Answer : The vapor pressure of [tex]CCl_4[/tex] at [tex]57.8^oC[/tex] is 0.519 atm.
Explanation :
The Clausius- Clapeyron equation is :
[tex]\ln (\frac{P_2}{P_1})=\frac{\Delta H_{vap}}{R}\times (\frac{1}{T_1}-\frac{1}{T_2})[/tex]
where,
[tex]P_1[/tex] = vapor pressure of [tex]CCl_4[/tex] at [tex]57.8^oC[/tex] = ?
[tex]P_2[/tex] = vapor pressure of [tex]CCl_4[/tex] at normal boiling point = 1 atm
[tex]T_1[/tex] = temperature of [tex]CCl_4[/tex] = [tex]57.8^oC=273+57.8=330.8K[/tex]
[tex]T_2[/tex] = normal boiling point of [tex]CCl_4[/tex] = [tex]76.72^oC=273+76.72=349.72K[/tex]
[tex]\Delta H_{vap}[/tex] = heat of vaporization [tex]CCl_4[/tex] = 33.05 kJ/mole = 33050 J/mole
R = universal constant = 8.314 J/K.mole
Now put all the given values in the above formula, we get:
[tex]\ln (\frac{1atm}{P_1})=\frac{33050J/mole}{8.314J/K.mole}\times (\frac{1}{330.8K}-\frac{1}{349.72K})[/tex]
[tex]P_1=0.5219atm[/tex]
Hence, the vapor pressure of [tex]CCl_4[/tex] at [tex]57.8^oC[/tex] is 0.519 atm.