This paper, the second in a three-part series, discusses a direct-bounding method to compute interval enclosures for reachable sets of continuous-stirred tank reactors (CSTRs) subject to unmeasured uncertainties and disturbances. The direct-bounding method extends the use of the generalized differential inequalities-based bounding method proposed in Scott and Barton, 2013 (Scott and Barton, 2013) to CSTR reaction systems. The key requirement of the bounding method in Scott and Barton, 2013 (Scott and Barton, 2013) is user knowledge of an a priori enclosure for the reachable set of the system, which is often nontrivial to construct for practical systems, including CSTR reaction systems. The direct-bounding method proposed here yields tight a priori enclosures for the reachable sets of CSTR reaction systems using the transformation derived in Tulsyan and Barton, 2016 (Tulsyan and Barton, 2016). The efficacy of the bounding method is validated on example problems, where it yields tight interval bounds for different CSTR reaction systems.