Equilíbrio de Misturas Simples

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166 5 SIMPLEMIXTURES
T/K xO2 yO2 p∗O2/Torr γO2
77.3 0 0 154
78 0.10 0.02 171 0.88
80 0.34 0.11 225 1.08
82 0.54 0.22 294 1.04
84 0.70 0.35 377 0.99
86 0.82 0.52 479 0.99
88 0.92 0.73 601 0.99
90.2 1.00 1.00 760 0.99
I5.6 (a) To develop the expression for K into the form requested it is useful to
rewrite [MA] and [M]free in terms of the total concentration of macro-
molecule, [M].�e total amount ofA in the dialysis bag is [A]in = [A]free+
[A]bound, but the amount of A bound is equal to the amount of themacro-
molecule ligand complex, MA: [A]bound = [MA], therefore
[A]in = [A]free + [MA] hence [MA] = [A]in − [A]free
Recall that [A]free = [A]out and that, by de�nition ν = ([A]in−[A]out)/[M],
it therefore follows that
[MA] = [A]in − [A]out = ν[M]
Now consider the macromolecule, the total concentration of which is
[M]. It follows that [M] = [MA] + [M]free. �e expression just derived
for [MA], [MA] = ν[M] is substituted in to give [M] = ν[M] + [M]free,
from which it follows that [M]free = [M](1 − ν)
With these expressions for [M]free and [MA], the expression for K is
developed into the requested form
K = [MA]c−○
[M]free[A]free
= ν[M]c−○
[M](1 − ν)[A]out
= νc−○
(1 − ν)[A]out
where [A]free = [A]out is also used.
(b) �e equilibrium constant K′ describes the equilibrium between a maco-
molecule with a single binding site, S, and the bound complex, SA
K′ = [SA]c−○
[S]free[A]free
In part (a) ν is de�ned as the average number of bound ligands permacro-
molecule, and is therefore given by ν = [A]bound/[M]. Whereas M has N
binding sites, S only has one site, so the average number of ligands bound
per S is ν/N . �is number is also expressed (by analogy with the earlier
discussion) as [A]bound/[S], so it follows that ν/N = [A]bound/[S]. �e
�nal step is to realise that the concentration of bound ligand is equal to