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).
Absorption Tower Mole Ratio Calculation
Mole Ratio and Flow Conditions Defined
- Inlet gas mole ratio (component A): $Y_{in} = 0.02$.
- Gas flow rate (carrier gas): $G = 50 \text{ kmol/h}$.
- Component A removal: 95%.
- Outlet gas mole ratio (component A): $Y_{out} = Y_{in} \times (1 - 0.95) = 0.02 \times 0.05 = 0.001$.
- Inlet liquid mole ratio (pure solvent B): $X_{out} = 0$.
- Equilibrium relation: $Y = 2X$. The slope of the equilibrium curve is $m = 2$.
Minimum Solvent Flow Rate Calculation
The minimum liquid flow rate ($L'_{min}$) is determined by the condition where the operating line slope ($L'/G$) equals the equilibrium slope ($m$).
- $L'_{min} = m \times G$
- $L'_{min} = 2 \times 50 \text{ kmol/h} = 100 \text{ kmol/h}$.
Actual Solvent Flow Rate Determination
The tower operates at twice the minimum solvent flow rate.
- $L' = 2 \times L'_{min}$
- $L' = 2 \times 100 \text{ kmol/h} = 200 \text{ kmol/h}$.
Operating Line Equation Setup
For a countercurrent absorption tower, the operating line equation is:
$L'(X - X_{out}) = G(Y - Y_{out})$
Substituting known values:
- $200(X - 0) = 50(Y - 0.001)$
- $200X = 50Y - 0.05$
Exit Liquid Mole Ratio Calculation
The "exit liquid stream" refers to the liquid leaving the bottom of the tower. We find the liquid mole ratio ($X$) corresponding to the inlet gas composition ($Y_{in}$).
- Substitute $Y = Y_{in} = 0.02$ into the operating line equation:
- $200X_{in} = 50(0.02) - 0.05$
- $200X_{in} = 1 - 0.05$
- $200X_{in} = 0.95$
- $X_{in} = \frac{0.95}{200} = 0.00475$.
Final Mole Ratio Rounding
Rounded to three decimal places, the mole ratio of A in the exit liquid stream is 0.005.
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?
- For absorption of $H_2S$ from a mixture with hydrocarbon vapour into an aqueous alkanolamine solution, the liquid phase mass transfer resistance is
