Mixing Calculator — Mass, Volume & Molar Concentration

The fundamental principle is the conservation of mass. The mass of a solute (the thing you're measuring concentration of) is conserved during mixing. For a two-component mixture, the resulting mixture concentration is the total solute mass divided by the total solution mass.

Where $\dot{m}_1, \dot{m}_2$ are the mass flow rates of the incoming streams (kg/h), and $C_1, C_2$ are their concentrations (e.g., mass fraction, ppm, molarity). $C_{mix}$ is the concentration of the resulting mixture.

Often, you know the concentration you want ($C_{target}$) and need to find how much of a second stream to add. By rearranging the mass balance, you can solve for the required flow rate of the second component.

Here, $\dot{m}_{2,req}$ is the required mass flow of stream 2 to achieve the target concentration. This is crucial for precise dilution or recipe formulation. Note: This equation fails if $C_2 = C_{target}$ (division by zero), meaning you can't reach the target by mixing these two streams.

Chemical Process Industries: Continuously blending raw material streams in a reactor feed. For instance, mixing a catalyst solution (high concentration) with a solvent to achieve the precise, lower concentration needed for a polymerization reaction, ensuring product quality and safety.

Water & Wastewater Treatment: Diluting a concentrated chemical disinfectant, like sodium hypochlorite (bleach), with water to achieve the correct dosage for treating drinking water. The calculator helps determine the flow rates for the dosing pumps.

Pharmaceutical Manufacturing: Preparing buffer solutions or drug formulations where active pharmaceutical ingredients (APIs) at a known concentration must be mixed with excipients to reach the final specified strength in a batch process.

Food & Beverage Production: Standardizing the concentration of ingredients like sugar, acid, or salt in a product stream. For example, blending a high-Brix fruit juice concentrate with water to achieve the desired sweetness level in the final beverage before packaging.

When starting to use this tool, there are several pitfalls that engineers, especially those with less field experience, often fall into. First and foremost, always keep the unit systems for concentration and flow rate consistent. For example, if you input the flow rate in [L/min] while setting the concentration as a mass fraction [kg/kg], the calculation result will be completely meaningless. It's safest to assume the tool does not perform unit conversions internally. Ensure everything is on a mass basis (kg, kg/h, mass fraction) or everything is on a volume basis (L, L/min, volume fraction).

Next, be aware of the pitfall of volume fractions in non-ideal mixing. For instance, mixing 100mL of ethanol with 100mL of water results in a total volume of approximately 192mL. If you calculate the volume fraction in this tool with the density parameter left at "1.0" (assuming ideal mixing), it will show a mixture concentration of 50 vol%, while the actual concentration is about 52 vol%. In designs requiring high precision, this discrepancy cannot be ignored. Therefore, understand that the basis of process design is mass, and also understand that this tool can provide accurate volume fractions converted from a mass basis if you input the densities correctly.

Finally, a precondition when using the reverse calculation feature. When calculating using the formula $$\dot{m}_{2,req}= \dfrac{\dot{m}_1(C_{target}-C_1)}{C_2-C_{target}}$$, meaningful answers are only possible if $C_{target}$ lies between $C_1$ and $C_2$. For example, it's possible to dilute a 5% solution (Stream 1) with a 3% solution (Stream 2) to achieve 4%, but impossible to reach 6%. If the tool shows negative flow rates or abnormal values, first suspect this precondition.