The unusual properties of liquid water are usually attributed to hydrogen bonding. A longstanding question is whether the continuum of strengths of hydrogen bonds in water can be usefully simplified to two states: 'intact' and 'broken'. We show that such a simplification is justified by two very different computational models of water. We then show that there is a unique value of the free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) for breaking a hydrogen bond in pure water that gives quantitative agreement with both Raman spectra and the known heat capacity of water: ΔG = 480 cal mol-1, ΔH = 1.9 kcal mol-1, and ΔS/k = 2.4. Breaking a water/water hydrogen bond in the first solvation shell around Argon, a nonpolar solute, leads to ΔG = 620 cal mol-1, ΔH = 2.4 kcal mol-1 and ΔS/k = 3.0. A prediction, not yet tested experimentally, is that the hydrophobic heat capacity should decrease dramatically in supercooled water.