268 Chapter 8. Chemical forces and self-assembly[[Student version, January 17, 2003]]
In this expression [X] denotescX/(1M). The quantity ∆G^0 is called thestandard free energy
changeof the reaction.
Even in aqueous solution, where the formula for the standard chemical potentialμ^0 found in
the Example on page 261 won’t literally apply, we can use Equation 8.16 as long as the solutions
are dilute. We just find ∆G^0 bylooking up the appropriateμ^0 ’s for aqueous solutions.
Your Turn 8e
Actually, chemistry books generally don’t tabulateμ^0 i,but rather list values of ∆G^0 f,i,the “free
energy of formation” of molecular speciesiunder standard conditions from its elemental con-
stituents, also under standard conditions. You can just use these values in place ofμ^0 iin Equa-
tion 8.15. Explain why this works.Your Turn 8f
Chemistry books sometimes quote the value of ∆Gin units ofkcal/mole, and quote Equation 8.16
in the handy formKeq=10−∆G(^0) /(??kcal/mole)
.Find the missing number.
Special biochemical conventions Biochemists make some special exceptions to the convention
thatc 0 =1M:
- In a dilute aqueous solution of any solute, the concentration of water is always about 55M.
Accordingly we take this value as the reference concentration for water. Then instead of
[H 2 O], Equation 8.16 has the factorcH 2 O/c 0 ,H 2 O=cH 2 O/(55M)≈1. With this convention
wecan just omit this factor altogether from the Mass Action rule, even if water participates
in the reaction. - Similarly, when a reaction involves hydrogen ions (protons, or H+), we choose their standard
concentration to be 10−^7 M.Asabove,this is the same asomittingfactors ofcH+/c 0 ,H+when
the reaction proceeds at neutral pH (see Section 8.3.2 below).
In any case the notation [X] will always refer tocX/(1M).
The choice of standard concentrations for a reaction influences the numerical value of the reac-
tion’s standard free energy change and equilibrium constant. When we use the special conventions
above, we denote the corresponding quantities as ∆G′^0 ,andK′eq(the “standard transformed free
energy change” and “transformed equilibrium constant”) to avoid ambiguity.
Beware: Different sources may use additional special conventions for defining standard quanti-
ties. Standard conditions also include the specification of temperature (to 25◦C)and pressure (to
105 Pa,roughly atmospheric pressure).
Actually, it’s a bit simplistic to think of ions, like H+,asisolated objects. We already know from
Chapter 7 that any foreign molecule introduced into a solvent like water disturbs the structure of the
neighboring solvent molecules, becoming effectively a larger, somewhat blurry object, loosely called
ahydrated ion. When we speak of an ion like Na+,wemean this whole complex; the standard
potentialμ^0 includes the free energy cost to assemble the entire thing. In particular, at any moment
aproton in water associates especially tightly withoneof the surrounding water molecules. Even
though the proton doesn’t bind covalently to its partner molecule, chemists refer to the combined
object as a single entity, thehydronium ionH 3 O+.Weare really referring to this complex when
wewrite H+.