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Lattice enthalpy of MgSO4 > that of BaSO4 (I dont consider the negative signs)
Hydration enthalpy of MgSO4 > that of BaSO4(negative values as well)
Enthalpy of solution = hydration enthalpy - lattice enthalpy 
Hydration enthalpy changes more rapidly than lattice enthalpy -> MgSO4 is more soluble.
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