Questions about the lime-soda softening method?

Lime milk reacts with carbonates in water to form insoluble CaCO3, or it reacts with alkaline substances, thereby achieving the purpose of water softening.  When the alkalinity in water is greater than the hardness, the lime-gypsum softening method should be used. Because while softening the water, it is also possible to reduce its sodium salt alkalinity; the reaction is as follows: 2NaHCO3 + CaSO4 + Ca(OH)2 = 2CaCO3↓ + Na2SO4 + 2H2O. When the hardness of the water is greater than its alkalinity, the lime-soda softening method can be used – lime is employed to reduce the carbonate hardness of the water, while soda (Na2CO3) is used to reduce the non-carbonate hardness.  The water quality treated by the lime softening method is unstable, as there is the following carbonate equilibrium equation in the water: Ca(HCO3)2 → CaCO3↓ + H2O + CO2. When the chemical reaction proceeds from right to left, CaCO3 dissolves, and at this point temporary hardness is re-established ； When the reaction proceeds to the right, the formation of CO2 leads to acidic corrosion, and CaCO3 may cause scaling.  Lime softening is often carried out simultaneously with coagulation treatment. The coagulation process enables the CaCO3 and Mg(OH)2 formed as a result of softening to aggregate into larger particles, which then precipitate and can be removed. This not only **reduces hardness but also clarifies the water. As a coagulant, ferrous sulfate FeSO4●7H2O is generally used (since aluminum-based coagulants require a pH range of 5.5–8.5), and the pH must be kept above 8.5 in order to oxidize Fe2+ to Fe3+, thereby preventing the formation of iron scale.