Ion concentrations of blended water sources

[masaba]

EDIT: Oops, This was user error, I'll leave my post up anyway, though.

My water comes from a mixed portion of two water sources that both provide publicly available reports. If I assume that my water is a 50/50 mix of these two sources, then it makes sense that the ion concentrations should be an average of those for the two sources.

Here's the problem. If I assume that the alkalinity is the average of the alkalinity for the two sources and enter all of the numbers into the Bru'n water spreadsheet, then the spreadhseet throws an error that my water report is out of balance.

However, if I instead calculate the bicarbonate and carbonate levels from the Bru'n water formula, average the resulting numbers, and put those into the spreadsheet the ion concentration error goes away. There seems to be a non-linearity here somewhere which doesn't make sense because supposedly all of these numbers are reported in mg/L. So, I am appealing to an expert to see if the second way of doing this is okay.

Of note is that both of the water reports have balanced ion concentrations if I enter them individually into the spreadsheet.

Thanks for any help.

 

[mabrungard]

It appears you may be incorrectly averaging your values, if both water report balance.

My largest concern in your situation is if the water quality differs greatly from those 2 sources and the supplier happens to alter the balance of those waters. Including calcium hardness and alkalinity test kits in your brewing kit may be a good idea. They are available from pet stores. I find that the Salifert brand works well.

The other option to assure consistent water quality is to employ a RO machine.

 

[ajdelange]

If I assume that my water is a 50/50 mix of these two sources, then it makes sense that the ion concentrations should be an average of those for the two sources.

Yes for everything except H+, OH-, HCO3- and CO3-- and hence the alkalinity. If the two volumes have the same pH then the alkalinities will average.

If I assume that the alkalinity is the average of the alkalinity for the two sources and enter all of the numbers into the Bru'n water spreadsheet, then the spreadhseet throws an error that my water report is out of balance.

If you mix two volumes of different pH then the alkalinities don't average. For example, equal volumes of water both with 100 ppm alkalinity but one of which has pH 7 and the other pH 9 mix to give water with pH 7.34 and alkalinity 112. Assuming that the mix has alkalinity of 100 (the average) would indeed result in an imbalance and the way in which such problems are solved is to first find the pH that balances the mix, then calculate the HCO3- and CO3-- concentrations at that pH and finally the alkalinity from those.

However, if I instead calculate the bicarbonate and carbonate levels from the Bru'n water formula, average the resulting numbers, and put those into the spreadsheet the ion concentration error goes away. There seems to be a non-linearity here somewhere which doesn't make sense because supposedly all of these numbers are reported in mg/L. So, I am appealing to an expert to see if the second way of doing this is okay.

That isn't going to work because the pH shift changes the distribution of bicarbonate and carbonate in each volume. In the example I gave the bicarbonate in the pH 7 sample would be 120.13 mg/L (note: I am using the chemistry of ideally dilute solutions because AFAIK all the spreadsheets do soand considering ionic strength effects in this case would only change the number to 120.00) and in the pH 9 sample it is 110.24 with an average of 115.18. The calculated bicarbonate for the mix is 119.4 which is actually pretty close. If you calculate the alkalinity from that using the rough formula you would get 94.4 for the alkalinity but if you calculate it from the correct 119.4 you would get 97.9 with most of the error (the correct alkalinity is 112) coming from the rough formula. The averaging of bicarbonate ion concentration does introduce an error because the pH shift is being ignored but not that much of one in this example anyway.

There are indeed nonlinearities here which must be dealt with if the problem is to be correctly solved. I'll sketch the procedure. If more detail is wanted post again
1)Determine the amount of carbo (carbonic, bicarbonate, carbonate) in each volume from the alkalinity and pH of each volume.
2)Normalize each by the total volume. Result is carbo/L for each.
3)From the pH of each determine the charge on the carbo and add the charge on hydrogen and hydroxyl ions.
4)Guess a pH for the mix (something between the pH's of the two volumes)
5)Repeat step 3 at the new pH and subtract the magnitudes of the charge changes for the two volumes.
6)Guess a new pH and repeat from 5) until the difference is 0. This is the pH of the mix.
7)From the pH of the mix and the total carbo compute the concentrations of bicarbonate and carbonate and from them the alkalinity.

The iterative process in required by the non linearity of the problem. You can do it manually but it is clearly much easier to put all this in a spreadsheet and let the Solver do it for you.

As a practical matter you could, when blending, just use your approach of averaging bicarbonate and carbonate and live with the error or you could adjust the pH of one or the other volumes to get them the same and reduce the alkalinity of the one you added acid to by the amount of the acid added. For example, 10% phosphoric acid is about 1 N so if you added 2 mL to 20 L of water you could subtract 50*2/20 = 5 ppm as CaCO3 from its alkalinity.

 

[ajdelange]

.. and the supplier happens to alter the balance of those waters.

He can't do that. All physically realizable waters are balanced unless you put a sample on the ball of a van de Graaff generator or something ridiculous like that.

 

[mabrungard]

AJ, I'm assuming you were being funny. The balance I was speaking of was the relative proportion from each water source. Anyone have a big VDG generator? Fun stuff!

 

[ajdelange]

I knew what you meant but was worried that other readers might not especially since OP specifically mentioned ion balance. The van de Graaff bit was indeed an attempt (though perhaps a weak one) at humor.