# For how long would 100W electric heater have to operate

Standard vaporisation enthalpy of benzene at boiling point is 30.8 kJ \${{mol}^{-1}}\$. For how long would 100W electric heater have to operate in order to vaporise a 100 g sample at that temperature? (Power= energy/time and 1W = 1 J\${{s}^{-1}}\$).

\${ ∆ }{ vap }\$H°(benzene) = 30.8 kJ\${{mol}^{-1}}\$
Molar mass of benzene, \$C
{6}H_{6}\$ = (6 x 12+ 6 x 1) g\${{mol}^{-1}}\$
= 78 g\${{mol}^{-1}}\$
Energy needed to vaporise benzene = 30.8 kJ\${{mol}^{-1}}\$ x 100g / 78 g\${{mol}^{-1}}\$
= 39.49kJ
So Time = energy/power = 39.49 / 100W = 39.49 x \${{10}^{3}}\$ J / 100J/s
= 394.9 s = 6.6 min
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