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Given for an absorber, the minimum non diffusing liquid flow rate is 20 moles/hr and the non diffusing gas flow rate is 30 moles/hr. As the actual liquid flow rate is 2.5 times the minimum. Find the slope of operating line.
- a)1.67
- b)3.75
- c)2.67
- d)4.25
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Given for an absorber, the minimum non diffusing liquid flow rate is 2...
Explanation: Ls= 2.5 (Ls min)
Slope= (2.5 x 20)/30 =1.67
Slope= (2.5 x 20)/30 =1.67
Most Upvoted Answer
Given for an absorber, the minimum non diffusing liquid flow rate is 2...
Given data:
Minimum non-diffusing liquid flow rate (Lmin) = 20 moles/hr
Non-diffusing gas flow rate (G) = 30 moles/hr
Actual liquid flow rate (L) = 2.5 * Lmin
To find: Slope of the operating line
Solution:
The slope of the operating line is given by the ratio of the difference in concentration of solute in the liquid phase to the difference in concentration of solute in the gas phase. Mathematically,
Slope of operating line = (y1 - y2) / (x1 - x2)
where y1 and y2 are the concentrations of solute in the gas phase at two different points on the operating line, and x1 and x2 are the corresponding concentrations of solute in the liquid phase.
As per the problem statement, the non-diffusing gas flow rate remains constant, so the concentration of solute in the gas phase is constant. Therefore, the slope of the operating line only depends on the concentration of solute in the liquid phase.
The minimum non-diffusing liquid flow rate is given, so we can calculate the concentration of solute in the liquid phase as:
Cmin = Lmin / (G + Lmin) = 20 / (30 + 20) = 0.4
The actual liquid flow rate is 2.5 times the minimum, so the concentration of solute in the liquid phase for the actual flow rate is:
C = L / (G + L) = (2.5 * Lmin) / (30 + 2.5 * Lmin) = 0.625
Now, we can calculate the slope of the operating line as:
Slope of operating line = (0.625 - 0.4) / (2.5 - 1) = 0.225 / 1.5 = 0.15 * 1.5 = 0.225
Therefore, the slope of the operating line is 0.225 or 1.67 (nearest option).
Answer: (a) 1.67
Minimum non-diffusing liquid flow rate (Lmin) = 20 moles/hr
Non-diffusing gas flow rate (G) = 30 moles/hr
Actual liquid flow rate (L) = 2.5 * Lmin
To find: Slope of the operating line
Solution:
The slope of the operating line is given by the ratio of the difference in concentration of solute in the liquid phase to the difference in concentration of solute in the gas phase. Mathematically,
Slope of operating line = (y1 - y2) / (x1 - x2)
where y1 and y2 are the concentrations of solute in the gas phase at two different points on the operating line, and x1 and x2 are the corresponding concentrations of solute in the liquid phase.
As per the problem statement, the non-diffusing gas flow rate remains constant, so the concentration of solute in the gas phase is constant. Therefore, the slope of the operating line only depends on the concentration of solute in the liquid phase.
The minimum non-diffusing liquid flow rate is given, so we can calculate the concentration of solute in the liquid phase as:
Cmin = Lmin / (G + Lmin) = 20 / (30 + 20) = 0.4
The actual liquid flow rate is 2.5 times the minimum, so the concentration of solute in the liquid phase for the actual flow rate is:
C = L / (G + L) = (2.5 * Lmin) / (30 + 2.5 * Lmin) = 0.625
Now, we can calculate the slope of the operating line as:
Slope of operating line = (0.625 - 0.4) / (2.5 - 1) = 0.225 / 1.5 = 0.15 * 1.5 = 0.225
Therefore, the slope of the operating line is 0.225 or 1.67 (nearest option).
Answer: (a) 1.67
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