Worked problem

Mixing Two Solutions: Flow and Concentration

Mix two streams of different flow and solute mass fraction with a steady-state mass balance, and find the flow of stream B for a 20% mixture.

Chemical & Process · Last reviewed October 17, 2026

Given

Stream A: 800 kg/h at 10% solute by mass. Stream B: 500 kg/h at 40% solute by mass. The two streams mix in a tank with no reaction and no accumulation (steady state). Concentrations are mass fractions.

Find

The mixed-stream flow and its solute mass fraction. Then, the flow of stream B that would give a 20% mixture with 800 kg/h of stream A.

Solution

Total mass balance: 800 + 500 = 1,300 kg/h leaves the mixer.
Solute balance: solute in = 800 × 0.10 + 500 × 0.40 = 80 + 200 = 280 kg/h. All of it leaves in the mixed stream.
Mixed mass fraction = 280 ÷ 1,300 = 0.2154, or 21.5% solute.
For a 20% mixture: 80 + 0.40 × B = 0.20 × (800 + B), so 0.20 × B = 80 and B = 400 kg/h.

Answer

1,300 kg/h at 21.5% solute  |  400 kg/h of stream B gives 20%

The mixture is a weighted average

The mixed concentration lies between the two inlet concentrations, closer to the one with the larger flow. Here it is 10% + (500 ÷ 1,300) × 30% = 21.5%. Averaging the two percentages without weights would give 25%, which is wrong because the streams are not equal.

Common mistakes

Averaging the concentrations without weighting them by the flow rates.
Adding volume flows when the solution densities differ. Mass is conserved, volume is not exactly.
Mixing mass fractions with mole fractions, or percent by weight with percent by volume.
Forgetting that the solute balance and the total balance are two equations from which both unknowns follow.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

Questions

Why is mass used instead of volume?

Mass is conserved in mixing. Volumes of liquid mixtures are often not additive, so mass balances are safer.

What if a reaction or heat effect happens on mixing?

The mass balance still holds, but the temperature and possibly the species change. An energy balance or a reaction term is then needed.

What does steady state mean here?

The flows and concentrations do not change with time, so the tank holds a constant amount and what comes in equals what goes out.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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