Currently there is no widespread agreement on an explanation for the stability of surface nanobubbles. One means by which several explanations can be differentiated is through the predictions they make about the degree of permeability of the gas-solution interface. Here we test the hypothesis that the gas-solution interface of surface nanobubbles is permeable by experimental measurements of the exchange of carbon dioxide. We present measurements by attenuated total reflection Fourier transform infrared (ATR-FTIR) and atomic force microscopy (AFM), demonstrating that the gas inside surface nanobubbles is not sealed inside the bubbles, but rather exchanges with the dissolved gas in the liquid phase. Such gas transfer is measurable by using the infrared active gas CO2. We find that bubbles formed in air-saturated water that is then perfused with CO2-saturated water give rise to distinctive gaseous CO2 signals in ATR-FTIR measurements. Also the CO2 gas inside nanobubbles quickly dissolves into the surrounding air-saturated water. AFM images before and after fluid exchange show that CO2 bubbles shrink upon exposure to air-equilibrated liquid but remain stable for hours. Also air bubbles in contact with CO2-saturated water increase in size and Ostwald ripening occurs more rapidly due to the relatively high gas solubility of CO2 in water.