Engineering
Dilution (C1*V1 = C2*V2) and two-stock blending (Pearson Square) formulas
Calculate a stock volume from concentration balance and illustrate two-stock blending under an additive-volume assumption.
Generalize C1*V1 = C2*V2 to two-concentration Pearson Square blending
C1*V1=C2*V2 calculates the stock volume for dilution when concentration is amount or mass per unit volume. Add diluent to reach the required final volume.
For nonreactive stocks with additive volumes and compatible concentration units, V_high=V_final*(C_target-C_low)/(C_high-C_low); the remaining volume is low-strength stock.
| Scenario (Final = 360 mL @ 5%) | High 20% Stock Needed | Low stock / diluent (additive-volume model) |
|---|---|---|
| Dilute 20% with Pure Water (0%) | 360 * (5 - 0) / (20 - 0) = 90 mL | 270 mL water |
| Blend 20% Stock + 2% Stock | 360 * (5 - 2) / (20 - 2) = 60 mL | 300 mL of 2% stock |
Concentration-balance formulas with input guards
Guard invalid targets outside [C_low, C_high] so impossible concentrations never output negative volumes.
=IF(OR(B2<D2, B2>A2, A2<=D2, D2<0, C2<0), "Out of Range", ROUND(C2 * (B2 - D2) / (A2 - D2), 2))Volume of solvent / low-concentration stock required
Equals FinalVolume minus HighStockVolume.
=IF(OR(B2<D2,B2>A2,A2<=D2,D2<0,C2<0),"Out of Range",ROUND(C2 - (C2 * (B2 - D2) / (A2 - D2)), 2))Inputs and interpretation
Use consistent mass-per-volume or amount-per-volume concentration units. Weight-percent concentrations cannot be combined by volume this way without density information. The two-stock volume subtraction assumes additive volumes and no reaction; real mixtures can contract or expand. For dilution, add diluent until the required final volume rather than assuming the calculated difference is always an exact measured solvent volume. This is a mass-balance example, not an operational laboratory procedure.
Try the example
Use the original values or change them to test your understanding.