The strength of the forces between bubbles of various hydrophobic gases is determined by monitoring the coalescence rate of bubbles. A theory is formulated to elucidate the role of hydrophobicity in the rupture of the film between two hydrophobic surfaces and to develop thereby a first-principles parameter for the strength of hydrophobic forces. The theory is shown to be in quantitative agreement with the experimental data. On the basis of these results, it is demonstrated that the vacuum is the most hydrophobic "solute" possible.