Crystallization Yield Calculator
Calculate crystal yield, mother liquor mass, and percent recovery for cooling and evaporative crystallization operations.
About this calculator
This calculator runs a straightforward mass balance on a crystallization step: it splits the Initial Solution Mass into solute and solvent using Initial Concentration, removes whatever fraction of that solvent the Solvent Evaporation percentage specifies, and then calculates how much solute the remaining solvent can still hold in solution at the given Solubility at Final Temp. Any solute beyond that remaining solubility limit is assumed to crystallize out, which is the Crystal Yield. Initial Concentration has an outsized effect on the result because it drives the Theoretical Yield (the total solute mass available to crystallize) directly, while Solubility at Final Temp only determines how much of that total stays behind in solution rather than crystallizing.
Final Temperature itself is not used anywhere in the arithmetic -- it exists purely as a label for you to look up the correct Solubility at Final Temp value from a solubility table or handbook for your specific solute, since solubility (not temperature directly) is what the formula needs. Solvent Evaporation lets you model evaporative or combined cooling-evaporative crystallization: raising it removes more solvent, which lowers how much solute the remaining solvent can hold and increases yield. What this model does not account for: crystallization kinetics, cooling rate, seeding, or impurity co-precipitation, all of which affect real crystal yield and purity but require more than an equilibrium mass balance to model.
Inputs
Results
Crystal Yield
195 kg
≈ 20 car tires
Percent Recovery
65%
How to Use This Calculator
- Enter the Initial Solution Mass in kg and the Initial Concentration as a mass fraction (e.g., 0.30 = 30% solute).
- Enter the Final Temperature in °C to which the solution will be cooled.
- Enter the Solubility at the Final Temperature in g/100g solvent — look this up in solubility tables or CRC Handbook for your solute.
- Set the Solvent Evaporation % if you are combining cooling and evaporation crystallization (evaporative crystallization).
- Read the Crystal Yield in kg and the Percent Recovery — higher recovery means less solute remains in the mother liquor.
- Use the Mother Liquor Mass to plan recycle or waste treatment of the remaining saturated solution.
How the result changes with Initial Concentration
| Initial Concentration | Crystal Yield | Percent Recovery |
|---|---|---|
| 0.15 | 22.5 kg | 15% |
| 0.23 | 108.75 kg | 48.33% |
| 0.45 | 367.5 kg | 81.67% |
| 0.75 | 712.5 kg | 95% |
What each input means
- Initial Solution Mass
- Total mass of the initial hot solution (solute + solvent).
- Initial Concentration
- Mass fraction of dissolved solute in the initial solution.
- Final Temperature
- Temperature to which the solution is cooled for crystallization.
- Solubility at Final Temp
- Solubility of the solute at the final temperature in grams per 100 grams of solvent.
- Solvent Evaporation
- Percentage of solvent removed by evaporation before or during crystallization.
How this is calculated
Worked example, using the default values
- Identify Input Parameters5 parametersInitial Solution Mass = 1000, Initial Concentration = 0.3, Final Temperature = 20, Solubility at Final Temp = 15, Solvent Evaporation = 0 = 5 input(s) provided
- Calculate Crystal YieldCrystal Yield195 = 195
- Calculate Percent RecoveryPercent Recovery65 = 65
- Calculate Mother Liquor MassMother Liquor Mass805 = 805
- Calculate Theoretical YieldTheoretical Yield300 = 300
Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why doesn't Final Temperature appear in the actual calculation?
Because the calculator needs the solubility VALUE at that temperature, not the temperature itself -- Final Temperature is there so you know which temperature's solubility figure to look up in a reference table and enter into Solubility at Final Temp. Different solutes have very different solubility-versus- temperature curves, so there is no universal formula the calculator could use to derive solubility from temperature alone.
Why does raising Solvent Evaporation increase my crystal yield?
Because removing solvent reduces how much solute the remaining solvent can hold at the given solubility -- with less solvent available to dissolve solute, more of the total solute mass is forced out of solution as crystals. This is the basis of evaporative crystallization, used industrially specifically because it lets you push yield higher than cooling alone would achieve at the same final temperature.
What is the Mother Liquor, and why does its mass matter?
Mother Liquor is the leftover saturated solution -- the remaining solvent plus whatever solute is still dissolved in it -- after the crystals are removed. Its mass matters for planning what happens next: it typically gets recycled back into the process to recover the solute still dissolved in it, or treated as waste, so knowing its mass is necessary for sizing that downstream equipment.
Can Crystal Yield ever be negative or exceed the Theoretical Yield?
No -- the calculator floors Crystal Yield at zero, which happens if the remaining solvent could actually hold MORE solute than you started with (an unsaturated result, meaning nothing would crystallize under those conditions). It can never exceed Theoretical Yield, since Theoretical Yield represents the entire solute mass in the original solution -- crystallizing more than that would mean creating solute from nothing.
Does a higher Initial Concentration always mean more Crystal Yield?
Yes, holding everything else fixed -- a higher concentration means more total solute mass to begin with (a larger Theoretical Yield), while the amount that stays dissolved in the mother liquor depends only on the fixed solubility and remaining solvent mass, not on how much solute you started with. That extra solute above what the solvent can hold has nowhere to go but into the crystal yield.
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