Answer : The value of [tex]\Delta H_{vap}[/tex] is 47.627 kJ/mol
Explanation :
To calculate [tex]\Delta H_{vap}[/tex] of the reaction, we use clausius claypron equation, which is:
[tex]\ln(\frac{P_2}{P_1})=\frac{\Delta H_{vap}}{R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]
where,
[tex]P_1[/tex] = vapor pressure at temperature [tex]23^oC[/tex] = 92 torr
[tex]P_2[/tex] = vapor pressure at temperature [tex]45^oC[/tex] = 351 torr
[tex]\Delta H_{vap}[/tex] = Enthalpy of vaporization = ?
R = Gas constant = 8.314 J/mol K
[tex]T_1[/tex] = initial temperature = [tex]23^oC=[23+2730]K=296K[/tex]
[tex]T_2[/tex] = final temperature = [tex]45^oC=[45+2730]K=318K[/tex]
Putting values in above equation, we get:
[tex]\ln(\frac{351torr}{92torr})=\frac{\Delta H_{vap}}{8.314J/mol.K}[\frac{1}{296}-\frac{1}{318}]\\\\\Delta H_{vap}=47627.347J/mol=47.627kJ/mol[/tex]
Therefore, the value of [tex]\Delta H_{vap}[/tex] is 47.627 kJ/mol
