Alkanethiol molecules in solution displace 1-adamantanethiolate self-assembled monolayers on Au{111}, ultimately leading to complete molecular exchange. Specifically, here, fast insertion of n-dodecanethiolate at defects in the original 1-adamantanethiolate monolayer nucleates an island growth phase, which is followed by slow ordering of the n-dodecanethiolate domains into a denser and more crystalline form. Langmuir-based kinetics, which describe alkanethiolate adsorption on bare Au{111}, fail to model this displacement reaction. Instead, a Johnson-Mehl-Avrami-Kolmogorov model of perimeter-dependent island growth yields good agreement with kinetic data obtained by Fourier transform infrared spectrometry over 100-fold variation in n-dodecanethiol concentration. Resealing the growth rate at each concentration collapses all the data onto a single universal curve, suggesting that displacement is a scale-free process. The rate of displacement varies as the square-root of the n-dodecanethiol concentration across the 0.01-1.0 mM range studied.