The competition between Reactions [1] and [2], H + S→no H2, H + RH→H2 + R, in aqueous 0.8N H2SO4 solutions was studied at 20° over the applied pressure range of 0–6.34 kbar by measurement of G(H2) from the gamma-irradiated solutions. With O2 as S, in aerated solutions, relative specific rates k10 / k20 were determined at atmospheric pressure for methanol, glucose, glycerol, ethanol, and isopropanol as RH. From the pressure dependence of k1 / k2 and an estimated ΔV1‡ = 1.6 ml mole−1 for S ≡ O2, values of ΔV2‡ in the range −5.5 to −6.7 ml mole−1 are obtained for the five H donors. The average value ΔV2‡ = − 5.9 ml mole−1 is taken as characteristic for Reaction [2]. Values of k10 / k20 at atmospheric pressure also were determined for four deaerated 0.8N H2SO4 solutions: (1) RH ≡ glucose and S ≡ benzyl alcohol; (2) RH ≡ glucose and S ≡ BrCH2COOH; (3) RH ≡ S ≡ acetone; (4) RH ≡ S ≡ ClCH2COOH. Because little or no pressure dependence of G(H2) and, therefore, of k1 / k2 was observed with these four solutions, ΔV1‡ ≈ ΔV2‡ = − 5.9 ml mole−1. Thus, for a variety of H-atom reactions, which are not diffusion controlled, the value of ΔV‡ is approximately constant. From this result a value of V̄(H) in the range 5.9–10.3 ml mole−1 is estimated. It also is concluded that abstraction of Br or Cl by H occurs, rather than electron transfer, in Reaction [1] with BrCH2COOH or ClCH2COOH as S, respectively. Anomalous results obtained in a deaerated 0.8N H2SO4 solution of glucose and allyl alcohol are discussed.