Find the incorrect statement (mix of blending, stoichiometry, vapor–liquid, and crystallisation):\nSelect the option that is WRONG.

Difficulty: Medium

Correct Answer: Feeding a supersaturated solution of concentration C to a crystalliser (solubility C1) yields an output solids rate of (C + C1)·V for volumetric feed rate V.

Explanation:


Introduction / Context:
This composite question checks your grasp across several core topics: blending calculations, limiting reactant and percent excess, vapor–liquid equilibrium saturation constraints for gas bubbles, and crystallisation mass balances. Spotting the incorrect statement requires quick, reliable reasoning across these areas.


Given Data / Assumptions:

  • Linear mixing of salt solutions by mass.
  • Reaction: C + O2 → CO2, with amounts given in gram-atoms (for elements) and gram-moles (for molecules).
  • Gas bubble in contact with a nonvolatile, nonabsorbing carrier gas; solvent vapor pressure Ps at the contact temperature.
  • Crystalliser fed with a supersaturated solution at solute concentration C (mass or molar units), with equilibrium solubility C1 at operating conditions.


Concept / Approach:
For blending, apply a one-component mass balance on solute. For limiting reactant, compare stoichiometric requirements. For the bubble, saturation implies the solvent partial pressure equals Ps; thus the gas-phase mole fraction equals Ps/Pg. For crystallisation, solids formation equals the excess solute over solubility—specifically (C − C1) multiplied by the feed volumetric rate V (with consistent units).


Step-by-Step Checks:

(a) Let x = kg of 25% solution; 0.25x + 0.50(100 − x) = 40 ⇒ x = 40 kg → statement is correct.(b) Stoichiometry requires 1 mol O2 per mol C. Available: 1.2 mol C and 1.5 mol O2 → carbon limiting, oxygen excess = (1.5 − 1.2)/1.2 × 100% = 25% → correct.(c) Long contact and insoluble carrier lead to y_solvent = Ps/Pg (saturation) → correct.(d) Correct expression is solids rate = (C − C1)·V, not (C + C1)·V → statement is wrong.


Verification / Alternative check:
Material balance over the crystalliser: solute in = C·V; solute out in mother liquor = C1·V; solids out = (C − C1)·V.


Why Other Options Are Wrong (or Right):

  • Only (d) is incorrect; (a)–(c) align with standard calculations.


Common Pitfalls:
Confusing gram-atoms with gram-moles; misapplying Raoult-type saturation to cases with soluble carrier gases; sign error in the crystallisation excess term.


Final Answer:
Option (d) is wrong; the correct solids rate is (C − C1)·V.

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