PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 367

11.4.1.2 Undissociated electrolyte.

The standard state of unit molar concentration,cst= 1 mol dm−^3 , [see6.5.3], or the standard

state of unit molality,mst= 1 mol kg−^1 [see6.5.3] is usually chosen. In the former case the

activity coefficient is defined by the relationa[ic]=

ci

cst

γi[c],[see equation (6.101)], in the latter

case by the relationa[im]=

m[im]

mst

γ[im].[see equation (6.102)].

In aqueous solutions of electrolytes at room temperature, the molar concentration in mol dm−^3

is approximately equal to the molality. In that case also the respective activities and activity

coefficients are approximately equal.

Example

An aqueous solution of acetic acid has the concentrationc= 0.3334 mol dm−^3. Its density att

= 20◦C isρ= 1.0012 kg dm−^3. The molar mass of the acid isM = 60.05 g mol−^1. Calculate

the molality of acetic acid.

Solution

The mass of 1 dm^3 of the solution m = ρ = 1.0012 kg; the mass of the acetic acid is

ma=c M= 0.3334×60.05 = 20.024 g = 0.020 kg. The mass of the water is thusmH 2 O=m

• ma= 1.0012 - 0.020 = 0.9812 kg. From the definition of molality, see1.6.5, it follows that

ma=

na

mH 2 O

=

0. 3334

0. 9812

= 0. 34 mol kg−^1.

We can see that the difference between the molality and molar concentration is negligible here.

In an infinitely diluted solution we have

γi[c]=γi[m]= 1. (11.37)

In dilute solutions the activity coefficients of an undissociated electrolyte are usually less than
10% different from one. We will thus mostly consider them to be unity.
S Symbols:In order to simplify the writing of this type of equations we will leave out the super-
script [c] or [m] in activities and activity coefficients whenever it is clear from the context which
of the standard states is meant.