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 that dilute conditions apply, operating line is linear and the mass transfer coefficients are constant throughout the column. The liquid and the gas flows inside the absorber (in kmol m⁻² h⁻¹) are 1000 and 200, respectively. The equilibrium relationship is y = 0.9 x, 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 overall gas transfer unit (HtOG) is 0.8 m and the number of overall gas transfer units (NtOG) is given by the following integral.

N_tOG = ∫ [from y1 to y2] 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 corresponding location. Which one of the following is the minimum length of the packing (in m) necessary to achieve the desired scrubbing?

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 that dilute conditions apply, operating line is linear and the mass transfer coefficients are constant throughout the column. The liquid and the gas flows inside the absorber (in kmol m⁻² h⁻¹) are 1000 and 200, respectively. The equilibrium relationship is y = 0.9 x, 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 overall gas transfer unit (HtOG) is 0.8 m and the number of overall gas transfer units (NtOG) is given by the following integral.

N_tOG = ∫ [from y1 to y2] 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 corresponding location. Which one of the following is the minimum length of the packing (in m) necessary to achieve the desired scrubbing?

Accepted Answer

The correct answer is B, 5.0. GATE 2026 official key: (B). Integrating the driving force yields NtOG ≈ 6.23; multiplying by HtOG (0.8 m) gives the packed height: 6.23 × 0.8 ≈ 4.98 m, which rounds to 5.0 m.