# What is the pH of HCl solution at $10^{-8}$M? [duplicate]

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?

• Do you know what is the pH of neutral water (with zero HCl)? – Ivan Neretin Oct 9 '17 at 15:42

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...

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.