Detailed Explanation:

Question:
In a crossflow filtration process, if the volumetric flow rate of the feed is 10 times that of the retentate, the concentration factor is:

• (1) 9

• (2) 9/10

• (3) 1/10

• (4) 10

Correct Answer:

(1) 9

Explanation:

In a crossflow filtration process, the concentration factor is a measure of the concentration increase of solutes in the retentate compared to the feed. This factor is calculated based on the volumetric flow rates of the feed and the retentate.

Concentration Factor Formula:

The concentration factor ($CF$) can be calculated using the following formula:

CF=VfeedVretentate−1CF = \frac{V_{\text{feed}}}{V_{\text{retentate}}} – 1CF=Vretentate​Vfeed​​−1

Where:

• VfeedV_{\text{feed}}Vfeed​ is the volumetric flow rate of the feed,

• VretentateV_{\text{retentate}}Vretentate​ is the volumetric flow rate of the retentate.

Given that the volumetric flow rate of the feed is 10 times that of the retentate, we can substitute into the formula:

CF=10VretentateVretentate−1CF = \frac{10V_{\text{retentate}}}{V_{\text{retentate}}} – 1CF=Vretentate​10Vretentate​​−1 $$CF=10-1=9$$

So, the concentration factor is 9.

Why the Other Options are Incorrect:

• Option (2) 9/10: This is incorrect because the concentration factor should increase with the feed flow rate being greater than the retentate flow rate.

• Option (3) 1/10: This would represent a drastic dilution, not the concentration of solutes.

• Option (4) 10: This represents the ratio of feed to retentate flow, but the correct concentration factor accounts for the increase in solute concentration, which is 9, not the direct flow rate ratio.

Conclusion:

In crossflow filtration, when the feed flow rate is 10 times that of the retentate, the concentration factor is 9. This indicates a significant increase in the concentration of solutes in the retentate as compared to the feed. Understanding this factor is crucial for optimizing filtration processes and achieving the desired separation and concentration.

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