Could you please make sure that you derive Equation 21.3.43 correctly, That is the most important part of the question

First, derive the starting equation from a mole balance on a segment of a tube of diametel D and length z. You may assume that the tube is empty, a=DL/(D/2)2. Then integrate this equation to arrive at Equation 21.3-43. 3-9. Driving Force to Use in Mass Transfer. Derive Eq. (21.3-42) for the log mean driving force to use for a fluid flowing in a packed bed or in a tube. (Hint: Start by making a mass balance and a diffusionrate balance over a differential area dA as follows: NAdA=kC(cAicA)dA=VdcA