# Re:Hardness tutorial

> From: "Bill Hamlin" <wjhamlin at hydro_mb.ca>
> Subject: General Hardness Tutorial (Sorry Long)
>
> Ok!
> I am biting the bullet.
> I have pulled out my periodic table, blown the dust off and with grim
> determination settled in to finally figure out out this general hardness
> stuff.

Good!

>  Actually it didn't seem too hard if I am understanding it
> correctly.

It isn't.  I went to my old textbooks and figured it out quite
quickly when I found a clear error in the first aquarium book I bought.
Oddly enough, the clear error concerned magnesium concentrations...

> 1 degree GH = 18 ppm CaCO3 = 18 mg/L CaCO3 = 18 mg/L MgCO3
> (I assume its the same for mg/L for Mg.) ???

It isn't the same.  The GH unit is defined as 10 mg of "CaO"
per litre, which is equivalent to about 17.9 mg of CaCO3 per litre.
Neither of these is actually there, of course.  We are actually
talking about a concentration of Ca++ ions, and these are measured in
molarities, which are dependent on the _number_ of ions per litre.
The atomic weight of Ca is 40, but that of Mg is 24 or so.  So...

CaCO3 has molecular weight 100
MgCO3 has molecular weight 84

18 mg/L CaCO3 is equivalent to 18 * 84/100 mg MgCO3

> Now to convert that to mg/L of calcium only we go to the periodic table
> and look up the atomic weights as follows:
>
> Ca = 40
> CaCO3 = 40 + 12 + 16*3 = 100
>
> Therefor
> 1 degree GH = (18 mg/L of CaCO3) * (40 units Ca) / (100 units CaCO3)
> 	    = 18 * 40 / 100 mg/L of Ca
> 	    = 7.2 mg/L for Ca

Yes.

> Similarly
> Mg = 24.3
> MgCO3 = 84.3
>
> Therefor
> 1 degree GH = (18 mg/L of MgCO3) * (24.3 units Mg) / (84.3 units CaCO3)
> 	    = 18 * 24.3 / 84.3

15 * 24.3/84.3

> 	    = 5.2 mg/L for Mg

= 4.3 mg/L for Mg

The easier way of doing it is:

7.2 mg/L for Ca is equivalent to 7.2 * 24/40 mg/L for Mg = 4.3 mg/L
>
> Now if I look to my water chemistry:
> Water Supply Analysis (City of Winnipeg)
> Total alkalinity	78 mg/L
> Total Hardness		76 mg/L
> pH			8.0
> Calcium			20.6 mg/L
> Magnesium		5.62 mg/L
>
> I can calculate the GH as follows
> Calcium: 20 mg/L / 7.2 mg/L/degree GH = 2.86 degrees GH
> Magnesium: 5.62 mg/L / 5.2 mg/L/degree GH = 1.08 degrees GH

1.31 GH for Mg

> Total: 2.86 + 1.08 = 3.94 degrees GH

2.86 + 1.31 = 4.17 (i.e. so close that it made no significant
difference!)  The total hardness can also be checked from this:
4.17 * 17.9 = 74.6 ppm, which is pretty close to the 76 quoted above.
>
> Now Steve P. recommends adding CaCO3 until you get 4 degrees GH so this
> should be adequate for most applications so my water should be pretty
> good right out of the tap (except for Chlorine and temperature of
> course).

Agreed.
>
> How did I do?
> Have I got the methodology right?

Almost.

The easiest way of all to do these calculations is to use molarities.
a 1 GH solution has 10 mg "CaO" per litre.  The molecular weight of CaO is
56, so the solution is 10/56 millimolar in Ca++, or 0.179 millimolar.
The required concentration of Ca++ is thus 0.179 * 40 = 7.16 ppm
Mg++         0.179 * 24.3 = 4.34 ppm
CaCO3        0.179 * 100 = 17.9 ppm
which is where that number comes from!

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