For the first time, the dynamic protonation equilibrium between an amino acid side chain analogue and bulk water as well as the diffusion properties of the excess proton were successfully reproduced through unbiased computer simulations. During a 50 ns Q-HOP MD simulation, two different regimes of proton transfer were observed. Extended phases of frequent proton swapping between acetic acid and nearby water were separated by phases where the proton freely diffuses in the simulation box until it is captured again by acetic acid. The pKa of acetic acid was calculated around 3.0 based on the relative population of protonated and deprotonated states and the diffusion coefficient of excess proton was computed from the average mean squared displacement in the simulation. Both calculated values agree well with the experimental measurements.