The unique structural, dynamical and chemical properties of air/water and oil/water interfaces are thought to play a key role in various biological, geological and environmental processes. For example, non-hydrogen-bonded ('dangling') OH groups--which create surface defects in water's hydrogen bonding network and are experimentally detected at both macroscopic (air/water or oil/water) and microscopic (dissolved hydrophobic molecule) interfaces--are thought to catalyse some chemical reactions. However, how the size, curvature or charge of the exposed hydrophobic surface influences water's propensity to form dangling OH defects has not yet been established quantitatively. Here we use Raman multivariate curve resolution to probe spectroscopically the hydrophobic hydration shell and, using a statistical multisite analysis, we show that such interfacial dangling OH structures are entropically stabilized and their formation is cooperative (the probability that a non-hydrogen-bonded OH group will form depends nonlinearly on the hydrophobic surface area). We thus expose an important difference between the chemical properties of molecular and macroscopic oil/water interfaces.