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If the salts are pure then they don’t provide trace elements other than Ca and Mg which are both considered trace elements.

GH is not total hardness. GH is specifically the measure of Ca and Mg ions, total hardness is a measure of all ions in the water.

Ca and Mg were chosen to represent overall GH as a measurement because Ca and Mg usually make up the majority of ions in an aquatic system, there are other ions that can contribute to total hardness but they aren’t usually of interest.

The importance of knowing GH is moderate to not significant for most practical uses. GH usually just helps figure out the ratio of Ca to Mg in a tank. If you have measured the GH of the water and you know the Ca content of the water (Ca tests are cheaper/more available than Mg tests) then you can figure out the Mg content of the water by subtracting the Ca content from the total GH content. This is really only useful if your plants are showing signs of Ca/Mg deficiency (twisting leaves usually).

If you are using RO water then its probably a good idea to add back these ions since RO water has essentially no ions in it. As you mentioned above it would cause a problem with osmotic pressure in fish. There would be an increased osmotic pressure for water trying to get into the fish and it’s cells. This could stress/kill fish if they were extremely sensitive or not adapted to these conditions (like saltwater fish put into freshwater conditions).

As long as there is a bit of Ca and Mg in the water there usually aren’t problems for fish or plants. Though the ideal ratio for plants seems to be about 4:1 Ca:Mg ratio.

Ca, Mg and K are all similarly taken up by plants and a huge increase in one can cause a block in the uptake of another ion. This leads to some weird deficiency symptoms that can look like one thing but actually be another. Ex: if there is too much Mg then the plant shows Ca deficiency symptoms because it can’t absorb Ca because the Mg ions are blocking the receptors for Ca ions. The aquarium enthusiast might think to add more Ca to fix the problem, but this won’t necessarily help since there are too many Mg ions in the system. This is a problem of excess and toxicity not one of deficiency. The same kind of thing happens with K but usually at much higher levels than with Mg or Ca.

Since you have RO water you know exactly what is going into the water and don’t have as much guess work as the rest of us.

Hope this helps.
 

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The hardening salts you are adding have more elements than just calcium and magnesium so it makes sense that there are 3/4ths more ions in there. In natural bodies of water the most abundant cations are from Ca and Mg.

"General Hardness (GH), from the German Gesamt Haerte meaning total hardness, is, most simply, a measurement of the sum of hardness cations, primarily calcium and magnesium, in solution. [This differs from total dissolved solids (TDS), which is the measurement of all conductive ions in solution.]" - http://www.kentmarine.com/botanica/gh.htm

In terms of using GH to determine "the osmotic pressure required for the well being of particular fish," it probably isn't necessary under most circumstances to use a GH test kit for this purpose - unless you have specific needs fish like African cichlids or discus fish etc…

Another thing to think about is that in blood only negative ions are able to transfer across the red blood cell's walls so anions that are present in the tank aren't as big of a deal because they can physically travel across the cell membrane and equalize the concentrations of anions on both sides which stops the process of osmosis from damaging the cell. Cations aren't able to travel across the membrane so they exert osmotic pressure on the cells and can cause harm if the concentrations are extremely different from what the fish can cope with.

GH wasn't created with any specific purpose in mind, it has been adapted over the years to specific needs like I mentioned before about determining Ca or Mg concentrations in a solution for deficiencies. Or for what you mentioned - getting an idea of what cations are present so you can attempt to match the concentrations.

GH is simply a measure of cations in solution - most of which turn out to be Ca and Mg in natural water systems (there are others like iron but it isn't usually present in very high levels so its contribution to the GH is negligible).
 

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I thought I should be more specific and mention that water hardness is the measurement of the amount of ions which have lost two electrons (divalent cations). Not all elements can lose two electrons and become divalent. There are still quite a few that can, but they aren’t common at all.

Iron, strontium, aluminum, and manganese are some others that can be detected but they simply aren’t as common in water as Ca and Mg, so GH is essentially – in most practical applications – a measure of only these two cations.
 
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