Cluster-cluster reaction rate constants are obtained from measurements of coalescence in nozzle-beam expansions. Coalescence is described by the Smoluchowski equations, modified to accommodate changes in volume and temperature. The asymptotic form of the cluster size distribution can reveal the scaling of the second-order rate constants K jk with the sizes of colliding particles. Scalings derived in the past are demonstrably incorrect and physically unjustifiable. Here, we use the physically reasonable scaling, K jk = K 11 j μ k μ , to study H 2 coalescence in a nozzle beam. Experimental size distributions fit the predicted asymptotic form, N k = Ak a e −bk , very well, with deviations identifying magic numbers. We obtain the base agglomeration cross section K 11 and the parameter μ, and thus all the rate constants, for H 2 . By comparing with products of geometric cross section and relative velocity, we find sticking coefficients. Experimental results for a nozzle-beam expansion of He are analyzed similarly, to yield K 11 and μ, and hence sticking coefficients, for He. These are compared to those for H 2 .