$D_{AB}=\frac{0\mathrm{.}001858T^{\frac{3}{2}}(\frac{1}{M_A}+\frac{1}{M_B}{)}^{\frac{1}{2}}}{P_{(equation1)}^2{}_D^2}$

is used to show that the temperature and pressure dependence of the diffusion coefficient $D_{A}B$ at a temperature and pressure $(T2,p2)$ can be estimated as follows:

$D_{AB}(T_2,P_2)=D_{AB}(T_1,P_1)(\frac{P_1}{P_2})(\frac{T_2}{T_1}{)}^{\frac{3}{2}}\frac{{}_D(T_1)}{{}_D(T_2)}$

$(equation2)$

where the value of $D_{AB}(T_1,p_1).T_1,$ and $p_1$ are given as constants. $($This is similar to the formulation of the Clausius$-$Clapeyron equation, where you had a "standard state" of vapo

formulation of the Clausius$-$Clapeyron equation, where you had a "standard state" of vapor pressure $=6\mathrm{.}11mb$ at $T=273K.$ From that standard state and the Clausius$-$Clapeyron equation, you can extrapolate to find the equilibrium vapor pressure of water at any temperature$)$

Consider ethylene gas in nitrogen gas at $298K.$ The diffusivity $(D_{AB})$ is $0\mathrm{.}163c{m}^2{s}^{-1}$ at $298K$ at atm $($source: Welty Table J$\mathrm{.}1).$ The reduced temperature is calculated using $T^{***}=\frac{T}{\frac{}{k}}$ and

Calculate the new value of $D_{AB}$ at a second temperature and pressure of $300K$ and $1015mb$ by following steps $($a$)-($e$).$

$($a$)$ Identify the given quantities and their values and units.

$($b$)$ Write down the equations associated with the problem, so you can choose from them. You are working with equation $2$ above, plus the definition of reduced temperature $T^{**},$ and you need to find $D_{AB}(T_2,p_2),$ plus any others that seem relevant.

$($c$)$ Use the formula sheet to get the collision integrals you need; note which method you chose.

$($d$)$ do you need to convert any units? Decide whether or not you have everything in the right units, and if not, write out the unit conversions before proceeding.

$($e$)$ Calculate $D_{AB}$ for ethylene in nitrogen at $300K$ and $1015mb,$ which is about $80F$ and could be in a high$-$pressure system at sea level.