The release of large amounts of sulfur to the stratosphere during explosive eruptions affects the radiative balance in the atmosphere and consequentially impacts climate for up to several years after the event. Quantitative estimations of the processes that control the mass balance of sulfur between melt, crystals, and vapor bubbles is needed to better understand the potential sulfur yield of individual eruption events and the conditions that favor large sulfur outputs to the atmosphere. The processes that control sulfur partitioning in magmas are (1) exsolution of volatiles (dominantly H₂O) during decompression (first boiling) and during isobaric crystallization (second boiling), (2) the crystallization and breakdown of sulfide or sulfate phases in the magma, and (3) the transport of sulfur-rich vapor (gas influx) from deeper unerupted regions of the magma reservoir. Vapor exsolution and the formation/breakdown of sulfur-rich phases can all be considered as closed-system processes where mass balance arguments are generally easier to constrain, whereas the contribution of sulfur by vapor transport (open system process) is more difficult to quantify. The ubiquitous “excess sulfur” problem, which refers to the much higher sulfur mass released during eruptions than what can be accounted for by amount of sulfur originally dissolved in erupted melt, as estimated from melt inclusion sulfur concentrations (the “petrologic estimate”), reflects the challenges in closing the sulfur mass balance between crystals, melt, and vapor before and during a volcanic eruption. In this work, we try to quantify the relative importance of closed- and open-system processes for silicic arc volcanoes using kinetic models of sulfur partitioning during exsolution. Our calculations show that crystallization-induced exsolution (second boiling) can generate a significant fraction of the excess sulfur observed in crystal-rich arc magmas. This result does not negate the important role of vapor migration in sulfur mass balance but rather points out that second boiling (in situ exsolution) can provide the necessary yield to drive the excess sulfur to the levels observed for crystal-rich systems. In contrast, in crystal-poor systems, magma recharge that releases sulfur-rich bubbles is necessary and most likely the primary contributor to sulfur mass balance. Finally, we apply our model to account for the effect of sulfur partitioning during second boiling and its impact on sulfur released during the Cerro Galan supereruption in Argentina (2.08 Ma) and show the potential importance of second boiling in releasing a large amount of sulfur to the atmosphere during the eruption of large crystal-rich ignimbrites.