# Is pH linear or exponential from 7.0? **URL:** \ **Category:** Factual Questions\ **Created:** [August 10, 2003, 3:28am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137 "2003-08-10T03:28:40Z")\ **Posts on this page:** 11\ **Page:** 1
**Author:** ![carver42](https://avatars.discourse-cdn.com/v4/letter/c/bc8723/32.png) [@carver42](https://boards.straightdope.com/u/carver42)\ **Post date:** [August 10, 2003, 3:28am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/1 "2003-08-10T03:28:40Z")
Is the difference between 2 pH values linear or exponential? ie. Is the difference between a pH 6 and 7 the same as the difference between pH 2 and 3? ---
**Author:** ![wolfstu](https://avatars.discourse-cdn.com/v4/letter/w/d6d6ee/32.png) [@wolfstu](https://boards.straightdope.com/u/wolfstu)\ **Post date:** [August 10, 2003, 3:35am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/2 "2003-08-10T03:35:30Z")
It’s logarithmic. pH 7 is ten times the propensity of Hydrogen of pH 6. Each integer is ten time higher than the last. Cite: [http://www.ec.gc.ca/acidrain/kids.html](http://www.ec.gc.ca/acidrain/kids.html) ---
**Author:** ![wolfstu](https://avatars.discourse-cdn.com/v4/letter/w/d6d6ee/32.png) [@wolfstu](https://boards.straightdope.com/u/wolfstu)\ **Post date:** [August 10, 2003, 3:37am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/3 "2003-08-10T03:37:06Z")
> [@](#): > > \*Originally posted by wolfstu \* > \*\* > Each integer is ten time higher than the last. > \*\* Ugh. “Each integer value of pH represents a value ten times higher than the last” So 7.0 is ten times 6.0 ---
**Author:** ![Squink](https://avatars.discourse-cdn.com/v4/letter/s/b5e925/32.png) [@Squink](https://boards.straightdope.com/u/Squink)\ **Post date:** [August 10, 2003, 3:43am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/4 "2003-08-10T03:43:12Z")
pH = -Log[H[sup]+[/sup]] ---
**Author:** ![Speaker\_for\_the\_Dead](https://avatars.discourse-cdn.com/v4/letter/s/c77e96/32.png) [@Speaker\_for\_the\_Dead](https://boards.straightdope.com/u/Speaker_for_the_Dead)\ **Post date:** [August 10, 2003, 3:47am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/5 "2003-08-10T03:47:13Z")
For the layperson (like me), that means the pH is equal to the negative log of the concentration of hydrogen atoms in a given solution. ---
**Author:** ![carver42](https://avatars.discourse-cdn.com/v4/letter/c/bc8723/32.png) [@carver42](https://boards.straightdope.com/u/carver42)\ **Post date:** [August 10, 2003, 4:18am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/6 "2003-08-10T04:18:25Z")
OK. Thanks, I have a pH meter and I’m trying to get the hot tub balanced and it seemed that it was not linear. ---
**Author:** ![Jon\_the\_Geek](https://avatars.discourse-cdn.com/v4/letter/j/bbce88/32.png) [@Jon\_the\_Geek](https://boards.straightdope.com/u/Jon_the_Geek)\ **Post date:** [August 10, 2003, 5:30am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/7 "2003-08-10T05:30:36Z")
> [@](#): > > \*Originally posted by Speaker for the Dead \* > For the layperson (like me), that means the pH is equal to the negative log of the concentration of **hydrogen atoms** in a given solution. (bolding mine) [nitpick]That should be hydrogen ions (or usually hydronium ions, depending on which definition of pH you’re using–technically, if I’m not mistaken, the “true” definition used by hard-core physical chemists is something like “the negative log of the ionic strength of hydrogen” or something like that, but my p-chem is WAY too rusty to remember how to word that correctly), not hydrogen atoms.[/nitpick] Sorry, this _is_ the SDMB. We can’t let you use such a sloppy definition 🙂 ---
**Author:** ![Dogface](https://avatars.discourse-cdn.com/v4/letter/d/9d8465/32.png) [@Dogface](https://boards.straightdope.com/u/Dogface)\ **Post date:** [August 10, 2003, 6:02am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/8 "2003-08-10T06:02:34Z")
Oh, pH is even messier than that. While it technically has something to do with hydronium, it’s actually a matter of the free electrons available in the solution, usually an inverse of the hydronium, but when one starts to throw Lewis acids into the matter, things get wacky. ---
**Author:** ![Bob55](https://avatars.discourse-cdn.com/v4/letter/b/e9c0ed/32.png) [@Bob55](https://boards.straightdope.com/u/Bob55)\ **Post date:** [August 10, 2003, 6:47am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/9 "2003-08-10T06:47:26Z")
> [@](#): > > \*Originally posted by jharmon \* > \*\*(bolding mine) > > [nitpick]That should be hydrogen ions (or usually hydronium ions, depending on which definition of pH you’re using–technically, if I’m not mistaken, the “true” definition used by hard-core physical chemists is something like “the negative log of the ionic strength of hydrogen” or something like that, but my p-chem is WAY too rusty to remember how to word that correctly), not hydrogen atoms.[/nitpick] \*\* I think this is called the ‘activity’ if I recall analytical chem correctly. There are huge tables which are needed to accurately calculate pH (based on the ions), but like you said what we use now is generally a good approximation. Carver, keep in mind that a pH electrode is temerature-dependent (but I’m not sure how much an effect his has), so you should probably test your water both hot and cold. ---
**Author:** ![Jon\_the\_Geek](https://avatars.discourse-cdn.com/v4/letter/j/bbce88/32.png) [@Jon\_the\_Geek](https://boards.straightdope.com/u/Jon_the_Geek)\ **Post date:** [August 10, 2003, 7:05am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/10 "2003-08-10T07:05:56Z")
Yes, activity is precisely the word I was looking for. I actually was working on an animation on pH a few months back for a general chemistry text, and had to force myself to stick to the textbook and not go off on a tangent (so I never quite got to the point of re-learning the complex definition, I just reminded myself that the complex definition existed). I almost put a couple questions in there about negative pH’s and pH’s greater than 14, but found that it really really depended on how you defined pH, so I think I ended up avoiding it completely. ---
**Author:** ![chaoticbear](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@chaoticbear](https://boards.straightdope.com/u/chaoticbear)\ **Post date:** [August 10, 2003, 10:19am UTC](https://boards.straightdope.com/t/is-ph-linear-or-exponential-from-7-0/194137/11 "2003-08-10T10:19:48Z")
even with the lewis acids, the definition -log(H\_3O+) would work… for example, NH\_4+ + H\_20 -\> NH\_3 + H\_3O (i can’t make an equillibrium sign…)