34 Cation Saturation Percentages
Rivka Fidel
- Define cation saturation percentage
- Define and calculate:
- Acid saturation
- Base saturation
- Exchangeable sodium percentage*
*Content for this learning objective is continued in the salt-affected soils chapter.
A cation saturation percentage is simply the percentage of a specific exchangeable cation out of the total exchangeable cations. Here we will mainly discuss acid saturation and nonacid saturation. Because exchangeable sodium percentage is discussed in the salt-affected soils chapter, only the formula is provided here.
Acid vs. Nonacid Cations
Before calculating acid saturation and nonacid saturation, we must first identify the acid cations and nonacid cations. Acid cations are positively charged ions that lower pH, namely H+ and Al3+. Nonacid cations are positively charged ions that do not have a significant effect on pH (these are also called “base cations”, but they are not bases). The most common nonacid cations in soil are Na+, K+, Mg2+ and Ca2+.
| Acid cations in soil | Nonacid cations in soil (“base cations”) |
|---|---|
| H+
Al3+ |
Na+
K+ Mg2+ Ca2+ |
Why are Nonacid Cations Frequently Called “Base Cations”?
As the name implies, nonacid cations are not acids, but they are also not bases. So why are they often called “base cations”? The common “base cations” – Na+, K+, Mg2+ and Ca2+ – are alkali metals and alkaline earth metals, found in the first two columns of the periodic table. As a result, they tend to be found in alkalis such as CaCO3. Because of this tendency to precipitate with basic anions like CO32-, concentrations of these cations is correlated with the concentration of basic anions found in soil, and the nonacid cations were therefore frequently used as a proxy for basicity or alkalinity of soil.
Acid Saturation
The acid saturation (AS) is the fraction of exchangeable acid cations out of the total exchangeable cations, in centimoles of charge per kilogram. Normally this is expressed as a percentage, so it can also be called acid saturation percentage. Since total exchangeable cations is the same as CEC, we write calculate the acid saturation as:
Units in both the numerator and denominator must be centimoles of charge per kilogram (cmolc/kg), just like when calculating CEC.
[latex]AS = \large{\frac{\left[ H^{+} \right] + \left[ Al^{3+} \right]}{CEC}} = \large{\frac{\left[ H^{+} \right] + \left[ Al^{3+} \right]}{\left[ H^{+} \right] + \left[ Al^{3+} \right] + \left[ Ca^{2+} \right] + \left[ Mg^{2+} \right] + \left[ K^+ \right] + \left[ Na^+ \right]}}[/latex]
When calculating a percent, we can add “x100%” to the formula as a reminder to move the decimal twice to the right at the end:
[latex]\%AS = \large{\frac{\left[ H^{+} \right] + \left[ Al^{3+} \right]}{CEC}} \times 100\%[/latex]
When we’re given units in mg/kg, we first have to convert to cmolc/kg. Let’s say we have a soil with exchangeable cation concentrations as shown in the below table. For convenience, the cations’ molar masses have also been added to the table, but these can easily be found in a periodic table.
|
Cation
|
Concentration
adsorbed to exchange sites (mg/kg) |
Molar mass
(mg/mmol) |
|
Ca2+
|
2200
|
40
|
|
Mg2+
|
800 | 24 |
|
K+
|
600
|
39
|
|
Na+
|
300 | 23 |
|
Al3+
|
200
|
27
|
|
H+
|
150 | 1 |
Now we’ll convert the units for each cation:
[latex]\large{\frac{2200\ mg\ Ca^{2+}}{kg\ soil} \times \frac{mmol}{40\ mg} \times \frac{cmol}{10\ mmol} \times \frac{2\ cmol_c}{cmol} = \frac{11\ cmol_c}{kg\ soil}}[/latex]
[latex]\large{\frac{800\ mg\ Mg^{2+}}{kg\ soil} \times \frac{mmol}{24\ mg} \times \frac{cmol}{10\ mmol} \times \frac{2\ cmol_c}{cmol} = \frac{6.7\ cmol_c}{kg\ soil}}[/latex]
[latex]\large{\frac{600\ mg\ K^{+}}{kg\ soil} \times \frac{mmol}{39\ mg} \times \frac{cmol}{10\ mmol} \times \frac{1\ cmol_c}{cmol} = \frac{1.5\ cmol_c}{kg\ soil}}[/latex]
[latex]\large{ \frac{300\ mg\ Na^{+}}{kg\ soil} \times \frac{mmol}{23\ mg} \times \frac{cmol}{10\ mmol} \times \frac{1\ cmol_c}{cmol} = \frac{1.3\ cmol_c}{kg\ soil}}[/latex]
[latex]\large{\frac{200\ mg\ Al^{3+}}{kg\ soil} \times \frac{mmol}{27\ mg} \times \frac{cmol}{10\ mmol} \times \frac{3\ cmol_c}{cmol} = \frac{2.2\ cmol_c}{kg\ soil}}[/latex]
[latex]\large{\frac{150\ mg\ H^{+}}{kg\ soil} \times \frac{mmol}{1\ mg} \times \frac{cmol}{10\ mmol} \times \frac{1\ cmol_c}{cmol} = \frac{15\ cmol_c}{kg\ soil}}[/latex]
Then add up the cmolc/kg from all 5 cations, to get the CEC:
11 cmolc/kg +6.7 cmolc/kg +1.5 cmolc/kg +1.3 cmolc/kg +2.2 cmolc/kg +15 cmolc/kg
=37.7 cmolc/kg
And finally divide the acid cations by the CEC:
[latex]AS = \large{\frac{\left[ H^{+} \right] + \left[ Al^{3+} \right]}{CEC}}[/latex]
[latex]\large{= \frac{2.2 \ cmol_c/kg + 15 \ cmol_c/kg}{37.7 \ cmol_c/kg}}[/latex]
Nonacid saturation
Mirroring acid saturation, nonacid saturation (NS) is the exchangeable nonacid cations out of the total exchangeable cations, in centimoles of charge per kilogram. Normally this is expressed as a percentage, so it can also be called nonacid saturation percentage (%NS). It can also be called base saturation (BS) or base saturation percentage (%BS). To calculate it, we divide exchangeable nonacid cations by the CEC:
[latex]NS = BS = \large{\frac{\left[ Ca^{2+} \right] + \left[ Mg^{2+} \right] + \left[ K^+ \right] + \left[ Na^+ \right]}{CEC}}[/latex]
Or as a %
[latex]\%NS = \%BS = \large{\frac{\left[ Ca^{2+} \right] + \left[ Mg^{2+} \right] + \left[ K^+ \right] + \left[ Na^+ \right]}{CEC}} \times 100\%[/latex]
Using the same soil as the %AS calculation, before we found that the concentrations of the individual cations were:
|
Exchangeable Cation
|
Concentration Adsorbed to exchange sites (cmolc/kg) |
|
Ca2+
|
11.0
|
| Mg2+ | 6.7 |
|
K+
|
1.5
|
| Na+ | 1.3 |
|
Al3+
|
2.2
|
| H+ | 15.0 |
Additionally, when we added up the cmolc/kg of all cations, we found that the CEC of the soil was 37.7 cmolc/kg. So now we can calculate %NS:
[latex]NS = BS = \large{\frac{\left[ Ca^{2+} \right] + \left[ Mg^{2+} \right] + \left[ K^+ \right] + \left[ Na^+ \right]}{CEC}}[/latex]
[latex]\large{= \frac{11+ 6.7 + 1.5 + 1.3}{37.7}} = 0.54[/latex]
=54%
Exchangeable Sodium Percentage
Exchangeable sodium percentage is used to quantify sodicity, as explained in the salt-affected soils chapter. Notice how the formula is similar to the other cation saturation percentages, in that you divide the cation(s) of interest – here, just sodium – by the CEC.
[latex]ESP = \large{\frac{ \left[ Na^+ \right]}{CEC}} \times 100\%[/latex]
When abbreviated ESP, the “P” stand for percentage. Hence the “x100%” is simply a reminder to move the decimal twice to the right at the end, to convert from a fraction to percent.
A cation saturation percentage is the % of exchange sites occupied by a certain type of cation. Here we’ve learned how to calculate 3 different cation saturation percentages.
- Acid saturation = fraction of surface exchange sites occupied by acid cations
- as a fraction: [latex]AS = \frac{\left[ H^{+} \right] + \left[ Al^{3+} \right]}{CEC}[/latex]
- as a percent: [latex]\%AS = \frac{\left[ H^{+} \right] + \left[ Al^{3+} \right]}{CEC} \times 100\%[/latex]
- Nonacid saturation = “base saturation” = fraction of surface exchange sites occupied by nonacid (“base”) cations
- as a fraction: [latex]NS = BS = \frac{\left[ Ca^{2+} \right] + \left[ Mg^{2+} \right] + \left[ K^+ \right] + \left[ Na^+ \right]}{CEC}[/latex]
- as a percent: [latex]\%NS = \%BS = \frac{\left[ Ca^{2+} \right] + \left[ Mg^{2+} \right] + \left[ K^+ \right] + \left[ Na^+ \right]}{CEC} \times 100\%[/latex]
- Exchangeable sodium percentage = % of surface exchange sites occupied by sodium ions:
[latex]ESP = \frac{ \left[ Na^+ \right]}{CEC} \times 100\%[/latex]
