Why is pH a negative logarithm?

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Discussion Overview

The discussion revolves around the reasoning behind the use of negative logarithms in the calculation of pH, particularly focusing on the implications of this choice in terms of convenience and representation of hydrogen ion concentration. The scope includes mathematical reasoning and conceptual clarification related to chemistry.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the necessity of using a negative logarithm for pH, seeking a conceptual understanding without a chemistry background.
  • Another participant suggests that the negative logarithm ensures that pH values remain positive, noting that hydrogen ion concentrations are typically less than 1.
  • It is proposed that using negative logarithms is more convenient since most pH values fall between 0 and 14, and this avoids dealing with negative numbers in most cases.
  • Some participants mention that there are scenarios where pH can be negative, particularly in strong acids, and that the choice of units is arbitrary.
  • There is a suggestion that the pH scale could be adjusted by using different bases for logarithms or by adding constants, which would not fundamentally alter chemical principles.

Areas of Agreement / Disagreement

Participants express differing views on whether the use of negative logarithms is a mathematical necessity or merely a matter of convenience. There is no consensus on a definitive explanation for the choice of negative logarithm in pH calculations.

Contextual Notes

Some limitations include the dependence on the definitions of pH and hydrogen ion concentration, as well as the implications of using different logarithmic bases or constants, which remain unresolved in the discussion.

opus
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I'm going over applications of logarithms in my College Algebra class and I'm at a part where it talks about pH scales, and it shows the pH concentration of a substance to be the negative logarithm of hydronium ions.
I want to know why the logarithm is negative, so I googled it and the answers all require Chemistry knowledge (obviously). Most answers that I've seen mention having water in the concentration as well and that has something to do with it.

Considering I don't have the Chemistry knowledge (and why I put this thread here instead of the Chemistry forum), is there a way to understand why we are taking the negative logarithm the measure the quantity of a substance?
 
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Actually I think I got it. After plugging some random numbers in, it seems the purpose is the have the pH be positive at the end, although I'm not sure why.
What was tripping me up was the fact that the hydrogen ions were always less than 1, but I suppose that's because it's the concentration of them, not how many there actually are. And since this number will have a negative exponent added to a number between 1 and 9, the result will be negative, which then gets negated again to be positive. Is this the case?
 
It is just more convenient as most numbers are between 0 and 14. You save a sign most of the time.
There are acids strong enough to create a negative pH. There is nothing special about 1mole/l, as both mole and liters are arbitrary units. Water has about 55 mole per liter, once you have more than 0.02 H3O+ molecule per water molecule the pH gets negative. From a modern point of view the fraction of molecules which are H3O+ would be a more natural choice.
 
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Ok great thank you. So it's not really a mathematical necessity. It's just something that is done for convenience?
 
You could replace the pH with its negative everywhere without consequences as long as you keep it consistent. You can also add a constant to it. You can also use base e, 2 or whatever you want. This scales the values but it still doesn’t change chemistry.
 
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Understood! Thank you.
 

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