Cation exchange capacity practice problems

Review:

One mole of any substance (element, molecule, compound, etc.) is the atomic mass of the element, molecule or compound. The mass of one mole of hydrogen is 1g; the mass of one mole of calcium ions is 40 g and the mass of one mole of nitrate ions (NO₃) is 62 g (N (14) + 3 O (16)=62.

In many chemical applications, a mole is too big a unit to be easily manipulated. In those cases, centimoles =0.01 moles or millimoles =0.001 moles are used instead of a mole. The mass of a centimole of hydrogen is 0.01 g and of a millimole is 0.001 g or 1mg (one milligram).

Moles of charge are the same as moles of anything else. One mole of charge is the charge (positive or negative) of one mole of an ion with either a +1 or -1 charge. An ion such as Ca²⁺ has 2 moles of charge for each mole of calcium atoms because it has two positive charges (it has two fewer electrons than protons). A trivalent atom such as aluminum has 3 moles of charge per mole of Al.

One mole of charge of any ion will always be equivalent to 1 mole of charge of any other ion.

This makes the mole of charge (mol_c) a handy unit when discussing cation exchange capacity in soils.

In soils, a mole of anions or cations is too big a number to be easily manipulated. The most common unit when calculating exchange capacity of soils, clay minerals or organic matter is centimoles of charge (cmol_c/Kg soil).

Practice problems.

The answers to these questions are on separate pages. The first examples are easier than the last. Start with number one and work your way to the end of the practice problems.

1. What is the mass of one mole, one centimole and one millimole of the following cations and anions?

H⁺, Ca²⁺, Na⁺, K⁺, SO₄^2-, NO₃^-, HCO₃^-

2. What is the weight of one mole of charge (mol_c) and one cmol_c of the same cations and anions?

3. What weight of CaCl₂ would you need to replace 4 mol_c of K⁺ in a soil?

4. How many mol_c of K⁺ does it take to replace 12 mol_c of Ca²⁺?

5. What weight of K⁺ is required to replace 12 mol_c Ca²⁺?

6. What weight of Ca²⁺ is required to replace 12 mol_c K⁺?

7. What weight of CaCO₃ is required to replace 12 mol_c K⁺?

8. What is the cation exchange capacity of a soil that has 6 cmol_c Kg^-1 H⁺, 6 cmol_c Kg^-1 Ca²⁺, 2 cmol_c Kg^-1 Mg²⁺, and 1 cmol_c Kg^-1 each K⁺ and Na⁺?

9. What is the weight of H⁺, Ca²⁺, Mg²⁺, K⁺ and Na⁺ on the exchange complex in question 8?

10. If the cation exchange capacity of a soil is 30 cmol_c kg^-1, how many cmol_c of H⁺, Ca²⁺, Mg²⁺, K⁺ and Na⁺ are on the exchange complex if the exchange complex has 5% H⁺, 50% Ca²⁺, 20% Mg²⁺, 23% K⁺ and 2% Na⁺? What is the weight of each of these cations on the exchange complex?

11. If a soil has a CEC of 25 cmol_c kg^-1 and 12% of the exchange capacity is saturated with Na⁺, what weight of CaSO₄ must be added to 1 kg of the soil to remove one-half of the sodium from the exchange complex? Assume 100% efficiency.