PDA

View Full Version : A ph question for the mathmatically inclined



bsfman
09-08-2011, 06:26 AM
The water in one of my systems has a high ph, but unfortunately when I test it with high ph solution, the resulting color does not match any of the color swatches on my test kit. I am GUESSING by trying to interpolate between colors that the ph is about 8.3, but that's just a guess and probably not very accurate.

So I decided to mix equal parts of the unknown ph water with some rainwater that shows a ph of 6.0, thinking I could test the resulting mix, find the ph, take the difference in ph from the 6.0 water and the mixture, then add that difference back to the ph of the mixture to find the original ph. In other words, I was assuming the mixture will be the arithmetic average of the ph of the two solutions. But then it occurred to me that ph is on a log scale, not an arithmetic scale, so the arithmetic average method may not be correct.

So here's my question: what is the ph of an unknown solution which when mixed in equal parts with a ph 6.0 solution, results in a mixed solution with 8.0 ph? (I figure Urbanfarmer will know how to do this). And if anybody has the formula for this calculation, I would like to see it. (I can plug it into an excel spreadsheet to simplify this problem in the future.)

Thanks to anybody who can help!

urbanfarmer
09-08-2011, 07:55 AM
The water in one of my systems has a high ph, but unfortunately when I test it with high ph solution, the resulting color does not match any of the color swatches on my test kit. I am GUESSING by trying to interpolate between colors that the ph is about 8.3, but that's just a guess and probably not very accurate.

So I decided to mix equal parts of the unknown ph water with some rainwater that shows a ph of 6.0, thinking I could test the resulting mix, find the ph, take the difference in ph from the 6.0 water and the mixture, then add that difference back to the ph of the mixture to find the original ph. In other words, I was assuming the mixture will be the arithmetic average of the ph of the two solutions. But then it occurred to me that ph is on a log scale, not an arithmetic scale, so the arithmetic average method may not be correct.

So here's my question: what is the ph of an unknown solution which when mixed in equal parts with a ph 6.0 solution, results in a mixed solution with 8.0 ph? (I figure Urbanfarmer will know how to do this). And if anybody has the formula for this calculation, I would like to see it. (I can plug it into an excel spreadsheet to simplify this problem in the future.)

Thanks to anybody who can help!
Sure. I have never done this before, but it seems straight forward enough...

pH is the negative log of the hydronium ion concentration. And you want to find the pH of an unknown in the following format assuming equal volumes of the liquid:


(pH1 + pH2) / 2 = pH3

Where pH1 is your rainwater, pH2 is your unknown liquid's pH, and pH3 is the mixture of the 2 in equal parts. You know pH1 and pH3 by using a pH test kit. We convert the pH value to an actual number. You want to determine pH2 from the known values:


(10^-6 + pH2) / 2 = 10^-8


pH2 = -9.8 x 10^-7

EDIT: The next step would be to take the value for pH2 and take the negative log (base 10) of it: -log(pH2)

Basically, if you get a negative number pH3 is not correct (some other chemical interactions likely occurred in the mixture prior to the reading or due to the chemicals used to get a reading OR some or all of the readings are wrong). We should get a pH3 equal to something CLOSE TO ph1 because it is such a large quantity of hydronium ions in comparison to the other quantity (since we know it's going to be somewhere above 7 or even 8).

It may be easier to see this conceptually if we put the magnitudes of the quantities in easier perspective:


(100 + pH2) / 2 = 1

As you can see, pH2 would have to be a negative value of hydronium ion concentration, which unless we're talking about anti-matter or antiprotons (which we're not), this is impossible.

The carbonic acid and a poor quality test kit are likely the culprits here or some other error introduced into the testing process. I would at a minimum get a different source of water like distilled bottled water, test it with the pH kit, and try to use that formula again.

WARNING! NO MATH BELOW...

PERSONALLY, the pH test kits from API are absolutely horrible in my experience. I have found using more than 1 testing method will often yield better results or at least tell you if one of the test kits or devices you have is wrong.

I have gone through 3 API pH test kits. For some reason, they never give a good reading. The regular pH test vs. the high pH test always give different results from the same kit!!! Not to mention both tests give readings that don't concur with 2 other methods, another chemical test kit and a digital pH meter.

Madmax478
09-08-2011, 03:51 PM
WARNING! NO MATH BELOW...

PERSONALLY, the pH test kits from API are absolutely horrible in my experience. I have found using more than 1 testing method will often yield better results or at least tell you if one of the test kits or devices you have is wrong.

I have gone through 3 API pH test kits. For some reason, they never give a good reading. The regular pH test vs. the high pH test always give different results from the same kit!!! Not to mention both tests give readings that don't concur with 2 other methods, another chemical test kit and a digital pH meter.

So what method of testing PH do you find that is the most accurate?

bsfman
09-08-2011, 04:15 PM
Thanks, Urban. Believe it or not, I followed the algebra, but plugging in some realistic numbers has yielded some unrealistic results. Not sure that equation adequately explains the results. (It's probably because I am incorrectly translating the equation into Excel though, or not interpreting the answer correctly). What result do you get if you plug 6.0 into pH1 and 9.0 into pH2? Heres what I'm coming up with:
pH1 = 0.000001
pH2 = 0.000000001
pH1+pH2 = 0.000001001
(pH1+pH2)/2= 0.0000005005000
(and here's where I am probably screwing up) I'm reading 0.0000005005000
as 5.0 times 10^-7 (rounding to the significant digit), which, if I understand correctly would be expressed as a pH of 7.5

Am I doing this correctly? 7.5 is basically the arithmetic average of 6 and 9.

urbanfarmer
09-09-2011, 06:22 AM
Thanks, Urban. Believe it or not, I followed the algebra, but plugging in some realistic numbers has yielded some unrealistic results. Not sure that equation adequately explains the results. (It's probably because I am incorrectly translating the equation into Excel though, or not interpreting the answer correctly). What result do you get if you plug 6.0 into pH1 and 9.0 into pH2? Heres what I'm coming up with:
pH1 = 0.000001
pH2 = 0.000000001
pH1+pH2 = 0.000001001
(pH1+pH2)/2= 0.0000005005000
(and here's where I am probably screwing up) I'm reading 0.0000005005000
as 5.0 times 10^-7 (rounding to the significant digit), which, if I understand correctly would be expressed as a pH of 7.5

Am I doing this correctly? 7.5 is basically the arithmetic average of 6 and 9.

Sorry about that bsfman, entirely my fault. I left out the final step because we got an incorrect value and my brain went pffffft

Once you have the value of pH2 you take the negative log of it. In this case:

-log(0.0000005005000) = 6.300595918 or about 6.3

This value is where we'd expect it. It should be higher than 6 (showing a decrease in concentration of hydronium ions) and lower than 9 (showing an increase in concentration of hydronium ions). Since we know that 6 is 1,000x greater than 9 it should be closer to 6 than 9 (in other words LESS than 7.5 the arithmetic mean of the 2).

To have a visual comparison of all the pH values (yes, I made this just for you)...

http://img23.imageshack.us/img23/7323/phgraph.jpg

Now compare just pH 6 to 9...

http://img38.imageshack.us/img38/4466/ph69graph.jpg

Remember, because we're talking log base 10, these numbers represent an exponential change. In other words, for each point of change in pH it's 10x times the quantity of hydronium ions. These graphs should show you when SCALED EQUALLY how insignificant the higher pH values become with respect to the starting pH value since it goes 10x, 100x, 1000x, so on and so forth no matter where you start!

It may be easier to see this conceptually if we put the magnitudes of the quantities in easier perspective (for your example of 6 and 9):

(pH1 + pH2) / 2 = pH3

We'll arbitrarily place a value for pH2 being the 9, a value of 1, which would mean pH1 has to be 1,000 times more or simply 1,000 in this case (this is the same as multiplying both quantities by 10^9 or 1,000,000,000):

(1000 + 1) / 2 = pH3
pH3 = 500.5

This is actually the same number that you got if we divide by 10^9 or 1,000,000,000 or 1 billion:

500.5 / 1,000,000,000 = 0.0000005005000

(and here's where I am probably screwing up) I'm reading 0.0000005005000
So, you are not screwing up, and I believe it's "easier" to see how that math works out in that formula with more "normal" quantities? I hope! ;)

So for instance, if we took the -log(500.5) we get -2.7, but if we divide it by 1 billion or -log(500.5 / 1000000000) we get 6.3 and as you can see from the calculated "pH" values they are TOTALLY different and seemingly UNRELATED if pH is viewed as a "normal" number. The "normal" number is the weird 0.0000001 type values. You can add, subtract, divide, multiply those normally to get the RIGHT hydronium ion concentration, but the pH reflects a log base 10 number. In other words, you can't take pH 6 and 9 and find the mean average between them to be 7.5 expecting a solution of 2 equal parts to yield this pH. As we see, it's 6.3 (AND THIS MAKES PERFECT SENSE).

IF I HAVE COMPLETELY LOST YOU, TELL ME SO. I will find a completely different way to explain this. Ask away!

urbanfarmer
09-09-2011, 06:56 AM
WARNING! NO MATH BELOW...

PERSONALLY, the pH test kits from API are absolutely horrible in my experience. I have found using more than 1 testing method will often yield better results or at least tell you if one of the test kits or devices you have is wrong.

I have gone through 3 API pH test kits. For some reason, they never give a good reading. The regular pH test vs. the high pH test always give different results from the same kit!!! Not to mention both tests give readings that don't concur with 2 other methods, another chemical test kit and a digital pH meter.

So what method of testing PH do you find that is the most accurate?
Get a parchment. Make a prayer asking for the pH of the solution. Sacrifice a goat. Wait until God tells you the Divine Truth of the matter, it should appear on the parchment...

LOL, but no seriously it's a crapshoot unless you spend money for a good pH meter. The best way I can think of is to use a digital pH meter and CALIBRATE it OFTEN. Possibly before each use if your readings are of GREAT importance (like doing research). Why wouldn't you have a better meter if you're doing research you ask? Maybe you're a lowly graduate student like me and you bought the $50 pH meter instead of the $500 pH meter... :lol:

Otherwise, I would use multiple test kits until you are using one you can "trust", but be sure to double check it every so often in case it goes bad. I don't know why I have had so much trouble with the API test kits... I wish they would JUST WORK damnit! A lot of people seem to be happy with them (or they just don't know they're not reading right, ignorance is bliss)...

My ONLY other guess is that there's some chemical in the tap water here that interacts with the test kit... since it's the same tap water all the time and ground water is polluted with different things in different parts of the world...

bsfman
09-10-2011, 06:25 AM
IF I HAVE COMPLETELY LOST YOU, TELL ME SO. I will find a completely different way to explain this. Ask away!


Thanks Urban. I pretty much understood the explanation. I figured there had to be something else beyond your original equation. Your explanation here dovetails with what I've recently read and charts I've seen on pH equilibria curves. Seems like the further away from pH 7.0 a solution gets, a great amount of acid or base is required to effect a small pH change, but closer to pH 7.0, a small amount will effect a great change. Definitely not a linear function! Your charts reflect the same!

Thanks again!

(By the way, I've decided to stopp obsessing about my pH. It is what it is and my fish are healthy and thriving).

urbanfarmer
09-10-2011, 09:23 AM
IF I HAVE COMPLETELY LOST YOU, TELL ME SO. I will find a completely different way to explain this. Ask away!


Thanks Urban. I pretty much understood the explanation. I figured there had to be something else beyond your original equation. Your explanation here dovetails with what I've recently read and charts I've seen on pH equilibria curves. Seems like the further away from pH 7.0 a solution gets, a great amount of acid or base is required to effect a small pH change, but closer to pH 7.0, a small amount will effect a great change. Definitely not a linear function! Your charts reflect the same!

Thanks again!

(By the way, I've decided to stopp obsessing about my pH. It is what it is and my fish are healthy and thriving).
So, I did all that work for nothing!!! :lol: But now that I think about it, that is true. The more acidic you want it the more hydronium ions (or acid) you need to affect a change. It's not centered around 7 though; 7 is the halfway point for both sides (sort of). The more you move away from 14 the more acid it takes (x10 every for point) and conversely it takes more base to move away from 1 (also x10 for every point).

BTW, I'm here in central FL... around when do the black soldier fly stop reproducing and doing their thing? I was worried my bin was done since we had some cool weather here, but today when I was about to pack up the bin I noticed a fly trying to get in. I think I'm going to find time in about 2 weeks to build a BSF bin that works, but I didn't want to do it if the season was just about over... what do you think?

Have you heard of anyone digging a hole in the ground and using that as a BSF bin/pit? For now I have just used it to get rid of meat scraps and I rarely pick out some maggots for the fish. I'm feeling really lazy about the whole thing! :lol:

bsfman
09-10-2011, 05:46 PM
BTW, I'm here in central FL... around when do the black soldier fly stop reproducing and doing their thing? I was worried my bin was done since we had some cool weather here, but today when I was about to pack up the bin I noticed a fly trying to get in. I think I'm going to find time in about 2 weeks to build a BSF bin that works, but I didn't want to do it if the season was just about over... what do you think?

Have you heard of anyone digging a hole in the ground and using that as a BSF bin/pit? For now I have just used it to get rid of meat scraps and I rarely pick out some maggots for the fish. I'm feeling really lazy about the whole thing! :lol:

I doubt they are done for the year yet, UF! They will continue mating so long as the weather is above about 78F. They do even better in the 80-90F range. Here in southwest Florida, I saw outdoor egglaying begin to decline in November. There was sporadic egglaying through December and January. I kept records of my egg harvesting throughout the past year and the reproductive rate really ramped up again beginning in early February. You can easily keep a colony alive through the winter here and your idea about using a hole in the ground is a good one! Keep the colony fed over the winter and they will emerge in the spring to kickstart things for you (and continue to compost your food waste in the interim!)