The radiative proton-capture reactions {sup 19}Ne(p,{gamma}){sup 20}Na, {sup 23}Mg(p,{gamma}){sup 24}Al, {sup 27}Si(p,{gamma}){sup 28}P, {sup 31}S(p,{gamma}){sup 32}Cl, and {sup 35}Ar(p,{gamma}){sup 36}K potentially influence energy generation and/or nucleosynthesis during explosive hydrogen burning in classical novae and/or type I x-ray bursts. The thermonuclear rates of these reactions are dependent on resonance energies E{sub r}=E{sub x}-Q and strengths {omega}{gamma}. The {sup 20}Ne({sup 3}He,t){sup 20}Na, {sup 24}Mg({sup 3}He,t){sup 24}Al, {sup 28}Si({sup 3}He,t){sup 28}P, {sup 32}S({sup 3}He,t){sup 32}Cl, and {sup 36}Ar({sup 3}He,t){sup 36}K reactions have been measured using a 32-MeV, {sup 3}He{sup 2+} beam; ion-implanted carbon-foil targets developed at the University of Washington; and the Munich Q3D magnetic spectrograph. This experiment has already yielded precision mass measurements of {sup 20}Na, {sup 24}Al, {sup 28}P, and {sup 32}Cl [C. Wrede et al., Phys. Rev. C 81, 055503 (2010)], which are used presently to constrain the corresponding (p,{gamma}) reaction Q values. The new {sup 24}Al and {sup 28}P masses resolve a discrepancy in the energy of the lowest-energy resonance in the {sup 23}Mg(p,{gamma}){sup 24}Al reaction and better constrain a direct measurement of its strength. Excitation energies in {sup 32}Cl and {sup 36}K have also been measured. An important new proton-unbound level has been found at E{sub x}=2196.9(7) keVmore » in {sup 36}K and the uncertainties in {sup 36}K excitation energies have been reduced by over an order of magnitude. Using the new data on {sup 36}K, the A=36, T=1 triplets have been reassigned. The thermonuclear {sup 35}Ar(p,{gamma}){sup 36}K reaction rate is found to be much higher than a commonly adopted rate and this could affect energy generation in type I x-ray bursts.« less