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### Author Topic: How do I calculate solution concentration  (Read 23068 times)

#### hogied

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##### How do I calculate solution concentration
« on: 08/03/2011 08:26:13 »
I work at a water bottling plant and I'm just trying to figure out how to test our mineral solutions.  I'd appreciate it if anyone can help me with this one.

One blend of water uses a sodium sulfate/sodium bicarbonate solution which is injected in RO water at a rate of .75ml per 1 gallon.  The mineral solution is made of 96 gallons RO water, 30.72 lbs sodium sulfate and 50 lbs sodium bicarbonate.  TDS on RO averages approx 0.8 ppm and the desired TDS on finished product is 12 - 18 ppm.  What should the TDS on the mineral solution be to give me the desired result on finished product.

« Last Edit: 08/03/2011 11:04:02 by hogied »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #1 on: 27/03/2011 00:14:49 »
I work at a water bottling plant and I'm just trying to figure out how to test our mineral solutions.  I'd appreciate it if anyone can help me with this one.

One blend of water uses a sodium sulfate/sodium bicarbonate solution which is injected in RO water at a rate of .75ml per 1 gallon.  The mineral solution is made of 96 gallons RO water, 30.72 lbs sodium sulfate and 50 lbs sodium bicarbonate.  TDS on RO averages approx 0.8 ppm and the desired TDS on finished product is 12 - 18 ppm.  What should the TDS on the mineral solution be to give me the desired result on finished product.

You multiply.

Might be a stupid question but you are adding the materail after the RO right? not before?

What is the material content of the 75ml sodium sulfate/sodium bicarbonate solution?

Is that us or uk gallon?

At a guess you need to up your lbs sodium bicarbonate by about 600 maybe more, and your lbs sodium sulfate 368.64 and again maybe more, I take it you wanna hit around 16 ppm, so you'll definately need more.

Don't go acting on that, as I said need more info but your numbers seem well out, but 96 gallons of RO is alot of RO.

Although I get the feeling you know and posted this as a joke to see what answer you got, Hows that?(mods I say that because it's his job)

« Last Edit: 27/03/2011 03:19:25 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #2 on: 27/03/2011 00:55:20 »
But any joking aside, you need to up your lbs sodium bicarbonate by about 750, and your lbs sodium sulfate by about 460.8, could really use that 75ml sodium sulfate/sodium bicarbonate solution figure thou.

Should give you 12.8 ppm

Just to clarify your lbs sodium bicarbonate should be atleast 800, and your lbs sodium sulfate atleast 491.52, for 12.8 ppm.

Do you want the figures for 16ppm? Well if you do you'll have to give the 75ml sodium sulfate/sodium bicarbonate solution figure, you dont have to AND I DONT HAVE TO ANSWER. the pain.
« Last Edit: 27/03/2011 02:09:47 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #3 on: 27/03/2011 03:39:11 »
So,

Basing in Uk gallons you're 96 gallons of RO water is about 437 litres

Converting the sodium bicarbonate 800 lbs to kg is 363kg and the 491 lbs of sodium sulfate would be 223 kg

So looking at it that's, wait a minute, 586kg of material added to 437 litres of water, that is not bad, it should give you a lot more than 0.8 ppm for the 437 litres of RO

You sure your figures are not a bit off?

You really put in 36.6kg of material and only got a 0.8 ppm, from 437 litres? You sure you're not putting it in before you run the water through the RO?

It is odd.

Wait, maybe the 75ml sodium sulfate/sodium bicarbonate solution is making the differnce? Maybe it's eating the other stuff on the side?
« Last Edit: 27/03/2011 04:21:09 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #4 on: 27/03/2011 04:23:34 »
« Last Edit: 27/03/2011 04:44:37 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #5 on: 27/03/2011 04:46:39 »
and ofcourse daltons
http://en.wikipedia.org/wiki/Dalton_(unit)

Someone on here, I think his question is, how do I calculate Daltons?

The kgs are 36.6 and his litres 437.

Anyone? he has been waiting since the 8th of this month. I dont think it's fair I work it out, gonna take me ages.

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #6 on: 27/03/2011 04:53:57 »
Anyone what is 36.6 / 1.660 538 782(83)×10−27?

Hogied if you ever come back and actually read any of this, it is funny, you learn a lot on this site.

But as best I can work out your ppm is 380.6948200540878ppm which is way over what you want. I have no idea how you got a figure of 0.8ppm

looks like you need to reduce your KGs, working out of metric cannot be helping you either.

Two secs and I'll see what your reduction should resonably need to be.
« Last Edit: 27/03/2011 05:14:02 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #7 on: 27/03/2011 05:57:27 »
Ok so to achieve 16.0ppm in 437 litres of RO water, the weight you add, needs to be about 209.76 grams. GRAMS.

0.46244 lbs. Total weight for both compounds combined.

your basically 210 grams all in.

So 130.2 grams of sodium bicarbonate 62%

and 79.8 grams of sodium sulfate 38%

In 437 litres of RO water should give you a 16.0 ppm.

Althought again I really do need the figures for the 75ml sodium sulfate/sodium bicarbonate solution. As it appears your amounts are seriuosly over what they should be.

Best I can do for you.

If you use the conveter I provided you can set the ppm you seek and it will tell you the weight you need to achieve it, relative to water quanity.

Still I look silly but I certainly learnt something. Very cool. I hope that helps, still I have no idea how you got 0.8 for the amount of material you were using.

« Last Edit: 27/03/2011 06:12:13 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #8 on: 27/03/2011 07:03:35 »
I work at a water bottling plant and I'm just trying to figure out how to test our mineral solutions.  I'd appreciate it if anyone can help me with this one.

One blend of water uses a sodium sulfate/sodium bicarbonate solution which is injected in RO water at a rate of .75ml per 1 gallon.  The mineral solution is made of 96 gallons RO water, 30.72 lbs sodium sulfate and 50 lbs sodium bicarbonate.  TDS on RO averages approx 0.8 ppm and the desired TDS on finished product is 12 - 18 ppm.  What should the TDS on the mineral solution be to give me the desired result on finished product.

I think I finally understood what you meant, what an idiot I am.

after only ever hearing about daltons a few hours ago, I am giving it up, with a TDS of 15.67KG. 9.7154 kg sodium bicarbonate and 5.9546 kg sodium sulfate and ppm of 16, for 96 gallons RO and 7200ml solution and nothing else.

The Daltons at 22.04819277108 and I seriously think that's probably totally wrong! But for all I have learnt trying to answer this question over the last few hours, that's my best go. I am now going to cry in my sleep.

certianly not deleting this when I wish to feel stupid I'll come and look at it.
« Last Edit: 27/03/2011 08:11:47 by Wiybit »

#### Bored chemist

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##### How do I calculate solution concentration
« Reply #9 on: 27/03/2011 10:40:25 »
Just to clarify matters, Daltons don't enter into this problem as far as I can see.

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #10 on: 27/03/2011 23:11:14 »
Just to clarify matters, Daltons don't enter into this problem as far as I can see.

Could you explain that? the Daltons change the ratios completly

If it was simply a case of ignoring the daltons, and mixing water with solids, it would be a lot easier.

The calculation for weight of solids:- Volume X concentration(ppm) X Daltons = Solid Weight
The calculation for Concentraion(ppm) is:- Weight + Volume + daltons = concentration at ppm.

So I do not understand why you think they are un-important.

Thanks for dragging me back to the topic thou.
« Last Edit: 27/03/2011 23:33:45 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #11 on: 28/03/2011 00:26:22 »
As a stab in the dark,

I think the calculation is first working out the molecular weight for sodium bicarbonate, then doing the calculations to arrive at 16ppm in 96 gallon RO mixture.

Doing the same for sodium sulfate, and then combining the two different figures to arrive at a mixture that has 16ppm for both substances in 96 gallon mixture, adjusting both as you do so.

There are two different issues at the same time TDS of the 96 gallon mixture at 16ppm(16ppm is probably best it gives you a variable of 2ppm up and down to stay with in the parameters of 12-18ppm) and the concentration of the 75ml solution to be added per gallon, to achieve that.
« Last Edit: 28/03/2011 00:34:31 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #12 on: 28/03/2011 01:33:58 »
84.01 molecular weight sodium bicarbonate,for a concentration at 9.92ppm, weight 370187.04064 grams.

142.04.Molecular weight sodium sulfate, for a concentraion at 6.08ppm, weight 383612.54144 grams.

96 gallons uk, Ro water or 437 litres, plus 7.2 liters of soultion, total liquid volume 444.2 litres.

Although it is kinda confusing that he is adding a 75ml solution to and gallon of RO water, but at the same time the solution is made up of 96 gallons of RO water.

Might be easier to reduce volumes, every gallon should be the same. one gallon equal 4.546 litres plus 75ml =4.621 litres

Yet that is way to many grams I think it's in the hundreds of kg, but then if only 75ml of that soultion is going to be added to a gallon of water maybe it should be thick.

Should you muliply the molecular weight, by the solid quanities?

« Last Edit: 28/03/2011 02:16:53 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #13 on: 28/03/2011 05:09:45 »
84.01 molecular weight sodium bicarbonate,for a concentration at 9.92ppm, weight 370187.04064 grams.

142.04.Molecular weight sodium sulfate, for a concentraion at 6.08ppm, weight 383612.54144 grams.

96 gallons uk, Ro water or 437 litres, plus 7.2 liters of soultion, total liquid volume 444.2 litres.

Looking at this another way, Daltons are stated to be one twelth of the atomic mass

so 84.01 / 12 gives you a dalton number of 7. for sodium bicarbonate,

and a dalton number of arround 12 actually 11.83 for sodium sulfate

so with a dalton number for sodium bicarbonate of 7, for a concentration at 9.92ppm in one gallon uk, weight needed is 315.67 grams

and with a dalton number for sodium sulfate of 12(11.83), for a concentration at 6.08ppm in one gallon uk, weight needed is 326.98 basically 327 grams.

TDS of 642.65 grams of material, in one gallon RO water should give you 16.00ppm.

And I think 642.65 grams might not saturate 75ml solution.  come on it is 75 droplets could happen

« Last Edit: 28/03/2011 05:35:28 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #14 on: 28/03/2011 05:18:36 »

Looking at this another way, Daltons are stated to be one twelth of the atomic mass

so 84.01 / 12 gives you a dalton number of 7. for sodium bicarbonate,

So if that's the way you work out daltons.

For 96 gallons of RO water you'll need 61.69kg of material to get a 16.0ppm in all of it.

But again that seems like a lot of material, almost double, 10kg(plus) under double, the 36.6kg you currently claim your using to get a 0.8ppm number.

And I am trusting the calculator to be correct
http://www.currentprotocols.com/tools/solution-concentration-calculator

-------------------

I have asked others how to work out daltons, but no one seems to know.

So if that's correct,

To work out daltons you take the molecular Atomic wieght of each substance, and devide by 12.

--------------------

Still I do kinda think you just posted this as a joke to see what people would say.
« Last Edit: 28/03/2011 05:41:12 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #15 on: 28/03/2011 06:39:08 »
What should the TDS on the mineral solution be to give me the desired result on finished product.

So after a secound day looking at this, my final answer which could be wrong and probably is, IS:-

Your TDS should be for a gallon(uk) of RO water 642.65 grams:- with % ratios of 315.67 grams sodium bicarbonate at 62% and 327 grams sodium sulfate at 38%.

Muliplied, that should give you a 96 gallon solution at 16ppm.
« Last Edit: 28/03/2011 09:39:11 by Wiybit »

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #16 on: 28/03/2011 09:19:03 »
What should the TDS on the mineral solution be to give me the desired result on finished product.

So after two days my final answer which could be wrong and probably is, IS:-

Your TDS should be for a gallon(uk) of RO water 642.65 grams:- with % ratios of 315.67 grams sodium bicarbonate at 62% and 327 grams sodium sulfate at 38%.

Muliplied, that should give you a 96 gallon solution at 16ppm.

Another idea assuming your figures are correct.

You could add the 75ml solution to your RO water every 0.1523 ml. a 20 times increase if your figures are right should give you a gallon at 16ppm. 3.046 litres RO water with 1.5 litres of RO solution. total 4.546 litres or one gallon UK.

#### rosy

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##### How do I calculate solution concentration
« Reply #17 on: 28/03/2011 10:30:08 »
Quote
Looking at this another way, Daltons are stated to be one twelth of the atomic mass

No. Absolutely not. Everything you have written here is the result of a misunderstanding. I'll explain below.

#### rosy

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##### How do I calculate solution concentration
« Reply #18 on: 28/03/2011 10:47:11 »
Right. I'm going to go from absolute basics, and work up, to explain to Wybit what he's flailing about trying to understand... then if I get time I'll answer the OP...

Firstly... each atom of a particular substance (hydrogen, carbon, uranium, lead, gold) has the same number of protons.

Atoms also (mostly, except some hydrogens) contain neutrons. The exact number of neutrons may differ slightly, although not generally by very much.

Neutrons and protons weigh, to a reasonable approximation, the same amount. Which makes the maths easier. The weight of an individual proton or neutron is (roughly) 1.66 x 10 -27 kg. This unit of mass is known as a Dalton. So one proton weighs (roughly) 1 Da, one neutron also weighs (roughly) 1 Da. That's all a bit approximate, because, actually, the exact weights of protons and neutrons vary a tiny bit depending on what atom they're in.

An atom of hydrogen my be hydrogen-1, hydrogen-2 or hydrogen-3, the atomic number (number of protons) is 1 in all cases, and there may be 0, 1 or 2 neutrons giving an atomic weight of (more or less) 1, 2 or 3 Da.

An atom of carbon contains 6 protons, and 6, 7 or 8 neutrons. These are described respectively as carbon-12, carbon-13, and carbon-14 . The definition of the Dalton is 1/12 of the weight of one atom of carbon-12 (which is why I said all the other masses were approximate).

Incidentally, weights are often expressed in grams/mole, where one mole of any substance is 6.022 x 10 -22 atoms (or molecules). The mole is a number chosen such that that number of atoms of carbon-12, 1 mole of carbon-12, weighs 12 g. (And thus 1 mole of hydrogen gas, H2 weighs about 2 g).

The molecular weight given on the periodic table for a particular element is the mass per mole.. it's an average number that tries to take into account the masses and abundances of the different naturally occurring isotopes of the element, thus chlorine is given as having a molecular weight of 35.5 because about 3/4 of naturally occuring chlorine atoms are chlorine-35, and the other quarter are chlorine-37.

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #19 on: 28/03/2011 11:29:06 »
Quote
Looking at this another way, Daltons are stated to be one twelth of the atomic mass

No. Absolutely not. Everything you have written here is the result of a misunderstanding. I'll explain below.

I was quoting a scientist I read that stated "one dalton was one twelth the molecular weight of a carbon atom"

Right. I'm going to go from absolute basics, and work up, to explain to Wybit what he's flailing about trying to understand... then if I get time I'll answer the OP...

Firstly... each atom of a particular substance (hydrogen, carbon, uranium, lead, gold) has the same number of protons.

Atoms also (mostly, except some hydrogens) contain neutrons. The exact number of neutrons may differ slightly, although not generally by very much.

Neutrons and protons weigh, to a reasonable approximation, the same amount. Which makes the maths easier. The weight of an individual proton or neutron is (roughly) 1.66 x 10 -27 kg. This unit of mass is known as a Dalton. So one proton weighs (roughly) 1 Da, one neutron also weighs (roughly) 1 Da. That's all a bit approximate, because, actually, the exact weights of protons and neutrons vary a tiny bit depending on what atom they're in.

An atom of hydrogen my be hydrogen-1, hydrogen-2 or hydrogen-3, the atomic number (number of protons) is 1 in all cases, and there may be 0, 1 or 2 neutrons giving an atomic weight of (more or less) 1, 2 or 3 Da.

An atom of carbon contains 6 protons, and 6, 7 or 8 neutrons. These are described respectively as carbon-12, carbon-13, and carbon-14 . The definition of the Dalton is 1/12 of the weight of one atom of carbon-12 (which is why I said all the other masses were approximate).

Incidentally, weights are often expressed in grams/mole, where one mole of any substance is 6.022 x 10 -22 atoms (or molecules). The mole is a number chosen such that that number of atoms of carbon-12, 1 mole of carbon-12, weighs 12 g. (And thus 1 mole of hydrogen gas, H2 weighs about 2 g).

The molecular weight given on the periodic table for a particular element is the mass per mole.. it's an average number that tries to take into account the masses and abundances of the different naturally occurring isotopes of the element, thus chlorine is given as having a molecular weight of 35.5 because about 3/4 of naturally occuring chlorine atoms are chlorine-35, and the other quarter are chlorine-37.

That's really great, but how do you work out a dalton? You basically saving that 1 da is 1 au, or hyrdogen weights one dalton.

If so what is the dalton for the sulfate and bicarbonate?

« Last Edit: 28/03/2011 11:33:22 by Wiybit »

#### rosy

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##### How do I calculate solution concentration
« Reply #20 on: 28/03/2011 11:34:02 »
Oh, and the original post.

I assume that TDS is total dry solids and that "RO water" has no dry solids (it's often useful, when posting questions on a board like this, to explain your terms, if they're not necessarily in daily use outside your field.

I'm not, having looked at it again, going to attempt to answer the question posed quantitatively, because there's no indication whether we're interested in US or UK gallons (or indeed some other sort). I'd suggest to the OP that if you still want an answer to this you re-post the question, converting all your units of mass, volume, etc. to grams and litres (the units of scientific study and, incidentally, internationally comprehensible), and re-post.

But actually it's a very straightforward calculation.
Total dry weight of dilute solution per litre = Total dry weight of concentrated solution * Volume of concentrated solution / Total volume of solution

Where the total volume of the solution is the concentrated solution volume plus the water it's added to. And the above can be rearranged as required to isolate the different terms.

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #21 on: 28/03/2011 11:35:27 »
Rosy is the Dalton number for sodium bicarbonate 84?

#### Jolly- Joliver

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##### How do I calculate solution concentration
« Reply #22 on: 28/03/2011 11:40:55 »
Oh, and the original post.

I assume that TDS is total dry solids

I thought it was "total disolved solids." as he wants the total solids disolved for a 12-18 part per mil, ppm.

And he stated in another post he's in Britian so I think it's UK Gallons
« Last Edit: 28/03/2011 11:44:40 by Wiybit »

#### rosy

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##### How do I calculate solution concentration
« Reply #23 on: 28/03/2011 11:44:33 »
Quote
I was quoting a scientist I read that stated "one dalton was one twelth the molecular weight of a carbon atom"

Which was entirely accurate, but that's the definition of a Dalton, and only applies to carbon atoms.

Quote
That's really great, but how do you work out a dalton? You basically saving that 1 da is 1 au, or hyrdogen weights one dalton.

If so what is the dalton for the sulfate and bicarbonate?

OK, firstly, you wouldn't describe it as "working out a Dalton", you'd describe it as "working out the molecular weight of the substance" (well, you would if I'm right about the question I think you're asking.

But yes, plus-or-minus the exact definition, 1 Da = 1 a.u.

So for sodium bicarbonate you'd work out the molecular weight as follows:

Formula - NaHCO3
(So that's 1 atom of sodium, one each of hydrogen and carbon, and three of oxygen, per formula unit)

I'm going to work in moles, because I'm a chemist and it's what I do...

One mole of sodium has a mass of 22.99 g
One mole of hydrogen has a mass of 1.00 g
One mole of carbon has a mass of 12.01 g
One mole of oxygen has a mass of 16.00 g

So 22.99 + 1.00 + 12.01 + 3 * 16 = 84 g / mole

Equivalently, one molecular formula's worth of sodium bicarbonate has a mass of 84 Daltons.

I'll leave the other compound as an exercise for the reader.

#### rosy

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##### How do I calculate solution concentration
« Reply #24 on: 28/03/2011 11:45:20 »
Quote
Rosy is the Dalton number for sodium bicarbonate 84?

Well, leaving out that I wouldn't call it a "Dalton number", you've got that spot on. ;)

#### The Naked Scientists Forum

##### How do I calculate solution concentration
« Reply #24 on: 28/03/2011 11:45:20 »