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What empirical formula do you use for determining CEC in sandy soils with no clay particles?

A correspondent wrote with that question about CEC (cation exchange capacity) calculations.

Sand is inert. It doesn't have structural negative charge, and even if it did, the surface area of sand is small. One can consider the CEC of sand to be nil.

But soil organic matter (OM) has a pH-dependent negative charge. One can estimate the CEC based on OM and soil pH. This equation is based on Contribution of organic matter and clay to soil cation-exchange capacity as affected by the pH of the saturating solution by Helling et al..

Express OM in units of g/kg. Then $OM(-311 + 268(pH)) = CEC$ with the CEC in units of mmolc/kg (millimoles of charge per kg of soil).

A sand with OM of 2% (20 g/kg) and a pH of 7 would have a CEC of 31 mmolc/kg. Keep the OM the same, but let the pH be 5.8, and the CEC will now be 25 mmolc/kg.

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