- Step 1: Calculate Cation Exchange Capacity to be Neutralized:
$$\Delta ESP = \text{Initial ESP} - \text{Final ESP} = 28\% - 8\% = 20\%$$
$$\text{Exchangeable Na to be replaced} = \frac{20}{100} \times 25\text{ meq/100 g} = 5.0\text{ meq/100 g soil}$$
- Step 2: Equivalent Weight of Gypsum ($CaSO_4 \cdot 2H_2O$):
$$\text{Eq. Wt.} = \frac{172.17}{2} = 86.08\text{ mg/meq}$$
$$1\text{ meq } CaSO_4/100\text{ g soil} = 860.8\text{ mg/kg} = 0.8608\text{ g/kg}$$
- Step 3: Soil Mass for 10 ha (Upper 15 cm):
$$\text{Volume} = 100,000\text{ m}^2 \times 0.15\text{ m} = 15,000\text{ m}^3$$
$$\text{Soil mass (assuming } \rho_b \approx 1.492\text{ g/cm}^3) \approx 2.238 \times 10^7\text{ kg}$$
$$\text{Gypsum per ha} = 5 \times 1.9264 = 9.632\text{ Mg/ha}$$
$$\text{Total Gypsum for 10 ha} = 9.632 \times 10 = 96.32\text{ Megagrams (Mg)}$$
- Conclusion: Total gypsum requirement is 96.32 Mg (metric tonnes). (Correct answer: Option 2)