Difficulty: Easy
Correct Answer: 1
Explanation:
Introduction:
Rejection quantifies how effectively a membrane excludes a solute. It is widely used in UF/NF/RO specifications and process control. Understanding its limiting values helps interpret analyzer readings and calculate product purity.
Given Data / Assumptions:
Concept / Approach:
By definition, if no solute appears in the permeate, C_p → 0 and R → 1. If solute freely passes, C_p ≈ C_f and R ≈ 0. Values greater than 1 or negative are unphysical for the simple definition and indicate measurement or definition issues (unless using specialized “sieving” forms with different baselines).
Step-by-Step Solution:
Write R = 1 − C_p/C_f.Set C_p = 0 for complete rejection ⇒ R = 1 − 0 = 1.Interpretation: 100% of solute is retained by the membrane.
Verification / Alternative check:
Manufacturer specs listing “rejection ≥ 95%” correspond to R ≥ 0.95, consistent with the definition. A perfect, idealized membrane would report R = 1 for that solute.
Why Other Options Are Wrong:
R = 0: implies no rejection.
R > 1 or R < 1 (other than 1): inconsistent with the standard definition for simple systems.
Common Pitfalls:
Final Answer:
1
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