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After using the negative logarithmic value of $\ce{H^+}$ ion concentration, I get a value of pH that results in base. Can you please help me?

Thank you in advance

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  • $\begingroup$ Do you know what is the pH of neutral water (with zero HCl)? $\endgroup$ – Ivan Neretin Oct 9 '17 at 15:42
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Well this is not pretty difficult, let's go !


Because chloride ions don't react with water we have, $$c_0=\ce{[HCl]=[Cl^-]}\tag1$$

Now for hydrogen ions, $$\ce{[H^+]=[HO^-]}\ce{+[Cl^-]}\tag2$$

We all, must, know that $$K_e=\ce{[H^+][HO^-]}\tag3$$

Then we have $$\ce{[H^+]}^2-c_0\ce{[H^+]}-K_e=0\tag4$$

You'll find your pH solving $(4)$.


Now between theory and practice you may not find a big difference...

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When you want to find $\mathrm{pH}$ of acid whose concentration is less than $10^{-6}$ you have to consider water's dissociation as $\ce{H+}$ and $\ce{OH-}$ too. Which is $10^{-7}$ at $\pu{25 ^\circ C}$. So concentration of $\ce{H+}$ into this case is actually, $10^{-6} + 10^{-7}$, giving $1.1 \times 10^{-6}$. Which will give you a $\mathrm{pH}$ of about $6.9$. We usually ignore water's dissociation because it is negligible but in cases like this it becomes necessary to consider it too.

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