Derivation of the Overall Mass Transfer Coefficient

[Tom Hardy]

Homework Statement

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.

 

[Chestermiller]

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 $N_1$.

 

[Tom Hardy]

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.