Activity, what’s important.

EA2002-03

J. M. Stroh

Because activity is the effective concentration it is of fundamental importance in geochemistry. Most lab instruments and techniques measure concentration, with the major exception of the pH meter, but all the equilibrium and thermodynamic relationships rely on activity.

The activity – concentration relation (should be familiar by now from Jeff's lecture):

where a is activity in moles per kilogram (molal), m is concentration in moles per kilogram (molal), and g is the activity coefficient (no dimension).

Moles per liter is virtually identical to moles per kilogram for dilute (<0.2 M) solutions at about standard temperature and pressure. But, molal units must be used at high concentrations.

For dilute solution the activity of water is about one, but at high ionic strength, or high temperature, this is not true.

How do we determine the activity of a species in solution? For most uncharged species assuming the activity is equal to concentration (g = 1) is adequate. For ions the activity varies with the total ionic strength of the solution (as you already know). Ionic strength is defined as:

where c is the concentration of the ith species and zI is the charge (Harris p. ). Note Harris uses the symbol m rather than I for the ionic strength. Geochemists usually use I and reserve m for the chemical potential.

To correct via the activity coefficient (symbol g) a variety formulas-methods are in use. For most applications we have to find the activity through activity coefficient formulas. These are in log form. The Debye-Huckel equation works well up to ionic strengths of about 0.1 molal (molar). See Harris p. 153.

where A and B are constants that vary with temperature, z is the ion charge and I the total ionic strength of the solution. At 25 degrees C; A = 0.5085 and B = 0.3281 x 108.

For very dilute solutions (I < 10-3), for example barite in equilibrium with pure water, the Debye-Huckel equation reduces to

The problem with individual ion activity coefficients get serious above 10-1 molal. One of the most useful expressions for the log activity coefficient at higher concentration is the Truesdell-Jones equation:

which has an adjustment parameter, b, for higher ionic strength solutions. How high is high? TJ will work up to 1 molal in almost any common water, and up to 2 molal in sodium chloride dominated waters.

Above 2 molal you get into the never-never land of brines where the Pitzer parameter approach is definitely the best. The specific ion-interaction theory works well, and has a simple formula, for concentrated brines. But, it lacks parameters for some common constituents in water.

Recommendations to the class. Unless told otherwise the TJ equation can be used with confidence with the Parkhurst values for a and b. This will be the standard for the geochemistry part of the class, with the Parkhurst (update and addition to the TJ) values for a and b given in Table 1.

For very dilute solutions will do with the A value of 0.5085

When should you use activities rather than concentrations? For the geochemistry part of the class, we will use activities routinely. Why? Many of the important species have a multiple charge, and/or the solutions have high (I > 0.05) ionic strengths. What about temperature? For most purposes use the 25 degree C values for A and B. There is a temperature dependence but it is not severe at +/- 10 degrees from 25. Table 1 gives the ai and bi parameters for the TJ equation. Table 2 gives the temperature change correction for the A and B parameters. Interpolate in table 2 if necessary.

Table 1. Parameters a and b for use in the Truesdell-Jones extended Debye-Huckel equation. Remember to multiply the a values by 10-8.

Ion / aI (x10-8) / bi / charge (z)
H+ / 4.78 / 0.24 / 1
Li+ / 4.76 / 0.20 / 1
Na+ / 4.32 / 0.06 / 1
K+ / 3.71 / 0.01 / 1
Cs+ / 1.81 / 0.01 / 1
Mg2+ / 5.48 / 0.21 / 2
Ca2+ / 4.86 / 0.15 / 2
Fe2+ / 5.08 / 0.16 / 2
Mn2+ / 7.04 / 0.22 / 2
Ba2+ / 4.55 / 0.09 / 2
Cd2+ / 5.80 / 0.10 / 2
Co2+ / 6.17 / 0.22 / 2
Cu2+ / 5.20 / 0.20 / 2
Ni2+ / 5.51 / 0.22 / 2
Pb2+ / 4.80 / 0.01 / 2
Sr2+ / 5.48 / 0.11 / 2
Zn2+ / 4.87 / 0.24 / 2
Al3+ / 6.65 / 0.19 / 3
F- / 3.46 / 0.08 / -1
Cl– / 3.50 / 0.015 / -1
ClO4- / 5.30 / 0.08 / -1
OH- / 10.65 / 0.21 / -1
HCO3- / 5.40 / 0 / -1
SO42– / 5.31 / -0.07 / -2
CO3-- / 5.40 / 0 / -2

Table 2. Temperature parameters for the A and B terms of the extended Debye-Huckel and Truesdell-Jones equations.

Temperature (C) / A / B (x108)
0 / 0.4883 / 0.3241
5 / 0.4921 / 0.3249
10 / 0.4960 / 0.3258
15 / 0.5000 / 0.3262
20 / 0.5042 / 0.3273
25 / 0.5085 / 0.3281
30 / 0.5130 / 0.3290
40 / 0.5221 / 0.3305
50 / 0.5319 / 0.3321
60 / 0.5425 / 0.3338