why polyphosphates are used as water softening agents?

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Solution

Polyphosphates are the sequestering agents (chelate forming compounds) which form co-ordination complex with different ions such as iron, manganese, calcium, magnesium, etc. Calcium and magnesium ions which are responsible for the hardness are trapped by phosphoric acid. The complex thus formed is quite stable as calcium, magnesium are held tightly and therefore can not replace the Na ions of soap and other cleaning/washing agents.
e.g sodium tripolyphosphate (Na₅P₃O₁₀)

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