1.25 moles of what? Water? Are you sure the problem asks about vaporization at 25ºC? Usually vaporization occurs at 100ºC. But if this is actually what is given to you, then...
q = mC∆T for heating the water from 15º to 25º and then q = m∆Hvap to convert it to vapor. Also, 1.25 moles H2O x 18 g/mole = 22.5 g.
To heat from 15 - 25 degrees: q = (22.5 g)(4.18 J/g/deg)(10 deg) = 941 J = 0.941 kJ
To vaporize the water at 25º: q = (1.25 moles)(44.0 kJ/mole) = 55 kJ
Total heat (in kJ) need = 55 kJ + 0.941 kJ = 55.9 kJ (to 3 sig. figs.)