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23-Chem-A1 Process Balances and Chemical Thermodynamics · December 2014

Question 1 of 7: Seawater Purification by Freezing

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — December 2014 — 04-Chem-A1 Process Balances and Chemical Thermodynamics. Three-hour, open-book exam; any non-communicating calculator permitted. Format: seven questions in three parts — answer one of Q1–Q2 (Part A, 15 marks), one of Q3–Q4 (Part B, 25 marks) and two of Q5–Q7 (Part C, 30 marks each); four questions total 100 marks. All seven are solved below for completeness. Property data are stated explicitly in each Given block; units follow the paper (mixed SI and US/older conventions).

Reference texts: Felder, Rousseau & Bullard, Elementary Principles of Chemical Processes (4th ed., Wiley) — material & energy balances, single-phase systems, combustion and recycle; Smith, Van Ness, Abbott & Swihart, Introduction to Chemical Engineering Thermodynamics (8th ed., McGraw-Hill) — VLE and excess-property (Margules) models, compressor work, and reaction equilibrium; supporting property data from Perry's Chemical Engineers' Handbook (9th ed.) and the NIST Chemistry WebBook (Antoine constants, C₀p polynomials, standard enthalpies and Gibbs energies of formation).

Question 1: Seawater Purification by Freezing (Part A, 15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A single freezing unit removes pure-water ice from seawater; the salt that does not leave as ice concentrates in the rejected brine.

Stream / datumValue
Ice produced (pure water, salt-free)2000 kg/h
NaCl in seawater feed2 wt%
NaCl in brine leaving10 wt%

Find. the mass flow rate $F$ of seawater fed to the freezing unit.

FreezingunitSeawater F2% NaClIce (pure H2O)2000 kg/hBrine B10% NaCl
Figure 1 — Freezing unit: seawater feed splits into salt-free ice and a concentrated brine. NaCl leaves only in the brine.

Approach. Two independent balances close the unit — a total mass balance and a NaCl balance — because the ice carries no salt.

  1. Salt leaves only in the brine. The ice is pure water, so every kilogram of NaCl entering in the feed must exit in the brine $B$. Writing the NaCl balance, $$0.02\,F = 0.10\,B \;\Rightarrow\; B = 0.20\,F.$$
  2. Total mass balance around the freezer. Feed equals ice plus brine: $$F = 2000 + B = 2000 + 0.20\,F.$$
  3. Solve for the feed. Collecting $F$ gives $0.80\,F = 2000$, so $$F = \frac{2000}{0.80} = \boxed{2500\ \text{kg/h}}.$$
  4. Back out the brine and check. $B = 2500 - 2000 = 500$ kg/h. The salt balance closes: feed salt $0.02(2500)=50$ kg/h equals brine salt $0.10(500)=50$ kg/h. ✓
QuantityResult
Seawater feed rate $F$2500 kg/h
Brine reject rate $B$500 kg/h (10 wt% NaCl)
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