Coral reefs are among the most biodiverse ecosystems in the world. Today they are threatened by numerous stressors, including warming ocean waters and coastal pollution. Here we focus on the implications of ocean acidification for the open ocean chemistry surrounding coral reefs, as estimated from earth system models participating in the Coupled Model Intercomparison Project, Phase 5 (CMIP5). We project risks to reefs in the context of three potential aragonite saturation (Ωa) thresholds. We find that in preindustrial times, 99.9% of reefs adjacent to open ocean in the CMIP5 ensemble were located in regions with Ωa > 3.5. Under a business-as-usual scenario (RCP 8.5), every coral reef considered will be surrounded by water with Ωa < 3 by the end of the 21st century and the reefs' long-term fate is independent of their specific saturation threshold. However, under scenarios with significant CO2 emissions abatement, the Ωa threshold for reefs is critical to projecting their fate. Our results indicate that to maintain a majority of reefs surrounded by waters with Ωa > 3.5 to the end of the century, very aggressive reductions in emissions are required. The spread of Ωa projections across models in the CMIP5 ensemble is narrow, justifying a high level of confidence in these results.