How Mass Balance Reveals Yield and Purity in Fractional Crystallization

Fractional crystallization is a selective separation

Fractional crystallization separates dissolved substances because their solubilities respond differently to temperature and solvent volume. A useful target dissolves well in hot solvent but poorly in cold solvent. After cooling, much of the target enters the solid phase while a more soluble impurity remains in the mother liquor.

An insoluble component is handled earlier. It is collected by filtration after the soluble salts dissolve, so this first separation depends on insolubility rather than crystallization.

Mass balance makes every reported percentage auditable

Each recovered mass is a difference between a container-plus-material measurement and the corresponding empty container or filter:

$$m_{material}=m_{container+material}-m_{container}$$

The composition or recovery percentage must then name its denominator. “Percent of the original sample recovered as KNO3” is:

$$\%\text{ recovered as }KNO_3=\frac{m_{recovered\ KNO_3}}{m_{original\ sample}}\times100\%$$

That is different from percent recovery of the KNO3 originally present, which requires knowing the starting KNO3 mass. A calculation can be numerically correct yet answer the wrong question if those denominators are confused.

Yield and purity usually trade against each other

Product remains dissolved in the cold mother liquor, adheres to glassware, or dissolves during washing. Those losses lower yield. Using less solvent and minimizing washing can recover more solid, but retained mother liquor may carry soluble impurity into the crystal cake.

Recrystallization repeats dissolution and cooling with a smaller product sample. It often improves purity because impurity stays in solution, but it also creates another opportunity for product loss. The best procedure therefore balances enough solvent for clean separation against excessive solvent that keeps the target dissolved.

Color comparison is a bounded purity estimate

If copper impurity is converted to a colored ammonia complex, its intensity can be compared with standards prepared under the same volume and viewing conditions. This is a semiquantitative result: report the closest standard or a bounded range. A color lighter than the lowest standard supports “below the comparison range,” not an exact zero concentration.

The strongest conclusion combines both dimensions: recovered mass describes yield, while the impurity comparison describes purity. Neither measurement alone proves that the separation was successful.