What is a rate law?
A rate law is an algebraic expression giving the flux through a process in terms of the molecular abundances or concentrations of the molecules involved and perhaps including a number of other physical forces.
Perhaps the most famous rate law in biology is the Henri-Michaelis-Menten rate law:
VmaxS/(Km+S)
which gives the flux through an enzymatically catalyzed process in which enzyme is limiting. There is much more on the formulation of rate laws in my text book. See for example, Writing Rate Laws for Enzymatically Catalyzed Processes.
Many rate laws are expressed as proportional to forces. This can quickly become a philosophical discussion, but the purest form of such rate laws is found in the "forces and fluxes" formulation of Onsager's phenomenological equations:
J1 = L11X1+ L12X2+ L13X3+ ...L1nXn
where J is a flux, X is a force, and the Ls are the phenomenological coefficients of proportionality.
Ohm's law is a more widely encountered example:
Here the flux is an electric current and the rate law is (1/R)(V1-V2). R is the resistance, and the two Vs are voltages measured at the two ends of the current path. This rate law gives a flux whose units are amperes if R is given in ohms and V in volts. An ampere is a couloumb per second, and so represents a flux of charge, often but not always electrons, from point 1 to point 2.
Other famous linear rate laws are bulk flow, and diffusion. These and many others can be seen as special cases of the general principle that fluxes are driven by gradients in chemical potential.
The simplest rate law of all is the linear, first order rate law
kS
which embodies the physical-chemical principle of mass action. Here k is the rate constant, and S is the concentration of the molecule that is moved or transformed by this process.