1.4
M
500
mL
0.7
mol
1.4
M
500
mL
0.7
mol
The Solution Mixture Calculator determines the final molar concentration when two solutions of the same solute but different concentrations are combined. This is one of the most common calculations in analytical chemistry, biochemistry, and clinical laboratory science. When you mix two solutions, the total number of moles of solute is conserved (assuming no chemical reaction), and the final concentration depends on the combined moles distributed in the combined volume. This calculator applies the fundamental equation C_final = (C₁V₁ + C₂V₂) / (V₁ + V₂) using proper unit conversions for molarity (mol/L) and volume (mL). It also reports the total moles of solute present, which is useful for stoichiometric calculations in subsequent reaction steps.
The calculation is based on the conservation of moles principle:
n_total = n₁ + n₂ = C₁ × V₁ + C₂ × V₂
Where concentrations are in mol/L and volumes in liters. The calculator converts your milliliter inputs to liters internally. The final concentration is:
C_final = n_total / V_total = (C₁V₁ + C₂V₂) / (V₁ + V₂)
This formula assumes ideal mixing — that the total volume equals the sum of individual volumes. For dilute aqueous solutions, this is an excellent approximation. For concentrated solutions or mixtures of dissimilar solvents, actual volumes may differ slightly due to molecular interactions.
The result is a weighted average of the two concentrations, weighted by their respective volumes. If one solution has a much larger volume, the final concentration will be closer to that solution's concentration. This principle is used in serial dilutions, buffer preparation, and standardization of reagent solutions. The calculator also provides total moles, which helps when planning reactions that require specific mole quantities.
The final concentration will always be between C₁ and C₂. If C₁ = C₂, the final concentration equals that value regardless of volumes. A larger volume of the more concentrated solution pulls the final concentration higher. The total moles value is particularly useful when this mixture will be used in a subsequent reaction — you know exactly how many moles of reactant are available. Always verify units: this calculator works with molarity (mol/L) and milliliters.
Inputs
Results
200 mL of 0.5 M and 300 mL of 2.0 M NaCl yield 500 mL at 1.4 M. Total moles: (0.5×0.2) + (2.0×0.3) = 0.1 + 0.6 = 0.7 mol.
Inputs
Results
Adding 50 mL of 10 M stock to 450 mL of pure water (0 M) produces 500 mL at 1.0 M. This is equivalent to a 1:10 dilution.
The mole conservation principle applies to any solvent system. However, the assumption of additive volumes may be less accurate for non-aqueous or concentrated solutions. For precise work with non-aqueous systems, measure the actual final volume after mixing.
This calculator is designed for mixing two solutions of the same solute. If you mix different solutes, each maintains its own concentration independently (assuming no reaction). You would need to calculate each solute's final concentration separately.
Molarity is temperature-dependent because volume changes with temperature. If the two solutions are at different temperatures, the volumes may not be exactly as measured. For precision, equilibrate both solutions to the same temperature before mixing and measuring volumes.
Use the equation C_f × V_total = C₁V₁ + C₂V₂ and solve for the unknown. For example, to find V₂ needed: V₂ = (C_f × V_total - C₁ × V₁) / C₂. This is the basis of the dilution equation C₁V₁ = C₂V₂ when one solution is pure solvent.
No. Molarity (M) is moles per liter of solution. Molality (m) is moles per kilogram of solvent. Molality is independent of temperature and pressure because it uses mass rather than volume. This calculator works with molarity.
Molarity is defined as mol/L. When volume is in mL, we divide by 1000 to get liters before calculating moles (n = C × V_in_L). The final concentration is then n_total / V_total_in_L, ensuring proper mol/L units.
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