Molar flux of the component A ($N_A$) diffusing through the stagnant component B can be expressed as:
$$N_A = \frac{D_{AB}P}{RT(z_2 - z_1)} \ln\left(\frac{P - P_{A2}}{P - P_{A1}}\right)$$
Log mean component B value in terms of pressure and mole fractions are also defined:
$$P_{BM} = \frac{P_{B2} - P_{B1}}{\ln(P_{B2}/P_{B1})}$$
$$x_{BM} = \frac{x_{B2} - x_{B1}}{\ln(x_{B2}/x_{B1})}$$
a) Show that,
$$N_A = \frac{D_{AB}P}{RT(z_2 - z_1)} \ln\left(\frac{P - P_{A2}}{P - P_{A1}}\right) = \frac{D_{AB}P}{RT(z_2 - z_1)} \ln\left(\frac{1 - x_{A2}}{1 - x_{A1}}\right)$$
b) If $N_A$ can be expressed as follows,
$$N_A = D_{AB} \left(\frac{1}{RT}\right) \left(\frac{P_{A1} - P_{A2}}{z_2 - z_1}\right) \left(\frac{P}{P_{BM}}\right)$$
Show that,
$$\frac{P}{P_{BM}} = \frac{1}{x_{BM}}$$
