BioPHYSICAL chemistry

and Cl−. The contribution of the chloride to the measured value for sodium

chloride can be subtracted resulting in the Gibbs energy of formation of

sodium alone:

Na (solid) + Cl 2 (gas) ↔Na+(aqueous) +Cl−(aqueous)

ΔG°f(NaCl) =−393.1 kJ mol−^1 (6.12)

ΔG°f(Na+) =ΔG°f(NaCl) −ΔG°f(Cl−)

=−393.1 kJ mol−^1 −(−131.23 kJ mol−^1 ) =−261.9 kJ mol−^1

By this type of analysis, the Gibbs energy of formulation can be determined

for different ions. Likewise, the enthalpies and entropies of formation can

be determined using hydrogen as the standard.

Ionic strength

The properties of solutions containing ions are influenced by both the

concentrations of the ions and the charges of the ions. A solution of sodium

chloride will contain monovalent sodium and chloride ions, while a solu-

tion of calcium chloride will have the divalent calcium ion as well as the

monovalent chloride ion. The ionic strength is a widely used dimensionless

parameter that provides a measure of both of these aspects. The ionic strength,

I, is determined by all of the ions in solutions and so is given by the sum

of the product of the molarity,mi, and the charge,zi, of allith ions:

(6.13)

As an example, the ionic strength of a 100 mM solution of sodium chloride,

NaCl, is determined by combining the contributions of the individual ions

that are each at a 100 mM concentration, or equivalently a 0.1 molarity:

(6.14)

The ionic strength of 100 mM magnesium chloride, MgCl 2 , is different

than 100 mM NaCl as the magnesium chloride will dissolve into divalent

magnesium ions, with monovalent chloride ions being at twice the molar-

ity of the magnesium:

(6.15)

Imz=+=++ mz−−(.)(

1

2

1

2

1

2

Mg^2222 Mg Cl Cl 01 2))(.)().^22

1

2

+−=02 1 03

Imz mz=+=++ −− (.)()

1

2

1

2

1

2

Na 22 2Na Cl Cl 01 1 +−=(.)( ).

1

2

01 1^201

Imzii

i

= ∑

1

2

2

1

2

122 PARTI THERMODYNAMICS AND KINETICS