Derivation of the Overall Mass Transfer Coefficient

In summary, the problem requires finding the overall mass transfer coefficient Kg, which can be obtained by using equations 2 and 3 to derive equation 1. The driving force is determined using Henry's law, P1=Hx1. By solving the three linear algebraic equations for N1, p1i, and x1i, the overall mass transfer coefficient can be determined.
  • #1
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Homework Statement


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The problem requires me to find the overall mass transfer coefficient or Kg.

Homework Equations


$$N_{1}=\frac{1}{\frac{1}{k_{p}+\frac{H}{k_{x}}}}(p_{1}-Hx_{1}), (1)$$
$$N_{1}=k_{p}(p_{1}-p_{1i}), (2)$$
$$N_{1}=k_{x}(x_{1i}-x_{1}), (3)$$

The Attempt at a Solution


So, I need to use equations 2 and 3 to get equation 1. The driving force:
$$(p_{1}-Hx_{1})$$
comes from using Henry's law, $$P_{1}=Hx_{1}$$ but I just do not understand where the overall mass transfer coefficient comes from, I have tried rearranging 2 and 3 to no avail, can someone help please.
 
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  • #2
Along with the equation ##p_{1i}=Hx_{1i}##, you have 3 linear algebraic equation in the 3 unknowns ##N_1##, ##p_{1i}## and ##x_{1i}##. Just solve these equations for ##N_1##.
 
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  • #3
Chestermiller said:
Along with the equation ##p_{1i}=Hx_{1i}##, you have 3 linear algebraic equation in the 3 unknowns ##N_1##, ##p_{1i}## and ##x_{1i}##. Just solve these equations for ##N_1##.

Thanks I did, I was just being silly before.
 

What is the overall mass transfer coefficient?

The overall mass transfer coefficient is a measure of how effectively a substance can be transferred from one phase to another, such as from a gas to a liquid. It takes into account all the resistances and driving forces involved in the mass transfer process.

How is the overall mass transfer coefficient calculated?

The overall mass transfer coefficient is calculated by dividing the mass transfer rate by the driving force. This can be represented by the equation Koverall = (mdot/A)*(1/ΔC), where mdot is the mass transfer rate, A is the transfer area, and ΔC is the difference in concentration between the two phases.

What factors affect the overall mass transfer coefficient?

The overall mass transfer coefficient is affected by the physical properties of the substances involved, such as their diffusivity and solubility, as well as the flow conditions, such as velocity and turbulence. It is also influenced by the geometry and characteristics of the transfer interface.

How can the overall mass transfer coefficient be improved?

The overall mass transfer coefficient can be improved by increasing the driving force, such as by increasing the concentration gradient or reducing the thickness of the transfer interface. It can also be enhanced by increasing the transfer area, increasing the fluid velocity, or introducing turbulence to promote mixing.

What are the applications of the overall mass transfer coefficient?

The overall mass transfer coefficient is a crucial parameter in many industrial processes, such as distillation, absorption, and extraction. It is also important in environmental engineering for processes such as air pollution control and wastewater treatment. In research, it is used to study and optimize mass transfer in various systems.

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