Читать книгу Geochemistry - William M. White - Страница 119
Example 3.3 Calculating activities using the Debye–Hückel equation
ОглавлениеGiven the composition for the average river water in column A in the table below, calculate the activity of the Ca2+ ion at 25° C using the Debye–Hückel equation.
Answer: Our first step is to convert these concentrations to molality by dividing by the respective molecular weights. We obtain the molal concentrations in column B. We also need to compute z2 (column C), and the product z2m (column D). Using equation 3.75, we calculate the ionic strength to be 0.00202 m. (Note, one must use the ionic strength in molal or molar, and not millimolar, units in the Debye–Hückel Equation.
| A | B | C | D | |
| Ion | g/kg | mol/kg × 103 | z2 | mz2 × 103 |
| Cl – | 0.0078 | 0.2201 | 1 | 0.2201 |
| 0.0112 | 0.1167 | 4 | 0.4667 | |
| HCO | 0.0583 | 0.9557 | 1 | 0.9557 |
| Mg 2+ | 0.0041 | 0.1687 | 4 | 0.6746 |
| Ca 2+ | 0.015 | 0.3742 | 4 | 1.4970 |
| K + | 0.0023 | 0.0588 | 1 | 0.0588 |
| Na+ | 0.0041 | 0.1782 | 1 | 0.1782 |
We substitute this value for I, then find å = 6, A = 0.5092, and B = 0.3283 in Table 3.1, and obtain a value for the activity coefficient of 0.8237, and an activity of 0.308 ×10−3 m. If we did the calculation for other temperatures, we would see that for a dilute solution such as this, the activity coefficient is only a weak function of temperature, decreasing to 0.625 at 300° C.
