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Cation Exchange Capacity (CEC) unit convertion - 陽離子交換容量單位轉換

2021/08/06
前半部是交換性陽離子 (K、Na、Ca、Mg) 的轉換，後半是定氮的

Convert cmol_c/kg to mg/kg (cation in ammonium acetate)

\(\begin{aligned} 1 \frac{cmol_c}{kg \ soil} &= \frac{10^{-2} mol\ charge}{1\ kg\ soil} \times \frac{1\ K^+}{1\ charge} \times \frac{39\ g}{1\ mol} \times \frac{1000\ mg}{g}=390\ \frac{mg}{kg}\ K^+ \\ &= \frac{10^{-2} mol\ charge}{1\ kg\ soil} \times \frac{1\ Na^+}{1\ charge} \times \frac{23\ g}{1\ mol} \times \frac{1000\ mg}{g}=230\ \frac{mg}{kg}\ Na^+ \\ &= \frac{10^{-2} mol\ charge}{1\ kg\ soil} \times \frac{1\ Ca^{2+}}{2\ charge} \times \frac{40\ g}{1\ mol} \times \frac{1000\ mg}{g}=200\ \frac{mg}{kg}\ Ca^{2+} \\ &= \frac{10^{-2} mol\ charge}{1\ kg\ soil} \times \frac{1\ Mg^{2+}}{2\ charge} \times \frac{24.3\ g}{1\ mol} \times \frac{1000\ mg}{g}=121.5\ \frac{mg}{kg}\ Mg^{2+} \end{aligned}\)

Convert soil mg/kg to extractant mg/L (用於估算上機濃度)

Experiment condition: 5 g / 100 ammonium acetate
\(\begin{aligned} 1 \frac{mg}{kg} \times \frac{5\ g\ soil}{100\ mL} \times \frac{1\ kg}{1000\ g} \times \frac{1000\ mL}{1\ L}=\frac{1}{20} \frac{mg}{L} \end{aligned}\)

綜上，若要將前人文獻的cmol_c/kg用於估算上機濃度則可直接轉換如下

\[\begin{aligned} 1 \frac{cmol_c}{kg \ soil} &= 19.5\ \frac{mg}{L}\ K^+ \\ &= 11.5\ \frac{mg}{L}\ Na^+ \\ &= 10\ \frac{mg}{L}\ Ca^{2+} \\ &= 6.075\ \frac{mg}{L}\ Mg^{2+} \end{aligned}\]

Convert extractant mg/L to soil mg/kg and cmol_c/kg

用於上機後回算CEC (please adjust your dry soil weight by water content!!)
若上機測得的100 mL萃取液濃度為C (mg/L)，則換算回土壤中的濃度 (mg/kg) 為

\[\begin{aligned} C\ \frac{mg}{L} \times \frac{100\ mL}{soil\ weight\ (g)}\times \frac{1000\ g}{1\ kg}\times \frac{1\ L}{1000\ mL}=\frac{100C}{soil\ weight}\frac{mg}{kg} \end{aligned}\]

後續再從mg/kg轉換成cmol_c/kg方法亦同

\[\begin{aligned} 1 \frac{mg}{kg}\ K^+ &= \frac{1}{390} \frac{cmol_c}{kg}\ K^+ \\ 1 \frac{mg}{kg}\ Na^+ &= \frac{1}{230} \frac{cmol_c}{kg}\ Na^+ \\ 1 \frac{mg}{kg}\ Ca^{2+} &= \frac{1}{200} \frac{cmol_c}{kg}\ Ca^{2+} \\ 1 \frac{mg}{kg}\ Mg^{2+} &= \frac{1}{121.5} \frac{cmol_c}{kg}\ Mg^{2+} \end{aligned}\]

Convert cmol_c/kg to mg/kg (NH₄⁺ in NaCl)

為定氮過程的計算，NaCl流洗液總體積100 mL
N = 鹽酸濃度 (單位為normal, N)，對於鹽酸而言normal concentration就是molar concentration (mol/L)，所以底下會寫mol/L以利理解
S = 樣本滴定體積 (mL)
B = 空白滴定體積 (mL)
A = 蒸餾所使用的體積 (mL)
土重記得校正成乾重
\(\begin{aligned} CEC\ (cmol_c/kg\ soil) &= N\ \frac{mol}{L} \times (S-B)\ mL \times \frac{100\ mL}{A\ mL} \times \frac{1}{soil\ weight\ (g)} \times \frac{100\ cmol\ charge}{1\ mol\ charge} \times \frac{1\ L}{1000\ mL} \times \frac{1000\ g}{1\ kg} \\ &=\frac{N \times (S-B) \times 10^4}{A \times (soil\ weight)} \end{aligned}\)