8.3. Dissociation[[Student version, January 17, 2003]] 271
8.2.4 The primordial soup was not in chemical equilibrium
The early Earth was barren. There was plenty of carbon, hydrogen, nitrogen, oxygen (though not
free in the atmosphere as it is today), phosphorus, and sulfur. Could the organic compounds of
life have formed spontaneously? Let’s look into the equilibrium concentrations of some of the most
important biomolecules in a mixture of atoms at atmospheric pressure, with overall proportions
C:H:N:O=2:10:1:8 similar to our bodies’. To help form high-energy molecules, let’s optimistically
assume a temperature of 500◦C.Mostly we get familiar low-energy, low-complexity molecules H 2 O,
CO 2 ,N 2 ,and CH 4. Then molecular hydrogen comes in at a mole fraction of about 1%, acetic
acid at 10−^10 ,and so on. The first really interesting biomolecule on the list is lactic acid, at an
equilibrium mole fraction of 10−^24 !Pyruvic acid is even farther down the list, and so on.
Evidently the exponential relation between free energy and population in Equation 8.16 must
betreated with respect. It’s averyrapidly decreasing function. The concentrations of biomolecules
in the biosphere today are nowhere near equilibrium. This is a more refined statement of the puzzle
first set out in Chapter 1:Biomolecules must be produced by the transduction of some abundant
source of free energy.Ultimately this source is the Sun.^3
8.3 Dissociation
Before going on, let us survey how our results so far explain some basic chemical phenomena.
8.3.1 Ionic and partially ionic bonds dissociate readily in water
Rock salt (sodium chloride) is “refractory”: Heat it in a frypan and it won’t vaporize. To understand
this fact, we first need to know that chlorine is highlyelectronegative.That is, an isolated chlorine
atom, though electrically neutral, will eagerly bind a free electron to become a Cl−ion, because
the ion has significantly lower internal energy than the neutral atom. An isolated sodium atom,
on the other hand, willgive upan electron (becoming a sodium ion Na+)without a very great
increase in its internal energy. Thus when a sodium atom meets with a chlorine atom, the joint
system can reduce its net internal energy by transferring one electron completely from the sodium
to the chlorine. Thus a crystal of rock salt consists entirely of the ions Na+and Cl−,held together
bytheir electrostatic attraction energy. To estimate that energy, writeqV from Equation 1.9 on
page 18 ase^2 /(4πε 0 d), wheredis a typical ion diameter. Takingd≈ 0. 3 nm(the distance between
atoms in rock salt) gives the energy cost to separate a single NaCl pair as over a hundred times the
thermal energy. No wonder rock salt doesn’t vaporize until it reaches temperatures of thousands of
degrees.
And yet, place that same ionic NaCl crystal in water and it immediately dissociates, even at
room temperature. That’s because in water we have an extra factor of (ε 0 /ε)≈ 1 /80; thus the
energy cost of separating the ions is now comparable tokBTr. This modest contribution to the
free energy cost is overcome by the increase of entropy when an ion pair leaves the solid lump and
begins to wander in solution; the overall change in free energy thus favors dissolving.
Ionic salts are not the only substances that dissolve readily in water: Many other molecules
dissolve readily in water without dissociating at all. For example, sugar and alcohol are highly
soluble in water. Although their molecules have no net charge, still each has separate positive and
(^3) The ecosystems around hot ocean vents are an exception to this general rule; they seem to feed on high-energy
molecules released from the vents