Explain, with equations, why ordinary soap does not lather easily in hard water.

If the water is hard, calcium and magnesium ions of the water combine with the negative ions of the soap to form a slimy precipitate of insoluble calcium and magnesium usually called soap curd (scum).

$\underset{\text{[soap]}}{2\text{NaSt}} + {\text{Ca(HCO}$3)2} \longrightarrow \underset{\text{[soap curd]}}{\text{CaSt}2} ↓ + {2\text{NaHCO}3}

${2\text{NaSt}} + {\text{Mg(HCO}$3)2} \longrightarrow {\text{MgSt}2} ↓ + {2\text{NaHCO}3}

In permanent hard water, the formation of soap- curd will go on as long as there are calcium and magnesium ions present.

${2\text{NaSt}} + {\text{CaCl}$2} {\longrightarrow} {\text{CaSt}2} ↓ + {2\text{NaCl}}

${2\text{NaSt}} + {\text{MgCl}$2} {\longrightarrow} {\text{MgSt}2} ↓ + {2\text{NaCl}}

${2\text{NaSt}} + {\text{CaSO}$4} {\longrightarrow} {\text{CaSt}2} ↓ + {2\text{Na}2{\text{SO}4}}

${2\text{NaSt}} + {\text{MgSO}$4} {\longrightarrow} {\text{MgSt}2} ↓ + {2\text{Na}2{\text{SO}4}}

As long as the formation of soap-curd continues, no soap lather will be formed and the cleaning of cloth or body will not be possible.