Thedifferential rate lawdescribes how the rate of reaction varies with the concentrations of various species, usually reactants, in the system. The rate of reaction is proportional to the rates of change in concentrations of the reactants and products; that is, the rate is proportional to a derivative of a concentration.
To illustrate this point, consider the reaction
A → B
The rate of reaction,r, is given by
r= - d [A]
dt
Suppose this reaction obeys a first-order rate law:
r=k[A]
This rate law can also be written as
r= - d [A]
dt =k[A]
This equation is a differential equation that relates the rate of change in a concentration to the concentration itself. Integration of this equation produces the correspondingintegrated rate law, which relates the concentration to time. When you viewed concentration-time curves in previous pages, you viewed the integrated rate laws.
d [A]
[A] = -kdt
Att= 0, the concentration of A is [A]0. The integrated rate law is thus
[A] = [A]0e-k t
(2)
Because the carbon in the coal has bonded to other carbon atoms. At room temperature the carbon atoms occasionally absorb enough energy from the environment to break a carbon bond and bond with an oxygen atom if one is available. But that is an exceedingly slow process.
But an oxygen-carbon bond requires much less energy to hold itself together than a carbon-carbon bond does. That extra energy is released to the environment and free to be absorbed by another C-C which may be broken apart with each C free to bond with an O or two. This releases yet more energy. But one first needs to somehow introduce the energy to break up a few trillion C-C bonds to raise the temperature so there's enough available energy to keep the process going.
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