The Dieterici equation of state $($EOS$)$ is an alternative to the Van der Waals and Virial EOSs, hatemu EOS $p=\frac{R{T}_e^{-\frac{a}{R}{T}_m}}{V_m-b},V_2=0\mathrm{.}118VL$

$T_c=\frac{a}{4bR}or{T}_c=\frac{a}{2V_c*R}$

$a=2*T_c^2*V_c^2*R-$ known

$v_c=2b$

$b=\frac{V_c}{2}$

$a=2.(289\mathrm{.}75\%)(0\mathrm{.}1188L)(0\mathrm{.}082057\frac{\text{L}\text{a}\text{t}\text{m}}{\text{m}\text{o}\text{l}}),b=0\mathrm{.}11884$mol

$+a=5\mathrm{.}611139717\frac{L^2*atm}{mo{l}^2}$

$x=0\mathrm{.}05944$mol

though it is no longer often used.

Dieterici EoS: $=$

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$4$

$22=2=$

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$4$

pc $=59\mathrm{.}77$ bar Vc $=0\mathrm{.}1188$ L$/$mol Tc $=289\mathrm{.}75$ K

$($a$)$ Calculate the coefficients a and b in the Dieterici EOS from the critical pressure $($pc$)$

and critical temperature $($Tc$)$ of xenon. Given:The Dieterici equation of state $($EOS$)$ is an alternative to the Van der Waals and Virial EOSs,

though it is no longer often used.

Dieterici EoS: $p=\frac{RT{e}^{-\frac{a}{R}T{V}_m}}{V_m-b},$

$p_c=\frac{a}{4e^2{b}^2},V_c=2b,T_c=\frac{a}{4bR}$

$p_c=\frac{59\mathrm{.}77}{b}ar,V_c=0\mathrm{.}1188\frac{L}{m}ol,T_c=289\mathrm{.}75K$

$($a$)$ Calculate the coefficients a and $b$ in the Dieterici EOS from the critical pressure $($pc$)$

and critical temperature $(Tc)$ of xenon. Given: