Concise Physical Chemistry

c13 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

ION ACTIVITIES 213

and

u◦−=

λ◦−

F

=

70. 6 × 10 −^4

96 , 485

= 73. 2 × 10 −^8 m^2 V−^1 s−^1

These unusual units deserve a note. The units of speed m s−^1 can be split off:

m^2 V−^1 s−^1 =mV−^1

(

ms−^1

)

and

(

ms−^1

)

mV−^1 =ms−^1

1

(

Vm−^1

)

In other words, the unit is a typical speed in meters per second per unit voltage

drop measured in volts per meter in the MKS system for the separation between the

electrodes in the cell.

13.9 ION ACTIVITIES

One would like to have activities and activity coefficients for single ion concentrations

to use just as activities, and activity coefficients were used for single molecule

concentrations in Chapters 7 and 12. Unfortunately, this is not possible because

single ions cannot be observed in the absence of a partner ion necessary to preserve

electroneutrality. Faced with this dilemma, we make an approximation that ionic

activities are equal:a+=a−. This is obviously not true, but it is the best we can do.

The best we can find is an average activity, the geometric mean,a±≡

√

a+a−. Other

definitions follow as they did for simple molecules:a±=γ±m,γ±≡

√

γ+γ−, and

γ±≡

√

a+

m

a−

m

=

a±

m

Debye and Huckel have given a rather involved treatment of the electrostatic forces

acting on an ion surrounded by other ions. They arrived at an expression forγ±in

the form of theDebye–H ̈uckel limiting law:

lnγ±=− 1. 172 |Z+Z−|

√

μ ̃

where – 1.172 is a combination of constants,|Z+Z−|is the product of atomic charges

(|Z+Z−|= 1 .0 in the cases we consider here), and

√

μ ̃is a concentration term which

is the summation ofallthe surrounding electrolytes, not just the electrolyte for which

we seekγ±. The symbolμis almost universally used to denote both Debye–Huckel ̈

ionic strength and Gibbs chemical potential. To diminish this source of confusion,