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Here's how to solve this problem:
Understanding the Concept
This problem involves liquid-liquid extraction, a technique used to separate components from a mixture by exploiting their different solubilities in two immiscible liquids (in this case, water and n-octane).
Key Information:
Diclofenac concentration in wastewater: 5.0 g/L
Desired removal percentage: 99.0%
Volume of wastewater: 100 L
Distribution coefficient (Ko): 25.0 (This represents the ratio of diclofenac concentration in n-octane to its concentration in water at equilibrium)
Calculation
1. Calculate the mass of diclofenac to be removed:
99% of 5.0 g/L
100 L = 495 g
2. Set up the mass balance equation:
Let 'x' be the volume of n-octane needed.
The mass of diclofenac in water after extraction: (5.0 g/L
100 L) - 495 g = 5 g
The mass of diclofenac in n-octane after extraction: 495 g
3. Apply the distribution coefficient:
Ko = (495 g / x) / (5 g / 100 L) = 25.0
4. Solve for x (volume of n-octane):
x = (495 g
100 L) / (5 g
25.0) = 396 L
Answer: You would need 396 L of n-octane for a single liquid-liquid extraction.
Therefore, the correct answer is (B).