Engineering
pH conversion and the logarithm of mean estimated hydrogen concentration
Compare arithmetic mean pH with the pH-scale value of a mean concentration under a dilute-solution approximation.
Two different summaries of logarithmic measurements
pH is defined from hydrogen-ion activity. Approximating activity with concentration gives pH≈-LOG10([H+]) when concentration is expressed relative to 1 mol/L.
For the two readings 4 and 6, the arithmetic mean pH is 5. The negative log of mean estimated concentration is 4.2967. They summarize different quantities; neither is universally the correct mean.
| Water / Lab Calculation | Formula | Result |
|---|---|---|
| pH from [H+] = 0.0001 M | =-LOG10(0.0001) | 4.00 (Acidic) |
| pOH at 25°C (Kw = 10^-14) | =14 - pH | 10.00 |
| Arithmetic mean pH | =AVERAGE(4,6) | 5.00 |
| Negative log of mean estimated concentration | =-LOG10(AVERAGE(10^(-B2:B3))) | 4.2967 |
Transform, average, then return to the pH scale
Array exponentiation 10 ^ (-B2:B3) converts every pH reading to [H+] molarity before averaging.
=ROUND(-LOG10(AVERAGE(10 ^ (-B2:B3))), 4)Convert [H+] molar concentration (mol/L) to pH
Negates base-10 logarithm LOG10(A2).
=ROUND(-LOG10(A2), 2)Inputs and interpretation
pH is defined using hydrogen-ion activity; concentration is an approximation for suitable dilute solutions. The transformed mean below is a descriptive statistic chosen for this example, not the universal correct average and not a general mixture-pH calculation. Mixing requires chemical equilibria, buffering and volume information. pH+pOH equals pKw, approximately 14 at 25°C under the stated aqueous approximation, not at every temperature.
Try the example
Use the original values or change them to test your understanding.