Mixture and Solution Problems

Fundamental Equation for Mixtures

mass of substance = (concentration / 100) × total mass. For a solution containing C% of a substance with total mass M: pure substance mass = C·M/100.

When mixing two solutions, the total mass of the pure substance is conserved: C₁·M₁/100 + C₂·M₂/100 = C₃·(M₁ + M₂)/100.

Setting Up a Mixture Equation

1. Identify what you are mixing and what you want to obtain.
2. Write the mass/volume balance: M₁ + M₂ = M₃.
3. Write the substance balance: C₁M₁ + C₂M₂ = C₃M₃.
4. Solve the system for the unknown.

Example

There are two salt solutions: 18% and 42%. How much of each to obtain 5 liters of a 30% solution?

Let x = liters of 18% solution. Mass balance: x + (5−x) = 5. Salt balance: 0.18x + 0.42(5−x) = 1.5.

Solving: 0.18x + 2.1 − 0.42x = 1.5, so −0.24x = −0.6, giving x = 2.5 liters.

Answer: 2.5 liters of each solution.