Reef Chemistry Question of the Day #122 Calcium Supplement

[Randy Holmes-Farley]

Reef Chemistry Question of the Day #122

Suppose that a liquid calcium additive comprised of calcium chloride in water is used to boost the calcium level in a reef aquarium. It is described on the bottle as containing 100,000 mg/L calcium ion. In order to boost the calcium level by 50 mg/L, how much must be added to an aquarium system containing 100 gallons of water? (Note that 1 gallon = 3.785 liters.)


A. 512.2 mL
B. 378.5 mL
C. 226.4 mL
D. 189.3 mL

Good luck!





























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[fishjelly]

Giving this one a shot...

100 g x 3.785 L/g = 378.5 L

To get a concentration of 50 mg/L in the tank:

378.5 L x 50 mg/L = 18925 mg of CaCl2 needed

18925 mg x (1 L/100,000 mg) = 0.18925 L of CaCl2 solution needed or 189.25 ml, so D?

 

[hart24601]

I will go with D using the ultra handy formula c1v1=c2v2. I use this formula all the time in work and reefing (and answering Randy's other questions!)

C1V1=C2V2

100,000 mg/L (V1) = 50mg/L (378L)
100,000 mg/L (V1) = 18900mg
V1 = 0.189L
= 189ml

 

[beaslbob]

you start out with y calcium and wind up at y+50 calcium
Just to make in interesting and more like algebra say you have and initial volume of z. (you know z is always the badie in the "word problems" the run around emptying out swimming pools, opening window, turning off lights, and other nasty stuff).
and the good guy is x the stuff added. So y*z is where you started. z+x is the final volume which is 50ml greater in calcium
(z+x)*(y+50) is final calcium
y*z is initial calcium
the amount of calcium added is 100,000x
(three dots in a triangle)
(Z+x)*(y+50)-z*y=100,000x
z*y+50Z+xy+50x-z*y=100,000x
z*(y+50-y)=99950x
99950x=50Z (it is nice and expected that the initial volume y cancels out)
x=50Z/99950
x=.00050025013Z
z=378.5
x=.189344672L or 189.344672 ml which is not one of the answers and no one even me wants to check my work.
with no increase in volume is it 189.25000000000000
Now I need to check the answer because I initially used 387.5 .:bigsmile:
edit the 189.25 runs (incorrectly) up to 189.3 which is answer D.
Obviously to be precisely correct Dr Randy's Answers do not have the correct answer.
But a perfectly acceptable answer for the home user.
But then in my home tank "about that much" would do.:xd:

 

[beaslbob]

Sorry
didn't mean to kill the thread.:squigglemouth:

 

[Randy Holmes-Farley]

And the answer is...D. 189.3 mL

Folks above have shown various ways of doing the math.

Happy Reefing!