Antoine's equation is a correlation for vapor pressures based on the ClausiusClapeyron equation. It has been used over limited temperature ranges.

$lo{g}_{10}{P}^{\text{v}\text{a}\text{p}}=A-\frac{B}{T+C-273\mathrm{.}15}$

where $T$ is in $K$ and Pvap is in bar. Use Page A$55$ of Poling et al$.$ for the coefficients needed for ethylbenzene.

a Calculate the vapor pressure of ethylbenzene at $347\mathrm{.}25K$ and $460K$ with Antoine's equation.

b

For the above, experimental values are $0\mathrm{.}13332$ bar at $347\mathrm{.}25K($Chaiyavech and van Winkle $1959)$ and $3\mathrm{.}325$ bar at $460K($Ambrose et al$.1967),$ respectively. For each temperature, report the relative deviation using the following equation:

$\frac{P_{\text{c}\text{a}\text{l}\text{c}}-P_{\text{e}\text{x}\text{p}}}{P_{\text{e}\text{x}\text{p}}}100[\%]$

c

A more elaborate method is a modified Wagner equation

$ln{P}_r^{\text{v}\text{a}\text{p}}=\frac{a+b{}^{1\mathrm{.}5}+c{}^{2\mathrm{.}5}+d{}^5}{T_r}$

where $P_r^{\text{v}\text{a}\text{p}}$ is the reduced vapor pressure $(\frac{P^{\text{v}\text{a}\text{p}}}{P_c}),T_r$ is the reduced temperature, and $$ is $(1-T_r).$ calculate the vapor pressure of ethylbenzene at $347\mathrm{.}25K$ and $460K$ with the Wagner equation. Based on the experimental data given in part $b,$ report the relative deviation for each data point.