Energy required to vaporize : 32.3 kJ
The heat to change the phase can be formulated :
Q = mLf (melting/freezing)
Q = mLv (vaporization/condensation)
Lf=latent heat of fusion
Lv=latent heat of vaporization
Mass of water = 14.27 g
Latent heat of vaporization ( boiling point of 100 ºC) : 2260 J/g
Energy required :
[tex]\tt Q=m.Lv\\\\Q=14.27\times 2260\\\\Q=32250.2~J\approx 32.3~kJ[/tex]