Why is concentration used as an input for pH calculations?

AI Thread Summary
The discussion centers on the use of inputs with units, such as concentration in moles per volume, in logarithmic functions like ln(x) and log(x) for calculating pH, pOH, and pKa. It raises the question of why these unit-based inputs are acceptable when logarithmic functions typically require unitless inputs. The response clarifies that pH is defined as pH = -log(a), where 'a' represents the activity of hydrogen ions, which is a dimensionless quantity. This distinction explains why concentration can be used in these calculations, as it is ultimately related to the dimensionless activity of ions rather than the units of concentration itself.
zyj
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This is something I've been wondering for a while, but I thought that the inputs for things like ln(x), e(x), sin(x), etc. had to be unitless. Then how come concentration, which has units of moles per volume (or I guess just per volume, since moles are just a number? I've never been sure about that...) is used as an input for log(x) to find pH, pOH, pKa, etc.?
 
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I've never thought about that myself.

I would suspect it is because formula pH is defined as, pH=-log(a) where a is the activity of the hydrogen ion and activity is dimensionless.
 

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