# Chemistry - Why don't everyday things burn?

## Solution 1:

The equilibrium constant for combustion of organic matter in air with oxygen is not small, but extremely large ($$K_\mathrm{eq} \gg 1$$), as is expected from a reaction that is simultaneously very exothermic and (usually) increases entropy due to the formation of more gaseous molecules than the input oxygen.

The major reason carbon-based life can exist at ambient temperature in an oxygen atmosphere is purely kinetic, not thermodynamic. You, the tree outside and everything else made of carbon is right now undergoing continuous combustion. However, in the absence of catalyst, this process is too slow below a couple hundred degrees Celsius for it to be self-sustaining. More technically, combustion of organic matter is a highly exergonic process, but the activation energy is high. The meagre amount of heat generated by the handful of molecules reacting is too quickly diluted into the surroundings, and the reaction does not accelerate and spiral out of control (a fire, as described by the eternal Feynman).

Very luckily for us, Life figured out this vast untapped source of chemical energy held back by kinetics approximately three billion years ago and developed a whole metabolic process to extract this energy in a stepwise fashion using catalysis, which we call aerobic respiration. Without it, multicellular organisms could well never had evolved.

## Solution 2:

Yes it the pesky activation energy that keeps us together!

It is quite illuminating to calculate the rate of a reaction with different activation energies using a simple approach, such as the Arrhenius equation at a constant temperature; $\mathrm{k=A*exp(-\Delta E/RT)}$. If we assume that the pre-exponential term A (the rate constant at zero activation energy or infinite, i.e. very high, temperature ) is $\mathrm{10^{13} s^{-1}}$ then the following values are obtained with different activation energies in kJ/mol.

$\Delta E$ =10, $k = 1.810^{11}$ s$^{-1}$
$\Delta E$ =40, $k = 1.110^{6}$ s$^{-1}$
$\Delta E$ =80, $k = 0.12$ s$^{-1}$
$\Delta E$ =100, $k = 0.000038$ s$^{-1}$ lifetime = 7.2 days
$\Delta E$ =140, $k = 4*10^{-12}$ s$^{-1}$ lifetime 7555 years
$\Delta E$ =180, $k = 4*10^{-19}$ s$^{-1}$ lifetime $6.9*10^{10}$ years
$\Delta E$ =200, $k = 1.5*10^{-22}$ s$^{-1}$ lifetime $2.1*10^{14}$ years

The age of the universe is approx $1.4*10^9$ years so even moderate activation barriers produce exceptionally slow reactions. Very many types of bonds have dissociation energies above 200 kJ /mol, e.g. C-C 350, C-H 413, but this is not the same as the activation energy which must be smaller than this, and by how much depends on the particular reaction. In unfolding a protein, the activation energy is essentially the dissociation (unfolding) energy, so if proteins are to last any appreciable time the activation energy has to be at least 100 kJ/mol.