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The method for testing water hardness that your lab in the attached link seeks to emulate is based on the use of tincture of green soap (TGS). Years ago, TGS was readily available but has been replaced by non-soap (detergent) hand cleaners. If you can locate TGS, the test proceeds by adding TGS, dropwise, to a 1 ounce sample of water and shaking between addition of drops to create suds. Either suds form or they don't. Keep adding TGS, dropwise, until you get suds. The number of drops is how you describe how hard the water is.

The suds will not form until all the calcium2+ is bound up to make calcium stearate (soap scum). The less calcium2+ the softer the water. Rain water and distilled water will form suds after the addition of 1 drop of TGS because there is no calcium2+.

This cannot be accomplished with non-soap detergents because detergents will form suds in soft as well as hard water because they do not form soap scum.

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