What Is the Concept Behind Finding Mole Fraction in Gas Absorption Problems?

In summary, a gas stream containing 3% A is passed through a packed column at 25 degrees Celsius and 1 atm to remove 99% of A by absorption in water. The gas and liquid rates are ##20\frac{mol}{hr ft^2}## and ##100\frac{mol}{hr ft^2}##, respectively. The ##(NTU)_{OG}## and ##(HTU)_{OG}## can be found using the equilibrium relation ##y^*=3.1x## and the values of ##K_x a## and ##K_y a##. The concept of mass balance is used to find the mole fraction of A in both the gas and liquid phases, and
  • #1
Rahulx084
99
1
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A gas stream containing 3% A is passed through a packed column to remove 99% of A by absorption in the water . The absorber operates at 25 degree Celsius and 1atm and the gas and liquid rates are to be ##20\frac{mol}{hr ft^2}## and ##100\frac{mol}{hr ft^2}##. Find the ##(NTU)_{OG}## , ##(HTU)_{OG}##.
Equilibrium relation: ##y^* =3.1x##



##K_x a##= ##60\frac{mol}{hr ft^3}##
##K_y a##= ##15\frac{mol}{ hr ft^3}##

In the given picture there is a question, I'm having huge confusion in finding out the mole fraction, I have put a solution to find the mole fraction in the picture, I know its wrong. This is where I'm stucked , I don't know the concept behind this . Please someone help me to get through this , where I'm wrong and what concept is used to find mole fraction in these questions or other varieties like this .
 

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  • #2
Rahulx084 said:
A gas stream containing 3% A is passed through a packed column to remove 99% of A by absorption in the water . The absorber operates at 25 degree Celsius and 1atm and the gas and liquid rates are to be ##20\frac{mol}{hr ft^2}## and ##100\frac{mol}{hr ft^2}##. Find the ##(NTU)_{OG}## , ##(HTU)_{OG}##.
Equilibrium relation: ##y^* =3.1x##



##K_x a##= ##60\frac{mol}{hr ft^3}##
##K_y a##= ##15\frac{mol}{ hr ft^3}##

In the given picture there is a question, I'm having huge confusion in finding out the mole fraction, I have put a solution to find the mole fraction in the picture, I know its wrong. This is where I'm stucked , I don't know the concept behind this . Please someone help me to get through this , where I'm wrong and what concept is used to find mole fraction in these questions or other varieties like this .
Let V and L be the molar flow rates per unit area (of column) of liquid and vapor. Let x represent the mole fraction of A in the gas phase, and let y represent the mole fraction of A in the liquid phase. Let ##phi(z)## represent the molar flow rate of A from the gas phase to the liquid phase per unit area of column at location z. Consider the section of the absorber between axial locations z and ##z+\Delta z##. What is the mass balance over this interval of A in the gas phase an of A in the liquid phase (in terms of the parameters identified so far)?
 
  • #3
Chestermiller said:
Let V and L be the molar flow rates per unit area (of column) of liquid and vapor. Let x represent the mole fraction of A in the gas phase, and let y represent the mole fraction of A in the liquid phase. Let ##phi(z)## represent the molar flow rate of A from the gas phase to the liquid phase per unit area of column at location z. Consider the section of the absorber between axial locations z and ##z+\Delta z##. What is the mass balance over this interval of A in the gas phase an of A in the liquid phase (in terms of the parameters identified so far)?
Mass balance in the elemental region ##dz##
##d(Vx)=d(Ly)=phi(z)##
Where ##V##=molar flow rate of Vapour phase
##L##= Liquid molar flow rate
##x##=Mole fraction of A in gas phase
##y##= Mole fraction of A in liquid phase
 
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  • #4
Here's my take on this. Let x* and y* be the concentrations of A at the gas-liquid interface. The liquid is flowing downward at rate L, and the gas is flowing upward at rate V. Let z be the vertical coordinate through the column. Let ##\phi(z)## the molar flow rate of A per unit height of column and per unit cross sectional area of column from the gas phase to the liquid phase. The mass balances on A are as follows:
$$L[x(z)-x(z+\Delta z)]=\phi \Delta z$$
$$V[y(z+\Delta z)-y(z)]=-\phi \Delta z$$
Taking the limit of these as ##\Delta z## approaches 0, we have:$$L\frac{dx}{dz}=-\phi$$
$$V\frac{dy}{dz}=-\phi$$
The interphase molar flow rate of A is related to the mole fractions in the liquid and vapor by:
$$\phi=K_ya(y-y^*)=K_xa(x^*-x)$$
The phase equilibrium relationship is $$y^*=Hx^*$$

Are you comfortable with this so far?
 
  • #5
Rahulx084 said:
##d(Vx)=d(Ly)=phi(z)##
Where ##V##=molar flow rate of Vapour phase
##L##= Liquid molar flow rate
##x##=Mole fraction of A in gas phase
##y##= Mole fraction of A in liquid phase
Chestermiller said:
Here's my take on this. Let x* and y* be the concentrations of A at the gas-liquid interface. The liquid is flowing downward at rate L, and the gas is flowing upward at rate V. Let z be the vertical coordinate through the column. Let ##\phi(z)## the molar flow rate of A per unit height of column and per unit cross sectional area of column from the gas phase to the liquid phase. The mass balances on A are as follows:
$$L[x(z)-x(z+\Delta z)]=\phi \Delta z$$
$$V[y(z+\Delta z)-y(z)]=-\phi \Delta z$$
Taking the limit of these as ##\Delta z## approaches 0, we have:$$L\frac{dx}{dz}=-\phi$$
$$V\frac{dy}{dz}=-\phi$$
The interphase molar flow rate of A is related to the mole fractions in the liquid and vapor by:
$$\phi=K_ya(y-y^*)=K_xa(x^*-x)$$
The phase equilibrium relationship is $$y^*=Hx^*$$

Are you comfortable with this so far?
Yes sir
 
  • #6
Do you know how to work with these equations to solve your problem?
 
  • #7
Rahulx084 said:
Yes sir
Chestermiller said:
Do you know how to work with these equations to solve your problem?
Yes I guess
 
  • #8
Rahulx084 said:
Yes I guess
If you'd like more help, I'll be glad to provide it. What is your first step in the solution to this problem?
 
  • #9
Chestermiller said:
If you'd like more help, I'll be glad to provide it. What is your first step in the solution to this problem?
Thank you sir , I got this now .
First I take initial basis for both the flow rates , I took 100kmol for the gas phase and 500kmol for liquid phase observing their flow rates , and then I calculated the mole fraction of solute in both entering as well as leaving stream from the given information and solved further using equilibrium relation.
 
  • #10
Rahulx084 said:
Thank you sir , I got this now .
First I take initial basis for both the flow rates , I took 100kmol for the gas phase and 500kmol for liquid phase observing their flow rates , and then I calculated the mole fraction of solute in both entering as well as leaving stream from the given information and solved further using equilibrium relation.
Excellent!
 
  • #11
Thanks for your efforts sir to make my concepts clear
 

FAQ: What Is the Concept Behind Finding Mole Fraction in Gas Absorption Problems?

1. What is mass transfer and absorption?

Mass transfer and absorption refers to the movement of one or more substances from one phase to another. This can occur through various mechanisms such as diffusion, convection, and chemical reactions. Absorption specifically refers to the process of one substance being taken up by another substance.

2. What is the role of mass transfer and absorption in industrial processes?

Mass transfer and absorption play a crucial role in various industrial processes, such as in the separation of components in a mixture, the purification of gases, and the removal of pollutants from wastewater. It is also important in the production of pharmaceuticals, food and beverages, and many other products.

3. How is mass transfer and absorption studied and quantified?

Mass transfer and absorption are studied through experimental methods, mathematical models, and numerical simulations. These methods can help determine the rate and efficiency of mass transfer and absorption, as well as the factors that influence these processes, such as temperature, pressure, and concentration gradients.

4. What are some factors that can affect mass transfer and absorption?

Some factors that can affect mass transfer and absorption include the properties of the substances involved, such as their solubility and diffusivity, the physical conditions such as temperature and pressure, the geometry and design of the system, and the presence of other substances that may interfere with the process.

5. How can mass transfer and absorption be optimized?

To optimize mass transfer and absorption, it is important to understand the underlying mechanisms and factors that influence the process. This can be achieved through experimental studies and modeling. Additionally, the design and operation of the system can be adjusted to enhance mass transfer and absorption, such as using efficient equipment, controlling flow rates, and maintaining suitable conditions for the process.

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