Knowing the controllability properties of reactions may be critical in the design phase of controlled systems. Analysis of the controllability properties of reactions is done here with control inputs being the temperature of the reaction, and the inflow rates of some species. The analysis is based on the Lie-algebra generated by the vector fields related to the differential equation of the reaction. We prove that the chemical reactions are strongly reachable on a subspace that has the same dimension as the number of independent reaction steps in every point except where the concentration of reactant species is zero, and show that this result holds for reactions in continuously stirred tank reactors as well. Finally, we analyze the controllability of the anode and cathode reactions of a polymer electrolyte membrane fuel cell with the inflow rates of hydrogen and oxygen being the control inputs and show that by using the inflow rates as control inputs the dimension of the subspace on which the system is controllable can be greater than the number of independent reaction steps.