Reef Chemistry Question of the Day #283: Effect of Salinity on Magnesium Ion

[Randy Holmes-Farley]

Reef Chemistry Question of the Day #283

Suppose that a reef aquarium has a specific gravity of 1.027 and you decide to lower it to a specific gravity of 1.026. You accomplish this lowering by removing some salt water and replacing it with pure RO/DI water (0 ppm TDS) at the same temperature.

If you have an accurate magnesium measurement of 1364 ppm before lowering it, what will the magnesium be closest to after lowering it?

A. 1306 ppm
B. 1313 ppm
C. 1324 ppm
D. 1342 ppm
E. 1351 ppm

Good luck!

Previous question of the day:

Reef Chemistry Question of the Day #282: Temperature Effects on Parameters

Reef Chemistry Question of the Day #282 Suppose your coral reef aquarium is chugging along nicely at 80 degrees F. You withdraw a sample to run some tests, and the temperature drops to 72 degree F before you are ready. Which of the following parameters will NOT have changed as the temperature...

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[taricha]

If you have an accurate magnesium measurement of 1364 ppm

trick question - you NEVER have an accurate Mg measurement

kidding.

Here's how it works in my head:
In the "1.027" the 1 is the water and the .027 is the other stuff, heh. So you've changed the other stuff from .027 to .026.
.026/.027 = 96.3%
so 1364 * 96.3% = 1313 or answer B)

I look forward to finding out why this is wrong.

 

[A_Blind_Reefer]

My math and observation skills always end up differing. So either one, or most likely both of my skills are lacking. Based solely off of test taking theory, I would most likely chose c or d, as they contain the same digits and c having the highest percentage of being correct. Of course that is based off decades old data which has most definitely changed over the years. Observation wise, I have never noticed much of a magnesium swing when lowering salinity in my aquarium. At least not the same as when I mix a fresh batch of salt water and test it at 1.025 and again at 1.026, in which there is a slight difference. I could be checking between 1.0250 and 1.0269…or 1.0259 and 1.0260, who knows.

 

[Randy Holmes-Farley]

And the answer is...

Suppose that a reef aquarium has a specific gravity of 1.027 and you decide to lower it to a specific gravity of 1.026. You accomplish this lowering by removing some salt water and replacing it with pure RO/DI water (0 ppm TDS) at the same temperature.

If you have an accurate magnesium measurement of 1364 ppm before lowering it, what will the magnesium be closest to after lowering it?

A. 1306 ppm
B. 1313 ppm
C. 1324 ppm
D. 1342 ppm
E. 1351 ppm


There are many ways to arrive at the answer, but as taricha noted, the easiest way is by the part of the sg that is not the 1.

In essence, and ion will change its concentration when sg changes from 1.x to 1.y by multiplying the initial concentration by the ratio y/x. In this case, we have:

Answer = 1364 x 26/27 = 1313 ppm

The reason this works is because concentration is linear with salinity, and the sg is linear with salinity. Hence, concentration is linear with specific gravity.

The reason the "1" needs to be ignored, and the answer is not the ratio 1.026/1.027 is because the value for any ion is not zero when specific gravity is zero (it never is zero), but rather all ions have zero concentration when specific gravity is 1.0000000.

Thus, for those mathematically inclined, the line plotting the concentration of magnesium vs sg is basically a straight line (not 100% accurate, but close) starting at magnesium = 0 and sg = 1, and rising as sg increases. One can derive an equation of a line that passes through (0,1), and (1364, 1.027) and use the resulting equation to determine the magnesium concentration X for the point (X, 1.026).

One can do this determination other ways as well, say by converting the sg to salinity in ppt, and then the magneisum concentration is necessarily linear witht he salinity. Same principle, but takes an extra step.

Happy reefing!