are M (mol/L) for molarity or mg/mL for mass concentration.

The calculator output is most useful when read as three connected ideas: final concentration (C_f in the selected unit), total volume (V_tot), and per-component contributions (volume share and solute contribution C_i \cdot V_i) to identify which stock solution dominates the mixture.

Mixing incompatible concentration families (molar units with mg/mL) without converting first.
Entering volumes in different units (µL vs mL) without checking the final unit selection.
Using concentrations from different solutes; the weighted-average model assumes the same solute is being mixed.
Ignoring non-ideal effects (volume contraction, evaporation, reaction); the model assumes volumes add and no chemistry changes the solute amount.

Micro example. Mix 10 mL of 2.0 M with 30 mL of 0.50 M.

\[ \begin{aligned} C_f &= \frac{(2.0\ \text{M})\cdot(10\ \text{mL}) + (0.50\ \text{M})\cdot(30\ \text{mL})}{10\ \text{mL} + 30\ \text{mL}} \\ &= \frac{20 + 15}{40}\ \text{M} \\ &= 0.875\ \text{M} \end{aligned} \]

Use solution mixing when combining 2–5 stocks (including solvent) to compute a final concentration and to compare component contributions. Avoid using it when the solute changes by reaction, when concentrations are reported on incompatible bases without conversion, or when non-ideal volume effects matter; a common next step is serial dilution planning or uncertainty/error propagation for pipetting.

Frequently Asked Questions

How do you calculate final concentration after mixing solutions?

The calculator uses a weighted average by volume: Cf = sum(Ci x Vi) / sum(Vi). Each term Ci x Vi represents the amount of solute contribution from that component, and the denominator is the total final volume.

Why must the concentration units be compatible when mixing solutions?

The formula requires all Ci values to represent the same type of concentration scale. M, mM, and µM are compatible with each other, but mg/mL is a different unit family and cannot be mixed with molar units without a molar mass conversion step.

How do I include pure solvent in a mixing calculation?

Add a solvent row using the Add solvent option, which sets C = 0, then enter only its volume. This increases the total volume and lowers Cf while keeping the solute sum unchanged.

What does CiVi mean in the results?

CiVi is the solute contribution term for component i used in the numerator of the mixing equation. Comparing CiVi values helps identify which component contributes most to the final concentration.

How do I paste data into the solution mixing calculator using CSV?

Use CSV / paste mode and follow the template columns name, C, Cu, V, Vu (header optional). Paste comma-separated or tab-separated rows, then load from the textarea or upload a CSV file to populate the component table.

Calculation steps

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Frequently Asked Questions