First-order chemical reactions (. decomposition of cisplatin, N 2 O 5 ; radioisotope decay) have concentration-independent rates, which is sometimes expressed as the half-life . Second-order rates (. decomposition of NO 2 ) are inversely proportional to concentration . To determine the order and rate constant of an unknown system, integral and differential methods can be used to linearize experimental data measuring concentration over time. Catalysts affect reaction rates by adsorbing, aligning, or otherwise physically manipulating reactants, changing the activation energy of a reaction. Reaction rates are also limited by mass transport of reactants and products. In solids, atoms move via diffusion , driven by concentration gradients , as described by Fick's first law ; the proportionality constant in this case is D, the diffusivity .