The　active-site　structure,　reaction　mechanism,　and　product　selectivity　of　the　industrially　important　selective　hydrogenation　of　1,3-butadiene　are　investigated　using　first　principles　for　an　emerging　single-atom　Pd　catalyst　anchored　on　graphene.　Density　functional　theory　calculations　suggest　that　the　mono-π-adsorbed　reactant　undergoes　sequential　hydrogenation　by　Pd-activated　H2.　Importantly,　the　high　selectivity　towards　1-butene　is　attributed　to　the　post-transition-state　dynamics　in　the　second　hydrogenation　step,　which　leads　exclusively　to　the　desorption　of　the　product.　This　dynamical　event　prevails　despite　the　existence　of　energetically　preferred　1-butene　adsorption　on　Pd,　which　would　eventually　lead　to　complete　hydrogenation　to　butane　and　be　thus　inconsistent　with　experimental　observations.　This　insight　underscores　the　importance　of　dynamics　in　heterogeneous　catalysis,　which　has　so　far　been　underappreciated.　©　2018　The　Royal　Society　of　Chemistry.