My teacher told me that 1 in 553 million water molecules dissociate.
However, since water has a pH of 7, shouldn’t 1 in every 10,000,000 water molecules dissociate?
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13$\begingroup$ You have a concentration of 10e-7 mol/L for pH 7 (at the usual conditions and approximations). How many molecule of water are there in one litre? $\endgroup$– Martin - マーチン ♦Commented Aug 29, 2022 at 21:30
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[. . .] water has a pH of 7, shouldn’t 1 in every 10,000,000 water molecules dissociate?
To answer this question, what does pH really mean?
Taken from Chemistry Libretexts - pH and pOH, pH is defined as follows,
The pH of a solution is therefore defined as shown here where $\ce{[H3O+]}$ is the molar concentration of hydronium ion in the solution: $$\mathrm{pH} = -\log \ce{[H3O+]} \tag{14.2.2}$$ (emphasis mine)
This means at pH $7$, there are $\pu{10^-7 mol}$ of $\ce{H3O+}$ in $\pu{1 l}$ of water.
This means that $\pu{10^-7 mol}$ of water dissociate. But now how many moles are there in $\pu{1 l}$ of water?
There are a total of $\pu{55.49952 moles}$ in $\pu{1 l}$ of water. Therefore $1$ in every $\pu{554995200 molecules}$ of water dissociate to be exact. This is assuming $\pu{0.9998395 g/cm3}$ to be the density of water though.
answered Aug 31, 2022 at 6:22
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$\begingroup$ pH is defined for activity a(H+), not concentration. IUPAC Gold Book ref.. Libretexts used the simplification for education reasons. // Molar amount with 4 valid digits cannot lead to molecule count with 9 valid digits. $\endgroup$– PoutnikCommented Aug 31, 2022 at 6:46
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$\begingroup$ @Poutnik The textbooks are also lazy about units when they do that. It makes more sense to write $$\mathrm{pH} \approx -\log \frac{[\ce{H3O+}]}{\pu{1 M}}\tag{ for dilute solutions}$$ $\endgroup$– Karsten ♦Commented Aug 31, 2022 at 9:21
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$\begingroup$ @Karsten Sure, as arguments of logarithms ( and most of other functions) must be unitless, as activity is, being defined as $\mu = \mu_0 + RT\ln{(a)}$. $\endgroup$– PoutnikCommented Aug 31, 2022 at 9:52