Unlike thermally driven catalytic reactions by metals, the reaction rates in photo-catalysis do not scale with neither the amount of metals nor with their size. Because of the complexity of multi-component photo-catalysts in powder forms, this phenomenon that has been routinely observed for over three decades, has so far no fundamental explanations. In order to probe into this, hydrogen production rates from ethanol over Au clusters with different sizes deposited on TiO₂(110) rutile single crystal, were studied by scanning tunneling microscopy (STM) and online mass spectrometry. A non-linear increase of the rate of hydrogen with increasing surface coverage of gold was observed. While Au particles with sizes ranging from 4 to 8 Å, marginally affected the reaction rate, the inter-particle distance was found to be crucial. Increasing the separation distance resulted in increasing the normalized reaction rate. These results are explained in terms of competition between particles for excited electrons to reduce hydrogen ions of surface hydroxyls to molecular hydrogen. The reason for nonlinearity is postulated to be due to two considerably different time scale, the picosecond scale (associated with Debye length) of charge transfer at the interface Au/TiO₂ and the much slower time scale of electron transfer in chemical reactions.