Hong Life CalculatorsUnderstanding the mixing material balance calculator — concept and principle
Blending two streams of different concentration is one of the most common tasks in chemistry, food processing, water treatment and even cooking. This calculator gives the concentration of the mixture, and also answers the reverse question: how much of the second stream you need to reach a target concentration. Flows can be in any consistent unit (kg, kg/h, L) as long as both streams use the same one and the concentration is on the same basis.
How it is calculated
- Mixed concentration: x = (m₁x₁ + m₂x₂) / (m₁ + m₂).
- Stream 2 needed for a target x_t: m₂ = m₁ · (x_t − x₁) / (x₂ − x_t).
Concentrations are in percent. The second result is undefined when x₂ equals the target, because stream 2 alone could never move the mixture away from its own value.
The principle
Mass is conserved: nothing is created or destroyed by mixing. Writing a balance for the total gives m₁ + m₂ = m, and for the component of interest m₁x₁ + m₂x₂ = m·x. Dividing the second by the first gives a weighted average, with each stream weighted by its flow. Solving the same balance for m₂ gives the target formula, often taught as the lever rule or the "alligation" method: the amount of each stream is proportional to the distance of the other stream's concentration from the target.
Worked example
- Inputs: stream 1 = 100 at 10%, stream 2 = 50 at 40%, target 20%.
- Component in: 100 × 10 + 50 × 40 = 1000 + 2000 = 3000.
- Total flow: 100 + 50 = 150.
- Mixed concentration: 3000 / 150 = 20%.
- Stream 2 for 20%: 100 × (20 − 10) / (40 − 20) = 100 × 10 / 20 = 50.
| Stream 2 concentration (%) | Mixed concentration (%) |
|---|---|
| 10 | 10 |
| 20 | 13.33333333 |
| 30 | 16.66666667 |
| 40 | 20 |
| 50 | 23.33333333 |
| 60 | 26.66666667 |
| 80 | 33.33333333 |
How to read the result
The mixed value always lies between x₁ and x₂, closer to the larger stream. If the required m₂ comes out negative, the target lies outside the range of the two streams and cannot be reached by mixing them. Equal distances from the target mean equal flows; here 10% is 10 points below and 40% is 20 points above, so twice as much of stream 1 is needed, matching 100 : 50.
Common mistakes
- Mixing mass percent with volume percent; volumes of solutions are often not additive.
- Using flows in different units for the two streams.
- Applying the balance when a reaction, evaporation or settling changes the component during mixing.
Frequently asked questions
Can I mix more than two streams?
Yes, the same idea extends: x = Σmᵢxᵢ / Σmᵢ for any number of streams.
How do I dilute with pure water?
Set x₂ = 0. The formula then gives the water needed, m₂ = m₁(x_t − x₁)/(0 − x_t).
Does it work for temperatures?
For streams of the same liquid with constant heat capacity, the mixed temperature is a similar flow-weighted average.
Sources: R. M. Felder and R. W. Rousseau, Elementary Principles of Chemical Processes, Wiley · D. M. Himmelblau and J. B. Riggs, Basic Principles and Calculations in Chemical Engineering, Prentice Hall