Alkalinity/pH calculation questions

[bitteritdown]

Suppose that using a Salifert Alkalinity test kit, I determine that my water has an alkalinity of 3.77 meq/L.

Also, suppose that I have 10% and 85% phosphoric acid solutions.

1.) How does one convert 3.77 meq/L to ppm (mg/L)?
2.) How does one calculate the amount of each acid required to bring my water to a pH of 5.4?

 

[Hanglow]

There's a guide on this sister forum
http://www.thehomebrewforum.co.uk/showthread.php?t=68369

Your acid addition will depend entirely on the grist and volume of liquor you intend to use, there are spreadsheets out there like brunwater or I like this one
http://homebrewingphysics.blogspot.co.uk/2016/03/brewing-water-calculator-mph-water.html

 

[ajdelange]

1. Multiply the mEq/L by 50 to get ppm as CaCO3. That is the way alkalinity is usually reported in North America but for your second question you want to stay with mEq/L.
2. 10% phosphoric acid solution is about 1.1 N which means that each mL delivers 1.1 mEq to pH's in the normal mash range. 85% phosphoric acid is about 14.9 N

The calculation of the amount of acid required to bring water of a certain pH and alkalinity to a target pH is fairly complex (you need to know the sample pH as well as the alkalinity - all the details are in the sticky at https://www.homebrewtalk.com/forum/threads/calculating-bicarbonate-and-carbonate.473408/) but the answer is almost always the same: you need to neutralize 90% of the alkalinity. Thus if you have alkalinity of 3.77 mEq/L you will need to add 0.9*3.77 = 3.39 mEq of acid to each liter treated. If you are using 10% acid that is 3.39/1.1 = 3.08 ml and for 85% it is 3.39/14.9 = 0.227 mL

 

[ajdelange]

.

 

[bitteritdown]

Thanks Hanglow and AJDelange.

I really wish there was a book that walked guys like me through the basics of doing these sort of calculations. Kinda like a water calculations/chemistry textbook. I've seen the Water Book but not sure it's simple enough for beginners or maybe if I'd just do more of these sorts of calculations I'd get the hang of it.

 

[Silver_Is_Money]

3.77 meq/L x 50 = 188.5 ppm as alkalinity (CaCO3)

3.77 meq/L x 61 = 230 ppm as bicarbonate (HCO3-)

 

[bitteritdown]

Yes, but magic numbers (err constants...) 50, 61... where do they come from? How are they derived?

 

[Silver_Is_Money]

Yes, but magic numbers (err constants...) 50, 61... where do they come from? How are they derived?

They are based upon molecular weights, and more specifically equivalent weights.

The molecular weight of CaCO3 is 100, but since calcium has 2 valance electrons its "equivalent weight" is half of that, or 50

The molecular weight of the HCO3- ion is 61, as is its equivalent weight

 

[bitteritdown]

Thanks for explaining that. The question is what book can be referred to in order to learn such things? A basic chemistry book? A basic water book?

 

[Silver_Is_Money]

Thanks for explaining that. The question is what book can be referred to in order to learn such things? A basic chemistry book? A basic water book?

Yes and yes, but these days online searches work well also.

 

[Silver_Is_Money]

A periodic table of the elements comes in handy also.

https://www.webelements.com

 

[ajdelange]

Yes, but magic numbers (err constants...) 50, 61... where do they come from?

50 is approximately half the molecular weight of calcium carbonate (which is 100.0869). 61 is approximately the molecular weight of a bicarbonate ion.

How are they derived?

If one suspends 100.00 mg (~1 mmol) of pure calcium carbonate in 1 L of water and bubbles CO2 through that water until the pH is 8.38 and one then measures the alkalinity of that water to a titration end point of pH 4.5 (ISO standard) he will require 2.0017 mEq of acid per liter. This is because approximately 1 mmol of carbonate ion has converted to bicarbonate and one mmol of carbonic acid has converted to bicarbonate). That's effectively 2 and that, when multiplied by 50 gives 100, the amount of CaCO3 dissolved. In natural waters the alkalinity comes mostly from limestone (CaCO3) dissolved by carbonic acid which came from underground CO2 (from bacterial respiration). 8.38 turns out to be the pH of water in equilibrium between limestone and an atmospheric CO2 level of 0.0003 atmospheres. So if you have a water sample with alkalinity x mEq/L and that water sample's pH is 8.38 and carbonate/bicarbonate plus the water itself are the only sources of alkalinity and the acid that dissolved the limestone was carbonic acid then the 50*x is very close to the amount of limestone dissolved in a liter of that water. Thus it became the practice in North America (and other places too) to express alkalinity as 50 times the actual alkalinity in mEq/L. Note that if one titrates a solution with 100 mg/L CaCO3 dissolved in it with a calcium chelating agent such as EDTA it will take 2 mEq/L of that agent because 100 mg/L CaCO3 is 1 mole and releases 1 mole when dissolved of Ca++ and HCO3- plus CO3-- totalling one mole. One mole of Ca++ is 2 Equivalents. It is, thus, the practice in the US (and elsewhere) to multiply the mEq/L chelant value by 50 and call that "Calcium hardness in ppm as CaCO3" just as it is to multiply the alkalinity mEq/L by 50 and call it "alkalinity in ppm as CaCO3". Where people start to get confused is where one adds, for example, some magnesium hydroxide to DI water and then speaks of its magnesium hardness as CaCO3 and alkalinity as CaCO3 even though the sample contains no CaCO3. Or where 100 mg of CaCO3 is placed in a liter of water and dissolved with a strong acid (carbonic acid is a weak acid) such as sulfuric or phosphoric to pH 8.38. In such cases only 1 mEq of acid is required to reach the alkalinity end point (because there is only 1 mmol of bicarbonate from the carbonate ion) and the alkalinity is now 50 even though the amount of CaCO3 dissolved was actually the same 100 mg/L.

These are the conventions and we are stuck with them. Just remember that when you see hardness as CaCO3 or alkalinity as CaCO3 that you should divide the number by 50 to get mEq/L of the metal or alkalinity. As we saw earlier in the thread these are the units we work with in doing calculations.

Now on to the 61. If one has a water sample at pH 7 with an alkalinity (ISO) of 2 mEq/L (100 ppm as CaCO3), and this alkalinity is solely due to bicarbonate, carbonate and the water itself and the anions are balanced solely by calcium and hydrogen ions the bicarbonate content of that water will be 121.95 mg/L. At other pH's the bicarbonate content, for 2 mEq/L alkalinity:

pH HCO3-
5 178.28
6 125.68
7 121.96
8 120.47
8.5 117.8
9 110.11

Because of the value of the first pK of carbonic acid (6.38) some things cancel out in the math and there is a sweet spot (say 6 > pH > 8.5 which covers most, but by no means all water supplies) where the bicarbonate content is approximately 61 times (the molecular weight of bicarbonate ion) the alkalinity. This is tantamount to saying that all the alkalinity in water in this range is due to bicarbonate and that's where this value really comes from: most spreadsheet authors assume all the alkalinity comes from bicarbonate. It doesn't though most of it does in many if not most municipal supplies (though there seems to be a tendency among municipal suppliers to push pH up in order to protect their mains).

Many spreadsheet authors do not implement the calculations necessary to determine the actual value of bicarbonate from alkalinity and so use 61*alkalinity(as CaCO3)/50 as their estimate of bicarbonate at any pH. Ordinarily this wouldn't be a problem as we don't really care much about bicarbonate but the worst offenders among the spreadsheet creators use bicarbonate as a proxy for alkalinity based on this approximation.

 

[ajdelange]

I really wish there was a book that walked guys like me through the basics of doing these sort of calculations. Kinda like a water calculations/chemistry textbook. I've seen the Water Book but not sure it's simple enough for beginners

I think this stuff is reasonably simple (if intricate) but I've been doing it for years and it wasn't easy at the start. Also I've had bitter arguments here with people who claim to teach chemistry which arguments revealed that they were not capable of understanding it so maybe I'm some sort of natural chemical genius but a quick discussion with my wife would certainly change your mind if that's what you were thinking. WRT the water book: John didn't want to put too much of the 'meat' into so if you find it difficult that implies that you have a rough road ahead.

it or maybe if I'd just do more of these sorts of calculations I'd get the hang of it.

I guarantee that that is indeed the case. As Levine says in the introduction do his p-chem book, you don't get into shape by reading a body building book - you have to do the exercises.

The question is what book can be referred to in order to learn such things? A basic chemistry book? A basic water book?

You need to know some basic (highschool/college freshman) chemistry i.e. what electron, protons, atoms and ions are, how to read a chemical equations, how the strengths of solutions are specified, a little about acids and bases and, the tough part, something about chemical equilibrium equations - the part of your chemistry courses you hated most if you took any. You'll also need some math i.e. the ability to work with logarithms and anti logarithms. IOW, engineers and scientists are going to have an easier time of it than poets and philosophers. I'd suggest looking at the Wikipedia article on Henderson - Hasselbalch Equation. It is the basis for all this stuff. If you can read and understand that then you should be able to follow what's at https://www.homebrewtalk.com/forum/threads/calculating-bicarbonate-and-carbonate.473408/ which is the only difficult part of brewing water chemistry in a nutshell. If there are parts of the Wikipedia article that puzzle you they would suggest where you need to go to build the required fundamental knowledge base.

With respect to a book on how to do the calculations: I've thought about it and would write it if I thought anyone would read it. Very few people are interested in such things. I put up the linked post on how to do the calculations about 3 years ago. In it I told how to do them but not why they were done in this way. I offered to explain the why's and wherefore's to anyone interested but have had enquiries from very few people.

 

[bitteritdown]

50 is approximately half the molecular weight of calcium carbonate (which is 100.0869). 61 is approximately the molecular weight of a bicarbonate ion.


If one suspends 100.00 mg (~1 mmol) of pure calcium carbonate in 1 L of water and bubbles CO2 through that water until the pH is 8.38 and one then measures the alkalinity of that water to a titration end point of pH 4.5 (ISO standard) he will require 2.0017 mEq of acid per liter. This is because approximately 1 mmol of carbonate ion has converted to bicarbonate and one mmol of carbonic acid has converted to bicarbonate). That's effectively 2 and that, when multiplied by 50 gives 100, the amount of CaCO3 dissolved. In natural waters the alkalinity comes mostly from limestone (CaCO3) dissolved by carbonic acid which came from underground CO2 (from bacterial respiration). 8.38 turns out to be the pH of water in equilibrium between limestone and an atmospheric pH level of 0.0003 atmospheres. So if you have a water sample with alkalinity x mEq/L and that water sample's pH is 8.38 and carbonate/bicarbonate plus the water itself are the only sources of alkalinity and the acid that dissolved the limestone was carbonic acid then the 50*x is very close to the amount of limestone dissolved in a liter of that water. Thus it became the practice in North America (and other places too) to express alkalinity as 50 times the actual alkaliity in mEq/L. Note that if one titrates a solution with 100 mg/L CaCO3 dissolved in it with a calcium chelating agent such as EDTA it will take 2 mEq/L of that agent because 100 mg/L CaCO3 is 1 mole and releases 1 mole when dissolved of Ca++ and HCO3- plus CO3-- totalling one mole. One mole of Ca++ is 2 Equivalents. It is, thus, the practice in the US (and elsewhere) to multiply the mEq/L chelant value by 50 and call that "Calcium hardness in ppm as CaCO3" just as it is to multiply the alkalinity mEq/L by 50 and call it "alkalinity in ppm as CaCO3". Where people start to get confused is where one adds, for example, some magnesium hydroxide to DI water and then speaks of its magnesium hardness as CaCO3 and alkalinity as CaCO3 even though the sample contains no CaCO3. Or where 100 mg of CaCO3 is placed in a liter of water and dissolved with a strong acid (carbnonic acid is a weak acid) such as sulfuric or pohosphoric tp pH 8.38. In such cases only 1 mEq of acid is required to reach the alkalinity end point (because there is only 1 mmol of bicarbonate from the carbonate ion) and the alkalinity is now 50 even though the amount of CaCO3 dissolved was actually the same 100 mg/L.

These are the conventions and we are stuck with them. Just remember that when you see hardness as CaCO3 or alkalinity as CaCO3 that you should divide the number by 50 to get mEq/L of the metal or alkalinity. As we saw earlier in the thread these are the units we work with in doing calculations.

Now on to the 61. If one has a water sample at pH 7 with an alkalinity (ISO) of 2 mEq/L (100 ppm as CaCO3), and this alkalinity is solely due to bicarbonate, carbonate and the water itself and the anions are balanced solely by calcium and hydrogen ions the bicarbonate content of that water will be 121.95 mg/L. At other pH's the bicarbonate content, for 2 mEq/L alkalinity:

pH HCO3-
5 178.28
6 125.68
7 121.96
8 120.47
8.5 117.8
9 110.11

Because of the value of the first pK of carbonic acid (6.38) some things cancel out in the math and there is a sweet spot (say 6 > pH > 8.5 which covers most, but by no means all water supplies) where the bicarbonate content is approximately 61 times (the molecular weight of bicarbonate ion) the alkalinity. This is tantamount to saying that all the alkalinity in water in this range is due to bicarbonate and that's where this value really comes from: most spreadsheet authors assume all the alkalinity comes from bicarbonate. It doesn't though most of it does in many if not most municipal supplies (though there seems to be a tendency among municipal suppliers to push pH up in order to protect their mains).

Many spreadsheet authors do not implement the calculations necessary to determine the actual value of bicarbonate from alkalinity and so use 61*alkalinity(as CaCO3)/50 as their estimate of bicarbonate at any pH. Ordinarily this wouldn't be a problem as we don't really care much about bicarbonate but the worst offenders among the spreadsheet creators use bicarbonate as a proxy for alkalinity based on this approximation.

Thank you (and Silver_Is_Money), those are the explanations I'm looking for.

I think this stuff is reasonably simple (if intricate) but I've been doing it for years and it wasn't easy at the start. Also I've had bitter arguments here with people who claim to teach chemistry which arguments revealed that they were not capable of understanding it so maybe I'm some sort of natural chemical genius but a quick discussion with my wife would certainly change your mind if that's what you were thinking. WRT the water book: John didn't want to put too much of the 'meat' into so if you find it difficult that implies that you have a rough road ahead.

I guarantee that that is indeed the case. As Levine says in the introduction do his p-chem book, you don't get into shape by reading a body building book - you have to do the exercises.

You need to know some basic (highschool/college freshman) chemistry i.e. what electron, protons, atoms and ions are, how to read a chemical equations, how the strengths of solutions are specified, a little about acids and bases and, the tough part, something about chemical equilibrium equations - the part of your chemistry courses you hated most if you took any. You'll also need some math i.e. the ability to work with logarithms and anti logarithms. IOW, engineers and scientists are going to have an easier time of it than poets and philosophers. I'd suggest looking at the Wikipedia article on Henderson - Hasselbalch Equation. It is the basis for all this stuff. If you can read and understand that then you should be able to follow what's at https://www.homebrewtalk.com/forum/threads/calculating-bicarbonate-and-carbonate.473408/ which is the only difficult part of brewing water chemistry in a nutshell. If there are parts of the Wikipedia article that puzzle you they would suggest where you need to go to build the required fundamental knowledge base.

With respect to a book on how to do the calculations: I've thought about it and would write it if I thought anyone would read it. Very few people are interested in such things. I put up the linked post on how to do the calculations about 3 years ago. In it I told how to do them but not why they were done in this way. I offered to explain the why's and wherefore's to anyone interested but have had enquiries from very few people.

FWIW, I would certainly be interested in such a book and you seem to be an articulate and knowledgeable enough person to write such a book. I'm always asking why and pursuing precision and accuracy, though that may come from too many years in software. The Water book isn't all that difficult... it does however take time and effort for it all to click again (from high school chemistry).

 

[ajdelange]

I'm always asking why and pursuing precision and accuracy, though that may come from too many years in software.

Wherever it comes from it suggests that you might well have a ball with this stuff. There are lots of nooks and crannies in water chemistry which is why I call it intricate rather than difficult.