This thesis investigates the physical mechanisms of air-water gas transfer through direct measurements of turbulence at the air-water interface. To enable this study, a new approach to the particle image velocimetry (PIV) technique is developed in order to quantify free-surface flows. PIV measurements of free-surface turbulence are performed with concurrent measurements of gas transfer in a specially constructed oscillating grid-stirred tank for a range of turbulent mixing and surface conditions. Surface turbulence, vorticity, divergence, and gas transfer are all affected by the presence of a surface film, with significant effects realized for relatively small surface pressures. Results show that while a relationship between surface turbulence and the gas-transfer velocity is an obvious improvement over that found using an estimate of the bulk flow turbulence, this relationship is dependent on the flow regime. However, the data from the grid turbulence experiments, and additional data from experiments with waves, can be reconciled by a single relationship between the gas-transfer velocity and the 1/2-power of the surface divergence, which agrees with previous conceptual models. These results demonstrate the important role of surface divergence in air-water gas exchange, and relate, in a physically meaningful way, the interactions between surface renewal, surfactants, and gas transfer.