A model is presented which allows a priori computation of mass transfer coefficients for bubbles (droplets) rising in quiescent Newtonian fluids. The proposed model is based on the front tracking technique and explicitly accounts for the bubble-liquid mass transfer process. The dissolved species concentration in the liquid phase is computed from a species conservation equation while the value of the concentration at the interface is imposed via an immersed boundary technique. Simulations are carried out to demonstrate the capabilities of the model to predict bubble shape, flow field as well as transport of a species from the bubble to the liquid phase.