P. The solubility of gas in the liquid is very high
Q. The solubility of gas in the liquid is very low
R. The liquid-side mass transfer coefficient is much higher than the gas-side mass transfer coefficient
S. The liquid-side mass transfer coefficient is much lower than the gas-side mass transfer coefficient
Understanding Gas-Film Controlled Absorption
In absorption processes, mass transfer occurs across both the gas and liquid phases. The operation is considered gas-film controlled when the resistance to mass transfer is predominantly in the gas phase, meaning the liquid phase allows transfer relatively easily. This occurs under specific conditions related to gas solubility and mass transfer coefficients.
Identifying Conditions for Gas-Film Control
Let's analyze the given conditions:
- P. High Gas Solubility: When a gas has very high solubility in the liquid, it dissolves readily. This implies low resistance to mass transfer within the liquid phase. Low liquid-side resistance means the gas film's resistance becomes the limiting factor. Therefore, high solubility contributes to gas-film control.
- Q. Low Gas Solubility: Conversely, very low solubility means the gas does not dissolve easily, increasing the resistance in the liquid phase. This typically leads to liquid-film control, not gas-film control.
- R. High Liquid-Side Mass Transfer Coefficient: The mass transfer coefficient ($k$) is inversely related to the resistance. If the liquid-side mass transfer coefficient ($k_L$) is much higher than the gas-side mass transfer coefficient ($k_G$) (i.e., $k_L \gg k_G$), the resistance in the liquid phase ($1/k_L$) is much smaller than the resistance in the gas phase ($1/k_G$). This indicates that the gas film presents more resistance, making the absorption process gas-film controlled.
- S. Low Liquid-Side Mass Transfer Coefficient: If $k_L$ is much lower than $k_G$ (i.e., $k_L \ll k_G$), the resistance in the liquid phase ($1/k_L$) becomes dominant. This makes the process liquid-film controlled.
Conclusion on Controlling Factors
The absorption operation becomes gas-film controlled when the resistance to mass transfer is higher in the gas phase than in the liquid phase. This occurs when:
- The gas has very high solubility in the liquid (Condition P).
- The liquid-side mass transfer coefficient is much higher than the gas-side coefficient (Condition R).
Therefore, the combination of conditions P and R leads to gas-film controlled absorption.
Important Questions from Absorption
- A gas stream with $2.01 \text{ mol }\%$ ammonia is to be scrubbed in a counter-current isothermal packed bed absorber using pure water to reduce its concentration to $0.01 \text{ mol }\%$. 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 $\text{kmol m}^{-2}\text{ h}^{-1}$) 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 ($H_{tOG}$) is $0.8 \text{ m}$ and the number of overall gas transfer units ($N_{tOG}$) is given by the following integral.
$$ N_{tOG} = \int_{y_1}^{y_2} \frac{dy}{y - y^*} $$
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 corresponding location. Which one of the following is the minimum length of the packing (in m) necessary to achieve the desired scrubbing? Benzene is removed from air by absorbing it in a non-volatile wash-oil at 100 kPa in a counter-current gas absorber. Gas flow rate is 100 mol/min, which includes 2 mol/min of benzene. The flow rate of wash-oil is 50 mol/min. Vapor pressure of benzene at the column conditions is 50 kPa. Benzene forms an ideal solution with the wash-oil and the column is operating at steady state. Gas phase can be assumed to follow ideal gas law. Neglect the change in molar flow rates of liquid and gas phases inside the column.
For this process, the value of the absorption factor (up to two decimal places) is ________________- A liquid $L$ containing a dissolved gas $S$ is stripped in a countercurrent operation using a pure carrier gas $V$. The liquid phase inlet and outlet mole fractions of $S$ are $0.1$ and $0.01$, respectively. The equilibrium distribution of $S$ between $V$ and $L$ is governed by $y_e = x_e$, where $y_e$ and $x_e$ are the mole fractions of $S$ in $V$ and $L$, respectively. The molar feed rate of the carrier gas stream is twice as that of the liquid stream. Under dilute solution conditions, the minimum number of ideal stages required is ________ (in integer).
- Pure gas P is being absorbed into a liquid. The dissolved P undergoes an irreversible reaction in the liquid film. The reaction is first order with respect to P. Which one of the following represents the concentration profile of P in the liquid film at steady state?
A countercurrent absorption tower is designed to remove 95% of component A from an incoming binary gas mixture using pure solvent B. The mole ratio of A in the inlet gas is 0.02. The carrier gas flow rate is 50 kmol/h. The equilibrium relation is given by $Y = 2X$, where Y and X are the mole ratios of A in the gas and liquid phases, respectively. If the tower is operated at twice the minimum solvent flow rate, the mole ratio of A in the exit liquid stream is ________ (rounded off to three decimal places).
