The ionisation constant of phenol is higher than that of ethanol because
Phenoxide ion is stabilised through delocalisation
Phenoxide ion is stable due to resonance. The -ve charge is delocalised in the benzene ring which is a stabilising factor in the phenoxide ion and because of this ionisation constant of phenol is higher whereas no resonance is possible in alkoxide ions derived from alcohol. The -ve charge is localised on oxygen atom in case of alcohol