Reef Chemistry Question of the Day #167 General Hardness

Randy Holmes-Farley · Jan 6, 2016

Reef Chemistry Question of the Day # 167

What is the general hardness (GH) in an aquarium where the following values are present?

Calcium 425 ppm
Magnesium 1300 ppm
Strontium 8 ppm

A. 425 ppm
B. 1300 ppm
C. 1725 ppm
D. 1733 ppm
E. 4333 ppm
F. 6428 ppm

Bonus is to explain your answer rather than looking it up somewhere

Good luck!

.

Taservices · Jan 6, 2016

I'd say the answer is D, since each identity is a divalent metal meaning that it should be included in GH results.

JimWelsh · Jan 6, 2016

I must confess I'm not familiar with how GH is calculated, but I do know how Total Hardness is calculated, and maybe I'll be lucky and they are the same. Total Hardness is expressed as ppm CaCO3, so the ppm of each cation should be converted to ppm CaCO3 by multiplying by 100/X where X is the atomic mass of the cation. Ca, Mg, and Sr all contribute to Total Hardness. So, that's 425 * 100.0869 / 40.078 + 1300 * 100.0869 / 24.305 + 8 * 100.0869 / 87.62 = 6424 ppm. I know Randy likes to round things when he does math, so perhaps that accounts for the 4 ppm discrepancy between my calculation and answer "F", but I'm still going with "F".

JimWelsh · Jan 7, 2016

EDIT: Where I said "100/X", I meant "100.0869/X". The 100 is the rounded version.

Randy Holmes-Farley · Jan 7, 2016

JimWelsh said:
So, that's 425 * 100.0869 / 40.078 + 1300 * 100.0869 / 24.305 + 8 * 100.0869 / 87.62 = 6424 ppm. I know Randy likes to round things when he does math, so perhaps that accounts for the 4 ppm discrepancy between my calculation and answer "F", but I'm still going with "F".

True, I rarely do calculations with 7 significant figures.

Cory · Jan 7, 2016

Where do you start if your not a chemist?

Randy Holmes-Farley · Jan 7, 2016

Cory said:
Where do you start if your not a chemist?

By looking up what GH is.

redfishbluefish · Jan 7, 2016

Not sure exactly what GH is....if it's the same as KH, then all three of our candidates, being +2's, add to the hardness. Therefore, I believe it is simply additive....So I say 1733....but that just seems too simplistic. Therefore I'm a little fuzzy on this one....that @JimWelsh might be right with this one.

JimWelsh · Jan 7, 2016

Randy Holmes-Farley said:
True, I rarely do calculations with 7 significant figures.

I do, whenever I have values known to such precision, as in molecular weights. I just round the result to the appropriate number of significant figures when I'm done. It helps make the end result more accurate than it otherwise would be in certain contexts, when throwing away precision too early will introduce rounding errors in the final result.

Randy Holmes-Farley · Jan 7, 2016

JimWelsh said:
I do, whenever I have values known to such precision, as in molecular weights. I just round the result to the appropriate number of significant figures when I'm done. It helps make the end result more accurate than it otherwise would be in certain contexts, when throwing away precision too early will introduce rounding errors in the final result.

Maybe the isotope ratios in my test tank differ from yours.

beaslbob · Jan 7, 2016

From what I understand gh is the positive ions.

I think calcium and magnesium but no strontium . So that's c

But with my luck it's d and strontium should be included.

chark · Jan 9, 2016

From reading it seams that all metal ions are included in GH. Ca and Mg make up the largest part and the others are usually just not talked about. So, the answer would be D. 1733 ppm.

JonasRoman · Jan 10, 2016

BradB · Jan 12, 2016

I think E. You don't count Strontium, at least based on what I looked up, and JimWelsh is at least on the right track. 1 Mg atom should count the same as 1 Ca atom, even though it is heavier and ppm is by weight.

Randy Holmes-Farley · Jan 13, 2016

BradB said:
I think E. You don't count Strontium, at least based on what I looked up, and JimWelsh is at least on the right track. 1 Mg atom should count the same as 1 Ca atom, even though it is heavier and ppm is by weight.

So which answer?

Cory · Jan 13, 2016

"

GH (general hardness)

Hardness is a characteristic of water due to the presence of dissolved calcium and magnesium. Water hardness is responsible for most scale formation in pipes and water heaters (calcium and magnesium carbonates, typically), and forms insoluble solids when it reacts with soaps. Hardness is often expressed in grains per gallon, parts per million or milligrams per liter, all as calcium carbonate equivalents. It is a measure often used in freshwater aquarium systems, but not often in marine systems, where its values are very large. Seawater has a total (general) hardness of about 6.3 g/L (6,300 ppm) of calcium carbonate equivalents. These linked articles detail aspects of magnesiumand calcium in seawater."

My answer is F and probably wrong lol. Bonus points fr Randy if he can guess where i got this infor from

Randy Holmes-Farley · Jan 13, 2016

And the answer...F. 6428 ppm

General Hardness counts all of the divalent metals, but only calcium, magnesium and strontium are high enough in seawater to be important, and strontium is such a very small contributor that most people ignore it.

Additionally, since General Hardness counts a bunch of different things in the water (just like alkalinity), one needs to have it measured in units where each ion contributes equally. For example, 100 ppm of magnesium has a lot more ions in it than 100 ppm of calcium. So the units are devised to correct for this fact.

There are a number of ways of doing this, and long ago the powers that be settled on a really stupid choice: ppm calcium carbonate equivalents (or similarly stupid measures like grains per gallon). So each concentration (like 1300 ppm magnesium) needs to be converted into how much calcium carbonate would have the same number of divalent cations.

here's how that is done:

1300 ppm (mg/kg) magnesium is the concentration

magnesium has a molecular weight of 24.305 grams/mole
calcium carbonate has a molecular weight of 100.0869 grams/mole
So each 24.3 grams of magnesium counts the same as 100.1 grams of calcium carbonate

So that means that 1300 ppm magnesium = 1300 x 100.1/24.3 = 5355 ppm calcium carbonate equivalents.

Doing the same for 425 ppm calcium gives 1061 ppm calcium carbonate equivalents

and for 8 ppm strontium, we get 7 ppm calcium carbonate equivalents.

So the total is 5,355 ppm + 1061 ppm + 7 ppm = 6423 ppm (rounding is the reason for the difference between answer F and this one).

We can see from the result that strontium is only contributing 0.1% of the answer, so that is why it is usually neglected.

Overall, reef aquarists do not usually use General Hardness because of the fact that we generally want to know calcium and magnesium independently, while freshwater folks and drinking water analysts sometimes treat them interchangeably and find General Hardness useful.

Happy Reefing!