What is the balanced chemical equation for the formation of soap scum?

The formation of soap scum typically involves the reaction of soap (usually a sodium salt of a fatty acid) with calcium or magnesium ions in hard water. Here's a general balanced chemical equation for the formation of soap scum using calcium ions as an example:

Let's consider sodium stearate ((\mathrm{NaC}{18}\mathrm{H}{35}\mathrm{O}_{2})) as the soap. The reaction with calcium ions ((\mathrm{Ca}^{2+})) in hard water can be represented as follows:

[ 2\mathrm{NaC}{18}\mathrm{H}{35}\mathrm{O}{2} + \mathrm{Ca}^{2+} \longrightarrow \mathrm{Ca}(\mathrm{C}{18}\mathrm{H}{35}\mathrm{O}{2})_{2} + 2\mathrm{Na}^{+} ]

This equation shows how sodium stearate reacts with calcium ions to form calcium stearate, which is a component of soap scum, and releases sodium ions into the solution.

For magnesium ions ((\mathrm{Mg}^{2+})), the equation would be similar:

[ 2\mathrm{NaC}{18}\mathrm{H}{35}\mathrm{O}{2} + \mathrm{Mg}^{2+} \longrightarrow \mathrm{Mg}(\mathrm{C}{18}\mathrm{H}{35}\mathrm{O}{2})_{2} + 2\mathrm{Na}^{+} ]

These reactions are examples of precipitation reactions where the insoluble calcium or magnesium salts of the fatty acid (soap scum) precipitate out of the solution135.