Why is concentration used as an input for pH calculations?

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SUMMARY

The discussion clarifies that concentration, measured in moles per volume, is used in pH calculations due to its relationship with the activity of hydrogen ions. The formula for pH is defined as pH = -log(a), where 'a' represents the activity of hydrogen ions, which is a dimensionless quantity. This distinction allows for the use of concentration in logarithmic functions without violating the requirement for unitless inputs in mathematical operations.

PREREQUISITES
  • Understanding of logarithmic functions, specifically log(x).
  • Basic knowledge of pH, pOH, and pKa concepts.
  • Familiarity with the concept of activity in chemistry.
  • Knowledge of units of concentration, specifically moles per volume.
NEXT STEPS
  • Research the concept of activity coefficients in chemistry.
  • Learn about the derivation of the pH formula and its implications.
  • Explore the relationship between concentration and activity in aqueous solutions.
  • Study the applications of logarithmic functions in chemical calculations.
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Chemistry students, educators, and professionals involved in analytical chemistry or anyone interested in understanding the mathematical foundations of pH calculations.

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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