Question:
A gas stream with 2.01 mol% ammonia is to be scrubbed in a counter-current isothermal packed bed absorber using pure water to reduce its concentration to 0.01 mol%. Assume dilute conditions apply, the operating line is linear and the mass transfer coefficients are constant throughout the column. The liquid and the gas flows inside the absorber (in \(\text{kmol}\,\text{m}^{-2}\,\text{h}^{-1}\)) are 1000 and 200, respectively. The equilibrium relationship is \(y^* = 0.9x\), where y is the mole fraction of ammonia in the gas phase and x is that in the liquid. Under these conditions, the height of an overall gas transfer unit (\(H_{tOG}\)) is 0.8 m and the number of overall gas transfer units (\(N_{tOG}\)) is given by the following integral.\[ N_{tOG} = \int_{y_2}^{y_1} \frac{dy}{y - y^*} \]The integration is performed between the two ends of the column, and y* is the equilibrium mole fraction in the gas phase corresponding to the composition of the liquid at the corresponding location. Which one of the following is the minimum length of the packing (in m) necessary to achieve the desired scrubbing?
A gas stream with 2.01 mol% ammonia is to be scrubbed in a counter-current isothermal packed bed absorber using pure water to reduce its concentration to 0.01 mol%. Assume dilute conditions apply, the operating line is linear and the mass transfer coefficients are constant throughout the column. The liquid and the gas flows inside the absorber (in \(\text{kmol}\,\text{m}^{-2}\,\text{h}^{-1}\)) are 1000 and 200, respectively. The equilibrium relationship is \(y^* = 0.9x\), where y is the mole fraction of ammonia in the gas phase and x is that in the liquid. Under these conditions, the height of an overall gas transfer unit (\(H_{tOG}\)) is 0.8 m and the number of overall gas transfer units (\(N_{tOG}\)) is given by the following integral.
\[ N_{tOG} = \int_{y_2}^{y_1} \frac{dy}{y - y^*} \]The integration is performed between the two ends of the column, and y* is the equilibrium mole fraction in the gas phase corresponding to the composition of the liquid at the corresponding location. Which one of the following is the minimum length of the packing (in m) necessary to achieve the desired scrubbing?
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Find $x_1$ from the overall mass balance, then use the absorption factor $A=L/(mG)$ in the Kremser equation to get $N_{tOG}$, and multiply by $H_{tOG}$.
Updated On: Aug 10, 2026
- 4.2
- 5.0
- 6.2
- 7.7
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The Correct Option is B
Solution and Explanation
Step 1: Terminal compositions. y1=0.0201, y2=0.0001, x2=0.
Step 2: Mass balance. \[ 200(0.02)=1000x_1 \Rightarrow x_1=0.004 \]
Step 3: Absorption factor. \[ A = 1000/(0.9\times200)=5.556 \]
Step 4: Kremser equation. \[ N_{tOG} = \frac{A}{A-1}\ln\left[(1-1/A)\frac{y_1}{y_2}+1/A\right] = 1.2195\times5.106=6.228 \]
Step 5: Minimum packing length. \[ Z=0.8\times6.228=4.98\approx5.0\ \text{m} \]
\[ \boxed{Z_{min} \approx 5.0\ \text{m}} \]Was this answer helpful?
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