:Sodium carbonate and sodium bicarbonate vs hard water

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There are claims that sodium bicarbonate
does not soften hard water the way sodium carbonate does. Is this true? Why does the hydrogen make such a big difference?

Thanks.

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Sodium carbonate releases 2 sodium ions into solution while sodium bicarbonate only releases 1.

When dissolved, sodium carbonate releases two sodium with a charge of +1 each and carbonic acid with a charge of -2.

Hard water is formed due to the presence of calcium and/or magnesium ions in the water. These have a charge of +2, and will bind to the carbonic acid. When they do, the calcium/magnesium carbonate that forms cannot dissolve in water, and will precipitate out.