Evaporation &
Crystallization Guide
Multiple-effect evaporation, steam economy, boiling point elevation, and crystal yield for the GATE Chemical Engineering paper.
Overview
Evaporation and crystallization both concentrate a solution, but they finish the job differently. Evaporation boils off solvent, usually water, and leaves a more concentrated solution behind. Crystallization goes a step further and pushes the solution past its solubility limit, so dissolved solute comes out as solid crystals. In the GATE CH syllabus, evaporation is really just applied heat transfer, energy balances around a heated vessel, while crystallization brings in something new: solubility and yield.
Evaporator design revolves around steam economy, and multiple-effect evaporation is how you get it. Chain several evaporator bodies in series so the vapor from one effect becomes the heating steam for the next, and the live steam needed per unit of water evaporated drops sharply compared to running a single effect. The one wrinkle on top of an otherwise straightforward energy balance is boiling point elevation, a solution boils hotter than pure solvent at the same pressure, and Dühring's rule is how you estimate by how much.
Crystallization problems come down to a mass balance driven by solubility: start with a hot, saturated feed, cool or concentrate it to a new temperature, and work out how much solid crystallizes out. You have to account for the mother liquor, which stays saturated at the final condition, and for any water of crystallization the solid carries with it. Both topics really boil down to careful bookkeeping, the same discipline from the Process Calculations guide, just pointed at solubility and latent-heat data instead of reaction stoichiometry.
Real GATE CH PYQ Frequency (2024–2026)
No questions in our 2024–2026 archive were tagged to this specific subtopic on its own, they're grouped under the broader Mass Transfer category. See the full topic weightage table for the real, computed numbers.
GATE Weightage
Evaporation & Crystallization typically contribute 1–3 questions (about 2–4 marks) to the GATE CH paper, a smaller section than Distillation or Absorption, tested mainly through single-effect and multiple-effect evaporator energy balances and crystallization yield calculations.
| Sub-area | Approx. Marks |
|---|---|
| Evaporator energy balances & steam economy | ~1–2 |
| Multiple-effect evaporation | ~0–1 |
| Crystallization yield & solubility | ~0–1 |
Sub-area split is a directional estimate (our archive doesn't tag marks at this granularity), for the real, computed topic-level total, see "Real GATE CH PYQ Frequency" above.
Key Subtopics
Single-effect evaporator energy balance
A steady-state enthalpy balance around one evaporator body, relating steam consumption, feed conditions, and vapor produced.
Boiling point elevation & Dühring's rule
A solution's boiling point exceeds the pure solvent's at the same pressure due to dissolved solute, estimated using Dühring's rule (a linear plot of solution boiling point vs. solvent boiling point at various concentrations). Dühring's rule is a distillation/evaporation topic, not a reaction-engineering or fluid-mechanics one, a common GATE MCQ distractor.
Multiple-effect evaporation
Several evaporator bodies arranged so vapor from one effect heats the next, cutting live steam requirements roughly in proportion to the number of effects, at the cost of more equipment and a smaller usable temperature difference per effect.
Steam economy
Kilograms of water evaporated per kilogram of live (fresh) steam consumed, the key performance metric that improves with more effects, up to a practical/economic limit.
Forward, backward & parallel feed
Different arrangements for how feed liquor and vapor flow through a multiple-effect train, chosen based on how feed viscosity/temperature sensitivity changes with concentration.
Crystallization fundamentals
Supersaturation as the driving force for crystal nucleation and growth, and the solubility curve that determines how much solute stays dissolved (as mother liquor) at a given temperature.
Crystallization yield calculations
A mass balance combining the solubility curve at the final temperature with any water of crystallization the product carries, to determine how much solid crystallizes from a given feed.
Crystallizer types
Cooling crystallizers (yield driven by solubility decrease with temperature) versus evaporative crystallizers (yield driven by solvent removal at roughly constant temperature).
Essential Formulas
Full formula reference →Single-effect evaporator enthalpy balance, steam S (latent heat λs) supplies the latent heat to vaporize V (latent heat λv), plus any feed preheating
Kilograms of total vapor produced per kilogram of live steam fed, approaches N (number of effects) for well-designed multiple-effect trains
Boiling point elevation, read from Dühring's chart or correlation for the specific solute-solvent system
Dühring's rule, solution boiling point plotted linearly against solvent boiling point at constant concentration
Overall solute mass balance for a crystallizer, feed F, mother liquor L (at the solubility limit xL), crystals C (composition xC, may include water of hydration)
Crystal yield from a mass balance when the crystals are anhydrous (no water of crystallization)
Visual Reference
Derivations & Physical Insight
Why Steam Economy Approaches N for an N-Effect Evaporator
In a single-effect evaporator, almost all the latent heat in the live steam goes straight into vaporizing water from the feed, so 1 kg of steam evaporates roughly 1 kg of water, a steam economy near 1, ignoring feed preheating and boiling point elevation. Multiple-effect evaporation is built on one simple observation: the vapor leaving that first effect still carries useful heat. Rather than condense it and lose that heat, feed it as the heating medium to a second effect running at lower pressure, and hence a lower boiling temperature.
That second effect boils off roughly another kilogram of water per kilogram of vapor it receives, and the same thing happens at the third, and the fourth, all the way down the train. So the original kilogram of live steam ends up doing work N times over, evaporating roughly N kilograms of total water across the whole train, even though only that first kilogram of fresh steam was ever fed in. Steam economy scaling with the number of effects is exactly why plants build more complex, more expensive multiple-effect trains instead of settling for one evaporator.
Why Crystal Yield Depends on the Solubility Curve, Not Just Concentration
For most solute-solvent systems, solubility drops as temperature drops. Cool a hot, concentrated solution past its saturation point at the new temperature and it simply can't hold all the solute anymore. The excess comes out as solid crystals, while the remaining solution, the mother liquor, sits exactly saturated at whatever the new, lower temperature's solubility limit happens to be.
That's why crystal yield is a mass balance anchored to the solubility curve, not just "whatever concentration excess exists." The mother liquor can't fall below saturation without more crystals forming, and it won't sit above it either, since going past the metastable limit just triggers immediate crystallization. So xL in the crystallizer mass balance gets read straight off the solubility curve at the operating temperature. It isn't something you solve for from an energy or volume argument.
Worked Practice Problems
Original practice problems in the GATE CH style, not copied from any question bank. Work them before reading the solution.
Steam Economy Estimate for a Triple-Effect Evaporator
Problem: A triple-effect evaporator train evaporates a total of 8100 kg/h of water using 3000 kg/h of live steam. Find the steam economy and compare it to the ideal (N = 3) estimate.
Given: Total vapor evaporated Vtotal = 8100 kg/h, live steam S = 3000 kg/h, N = 3 effects.
Answer: Steam economy = 2.7 kg water/kg steam (slightly below the ideal N = 3, reflecting real losses like boiling point elevation and sensible-heat requirements).
Crystal Yield from a Cooling Crystallizer (Anhydrous Product)
Problem: A feed solution (1000 kg, xF = 0.40 mass fraction solute) is cooled to a temperature where the solubility is xL = 0.20 mass fraction. Assuming anhydrous crystals (xC = 1.0) and no water loss by evaporation, find the mass of crystals produced.
Given: F = 1000 kg, xF = 0.40, xL = 0.20, xC = 1.0 (pure anhydrous crystals).
Answer: C = 250 kg of anhydrous crystals (with 750 kg of mother liquor remaining, saturated at xL = 0.20).
Topic-wise PYQ Frequency
Evaporator energy balances
GATE 2025 Q30 tested evaporation directly (categorized under heat transfer), evaporator energy balances are a recurring but lower-frequency numerical.
Crystallization yield
Less consistently tested as a standalone numerical in recent papers than distillation or absorption, but solubility-based mass balances follow the same pattern as other Mass Transfer yield calculations.
Multiple-effect evaporation & steam economy
A conceptual favorite (why economy scales with N) even when not tested as a full numerical.
Recommended Study Order
- 1
1. Single-effect evaporator energy balance
The foundational calculation, practice the steam-to-vapor enthalpy balance before adding boiling point elevation or multiple effects.
- 2
2. Boiling point elevation (Dühring's rule)
A quick correction layered onto the basic energy balance once it's solid.
- 3
3. Multiple-effect evaporation & steam economy
Builds directly on the single-effect balance, applied N times in series, focus on why economy scales with the number of effects.
- 4
4. Crystallization yield calculations
A distinct, solubility-driven mass balance, study as a self-contained topic once material-balance habits from Process Calculations are solid.
Common Pitfalls
✗ Assuming steam economy exactly equals the number of effects N.
✓ N is the ideal ceiling; real steam economy is somewhat below N due to boiling point elevation, feed preheating requirements, and heat losses.
✗ Ignoring boiling point elevation when computing the temperature driving force across an evaporator effect.
✓ The available ΔT for heat transfer is the steam temperature minus the solution boiling point (not the pure-solvent boiling point), subtract BPE from the naive ΔT estimate.
✗ Forgetting to account for water of crystallization when the product is a hydrate (e.g., CuSO4·5H2O) rather than an anhydrous solid.
✓ If crystals are a hydrate, xC in the yield mass balance is not 1.0, compute the mass fraction of the anhydrous solute within the hydrated crystal formula first.
✗ Treating mother liquor composition as a free variable instead of reading it from the solubility curve at the final temperature.
✓ Mother liquor is always at (or extremely close to) saturation at the crystallizer's operating temperature, look up xL from solubility data, don't solve for it as an unknown.
Put It Into Practice
Work the steam-economy and crystal-yield problems above with a clear mass/energy balance diagram, then apply the same approach to any Evaporation or Crystallization questions in the full GATE previous-year test set.
Further reading: How Multi-Effect Evaporators Save Steam in Industry
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