1. ## Math and chemistry

Math...

Okay, so I am trying to remember how to work percentile chemistry solutions.

Rather than the answer, would someone direct me to a resource how to work this?

Reservoir contains a solution of 50% salinity.
Replacing 20% of the reservoir with 100% distilled water changes the salinity to 40% salinity.

Replacing another 20% of the reservoir with 100% distilled water changes the salinity to 32% salinity, etc.

What is the shortcut to finding out how many water changes reaches less than 1% salinity?

2. ## Re: Math and chemistry

I'll shorthand some things, like "amount of salt". So right now, there's V amount of water in the reservoir. If it's at 50% salinity, that means there's V/2 amount of salt in it:

Salinity = salt/water = X/V = 1/2, salt therefore is V/2.

Every time you do your 20% swap, you're taking out 20% of the remaining salt (leaving 80% of what was there), but the volume of water is always the same, so the new salinity is:

Salinity = salt/water = [ (V/2) x (0.8)^n ] / V = (0.8)^n x 0.5, where n is the number of times you swap in new water.

If salinity is less than 1%:

(0.8)^n x 0.5 < 0.01
(0.8)^n < 0.02
n x log 0.8 < log 0.02 (if you remember your logarithms)
n > log 0.02 / log 0.8 (log of a number less than 1 is negative, so flip the inequality when you divide)
n > 17.5

It'd take 18 swaps minimum.

3. ## Re: Math and chemistry

I'll add that the first thing you get if you directly convert the word problem into an equation --

S_n = S_(n-1) * (1 - 0.2)
S_0 = 0.5

is known as a recurrence, recurrence relation, or recurrence equation. I'm using the underscore to indicate a subscript -- you could read that as "The Salinity at step n equals 0.8 times the salinity at step n minus one. If n=0; the salinity is 0.5."

I don't have a source to recommend to you on solving recurrences. I think a chem class may expect you to either recognize "S_n = 0.5 * 0.8^n" without explicitly thinking about recurrences or to step through it and count that it took 18 iterations.

4. ## Re: Math and chemistry

Thanks, D. I don't think i ever got this far in math to figure this out myself, but i think i can use it to work on what i want to get competed - i made my own salt mix for my aquarium and basically need to correct it before I can stock it.

5. ## Re: Math and chemistry

Nice, sounds like a fun project. In that case I think using the dilution equation at the top of this wikipedia page would let you calculate just how much of the saline solution to keep, giving you the option to do it in one step. https://en.wikipedia.org/wiki/Dilution_(equation) I don't know anything about aquariums and it's been a while since I basic chem, though.

Spoiler for here is how I would work that equation:

c1 = 0.5,
v1 = what we want to calculate,
c2 = 0.01,
v2 = final volume, we'll call it 1.

0.5 * v1 = 0.01 * 1
v1 = .02 = keep two percent of the original solution and fill the rest out with water.

As a sanity check .8^17.53 should equal 0.02

6. ## Re: Math and chemistry

(I edited my second post for an error, don't kill your fish.)

7. ## Re: Math and chemistry

My wife, who does this sort of thing for part of her living, answered with "You'd throw out the water and start over. And buy a water meter."
=)

8. ## Re: Math and chemistry

I would, but my nitrogen cycle is already completed, and the original saline solution was there for phosphate integration. The inverts in there cannot be switched over or it would shock their system.

My equation is actually a 13% water change, so there will be tremendous waste over the next 4 weeks, but it is all on purpose.

9. ## Re: Math and chemistry

Originally Posted by Tinthalas Tigris
I would, but my nitrogen cycle is already completed, and the original saline solution was there for phosphate integration. The inverts in there cannot be switched over or it would shock their system.

My equation is actually a 13% water change, so there will be tremendous waste over the next 4 weeks, but it is all on purpose.
All I can say is I thank you, because I know nothing of this sort of thing but my wife is over in a corner rambling about percents and cycles the same way we all used to talk about DPS, HoTs, and various skill checks =)

Inverts? You raising lobsters? You're raising lobster aren't ya!

10. ## Re: Math and chemistry

13% gives you n > 28.09. Unless the salinity being under 1% is absolutely critical, doing one swap per day for the four weeks you were planning will get you there just fine (1.01% salinity).

11. ## Re: Math and chemistry

Originally Posted by Delores Mulva
13% gives you n > 28.09. Unless the salinity being under 1% is absolutely critical, doing one swap per day for the four weeks you were planning will get you there just fine (1.01% salinity).
Precisely ;-)