Magnesium — Part I
http://web.archive.org/web/20030624...twork.com/fish2/aqfm/1999/mar/bio/default.asp
"How is magnesium concentration measured?
There are a number of methods for measuring magnesium in seawater, but before we review them, it is useful to know more about magnesium and chemically related elements. If you look at a periodic table, magnesium is usually found in the second column from the left. In this representation, elements that are most similar chemically are found in vertical columns. From this, you can accurately guess that some of the elements most similar to magnesium in their chemical properties are beryllium (Be), calcium (Ca), strontium (Sr) and barium (Ba). They are called group 2 elements or the alkaline earth elements. All of them would like to lose two electrons and become divalent cations. When someone refers to “magnesium” dissolved in water, or the biological roles of magnesium, one can safely infer that they are talking about the ion, Mg++.
The group 2 ions, Mg++, Ca++, Sr++ and Ba++ are all present in natural seawater, and that turns out to be their order of abundance in seawater. Magnesium is most abundant and barium the least abundant of those four ions. Many of their other chemical properties are also arranged in that order. For example, barium is the least soluble in solutions containing sulfate, strontium next to the least soluble, then calcium. Magnesium is quite soluble in sulfate solutions.
As you might guess, this trend in solubilities can be used to our advantage in measuring the magnesium concentration of seawater. All of the above ions are relatively insoluble in solutions containing phosphate. The solubility of the hydroxides of these elements also follows an interesting trend: magnesium hydroxide is very insoluble, calcium hydroxide is relatively insoluble, and strontium and barium hydroxides are relatively soluble. (Beryllium is also a group 2 metal, but it is sort of an oddball in terms of its chemical properties; it isn’t present in appreciable quantities in the ocean and as far as I know, there is no positive biological role for Be++, so it won’t be discussed further.)
The classical technique for determining magnesium in seawater was to first do a sulfate precipitation, filter that solution, then add an ammonium phosphate solution, filter out the magnesium ammonium phosphate, convert the magnesium ammonium phosphate into magnesium pyrophosphate in an oven, and carefully determine the mass of magnesium pyrophosphate with an analytical balance. If that sounds like quite an adventure in filtration, drying and weighing, it was — and that explains why magnesium in seawater is seldom measured by that technique today.
Today, most oceanographers measure magnesium by atomic emission or atomic absorption spectroscopy, which is much more convenient and can be quite accurate.
Most aquarium hobby test kits diverge from the classical approach after precipitation of Ca++, Sr++ and Ba++ with sulfate, and measure the soluble magnesium with an EDTA titration.
There is another way to exploit the solubilities of these hydroxides of these ions to get at the magnesium concentration, but this involves doing two EDTA titrations rather than one. This is often referred to as the difference method, in which the total concentration of divalent cations is determined by EDTA titration as a first step. In the second step, the magnesium ion is precipitated with a strong base as magnesium hydroxide, and a second titration is performed to give the sum of the Ca++, Sr++, and Ba++ concentrations. Because Ca++ is by far the most abundant of those three ions, within the experimental errors of test kits in the hobby this gives the calcium concentration.
The concentration of magnesium can then be determined by difference, by subtracting the (molar) concentration of calcium from the (molar) concentration of divalent cations. This “difference” method was traditionally used for freshwater samples, before the professionals became impatient and rich and started doing spectroscopic determinations of these ions. While doing two titrations sounds like more work, in practice, whenever aquarists want to determine magnesium, they will probably also be interested in the calcium concentration of the water, so there is really no wasted effort.
The first titration described above, where all of the divalent cations are measured, is often called a total hardness test kit. The second test is usually called a calcium hardness test kit. Often these concentrations are expressed "hardness as calcium carbonate (CaCO3).” The “as CaCO3” may be confusing to some people, and you may wonder why on earth anyone would express a concentration on such a roundabout concentration scale. I have enormous empathy with readers who are asking that question. Rather than trying to justify the unjustifiable, I’ll just make some observations and show you how you can turn that to your advantage.
The most important observation is that EDTA titrations determine the number of soluble divalent ions, not their mass. Magnesium ions and calcium ions have different masses, but both bind one EDTA molecule. So it is a problem to express the results of a total hardness titration in milligrams per liter (mg/L). You could fairly express the results of a total hardness concentration “as calcium ions” or “as magnesium ions.” Historically, the formation of mineral deposits in boilers was a big problem when untreated, hard water was used for filling and topping them off. A lot of that scale was calcium carbonate, so “as CaCO3” was a likely enough way of expressing that concentration in a way that had significance to users.
Another way to think about it is that today, much of the hardness in fresh waters (rivers, streams, lakes) is derived from the dissolution of calcium carbonate from rocks near the surface of the earth. So expressing total hardness “as CaCO3” says something about the source of that hardness.
That’s all well and good, but how does that help you to determine the magnesium ion concentration in an aquarium by using a calcium test kit and a total hardness test kit? Well, it emphasizes the importance of expressing the various quantities on a common concentration scale. What you will most likely encounter is a situation where you have a calcium test kit from the aquarium trade that reads in mg/L calcium, and a total hardness test kit that reads in “mg/L, as CaCO3.” You might also have total and calcium hardness test kits that both read “in mg/L, as CaCO3.” We will discuss both cases, in order.
For example, you might determine a total hardness concentration of 6300 mg/L, as CaCO3, and know that the calcium concentration in your tank is 400 mg/L, as calcium ions. What is the magnesium concentration? The atomic mass of calcium is 40.08 grams per mole. The formula weight of calcium carbonate is 100.09. The atomic mass of magnesium is 24.305 grams per mole. Now we know everything we need to do the conversion. It is easiest for me to do this in a molar concentration scale.
To convert total hardness from “mg/L as CaCO3” to moles/L divalent ions:
(6300 mg/L divalent ions, as mg/L CaCO3)/(100.09 milligrams/millimole CaCO3) = 62.94 millimoles/L
To convert the calcium concentration to millimolar:
(400 mg/L Ca++, as Ca++)/(40.08 milligrams Ca++/ millimole Ca++) = 9.98 millimoles/L Ca++.
The magnesium concentration in millimolar is:
(62.94 millimoles/L total) - (9.98 millimoles/L Ca++) = 52.96 millimoles/L Mg++.
The magnesium concentration in mg/L is:
(52.96 millimoles/L Mg++) x (24.305 milligrams Mg++/millimole Mg++) = 1287 mg/L Mg++.
If you wish to express this quantity in parts per million (w/w) you should actually correct for the density of the solution, which might be about 1.026 kilograms per liter (kg/L).
(1287 milligrams/L Mg++) / (1.026 grams/L solution) = 1254 ppm (w/w) Mg++.
The other case I wish to discuss is one where the both the total hardness and the calcium hardness test kit read “mg/L as CaCO3.” Let’s say we have a total hardness result of 4200 mg/L, as CaCO3 and a calcium hardness of 850 mg/L, as CaCO3. There are a number of ways to skin this cat, many of which are about equally good. This may be the simplest way.
To get the magnesium concentration, as CaCO3:
(4200 mg/L total hardness, as CaCO3) - (850 mg/L Ca++ as CaCO3) = 3350 mg/L Mg++, as CaCO3.
To convert the magnesium concentration from “mg/L as CaCO3”to mg/L Mg++,
(3350 mg./L Mg++ as CaCO3) x (24.305 mg Mg++)/(100.09 mg CaCO3) = 813 mg/L Mg++.
And the calcium concentration will be:
850 mg/L Ca++, as CaCO3 x (40.09 mg Ca++ / 100.09 mg CaCO3) = 340 mg/L Ca++.
You will notice that the total number of steps is smaller for the second case. That is because both measurements start on a concentration scale that allows us to take the difference directly. You also may notice that both the calcium and magnesium concentration are significantly lower than natural seawater for this example case.
In a rational world, we would express these concentrations on a molar concentration scale. There are a number of closely related concentration scales that might be used, but it is fairly common for people doing benchwork to use moles per liter. If one had a test kit that expressed “total divalent cations” in moles per liter, and another test kit that expressed the calcium concentration of a solution in moles per liter, then for a total divalent ion concentration of 55.5 millimolar, and a calcium concentration of 10.2 millimolar, the magnesium concentration is:
55.5 millimolar total divalent ions - 10.2 millimolar Ca++ = 55.3 millimolar Mg++.
If that is our accustomed concentration scale, then we are done. See how simple that was? If we want mg/L calcium and magnesium, then we are two very simple conversions from the desired answer.
10.2 millimoles/L Ca++ x 40.08 milligrams Ca++/millimole Ca++ = 409 mg/L Ca++
and
55.3 millimolar Mg++ x 24.305 milligrams Mg++/millimole Mg++ = 1344 mg/L Mg++.
Pretty simple, right? That is the most concise demonstration of why chemists prefer to use mole-based concentration scales. There are more thermodynamically rigorous concentration scales, like mole fraction, and concentration scales that work better for oceanography, such as moles per kilogram of solution. It is easy to go from moles per liter to moles per kilogram of solution, provided that you know the density of the solution. For example,
(10.2 millimoles/L Ca++) / (1.026 kilograms/L) = 9.94 millimoles/kg.
That's probably more than you wanted to know about how magnesium is measured, and the various concentration scales used to express its concentration." :lol:
This is why the mag test kits in our hobby are not that accurate compared to other methods that take longer. Our hobby grade mag kits are like a short cut version for testing mag, which can significantly decrease the final accuracy. 
