Problem $3(3$ pts$).$ Solve for $N_{A}dz,$ which is equal to the definite integral from $p_{A,0}$ to $p_{A,1}$ :

$N_{A}dz={\displaystyle \underset{p_{A,0}}{\overset{p_{A,1}}{}}}\frac{-D_{AB}}{RT}\frac{d{p}_A}{1-\frac{p_A}{p}}$

where $N_A$ is the absolute flux $($net flux or flux relative to a stationary observer, in molar units mol $m^{-2}{s}^{-1}),$ dz is the distance in the $z-$direction, $R$ is the universal gas constant, $T$ is the absolute temperature $($i$.$e$.,$ in Kelvin or Rankine units$),p_A$ is a partial pressure of ideal gas $"A",$ and $D_{AB}$ is the $($constant$)$ diffusivity. The total pressure is $1$atm and remains constant despite the change in $p_A.$ Show all your steps as you compute the integral and plug in the bounds. The final answer contains a natural log$.$