[AL]

Hello,

I am trying to figure out the volume of 0.3M HCl required to change the pH of 1 L of water from 11.5 to 8.0. I have figured out concentrations of H⁺ at pH 8 (10^-8) and at pH 11.5 (3.16x10^-12) but unsure of where to go from here.

I let (1+x)=volume of the solution after X liters of HCl have been added
and 0.3x = moles of H⁺ in the water.
I wanted to use the equation below to solve for x, but I am starting at pH = 11.5 so I do not think it works.

(0.3x)/(1+x) = 10^-8

I greatly appreciate any help on this.

[Borek]

In general there is not enough information to solve this question, as you are not told WHY the solution has pH 11.5 - and that's the crucial thing. Is it because of the strong base? Weak base? Buffer? Each version has a different answer (in the latter cases answer depends not only on concentrations, but also on dissociation constants).

This simplest version is to assume solution contains strong base - and calculate how much acid must be added to lower the pH.

[AL]

The pH is high due to Ca(OH)₂.

Any hints how I can start calculating amount of acid needed, or do I still need more information? I am so frustrated with this problem!

[Borek]

Ca(OH)₂ is a strong base, you can assume it is 100% dissociated.

Calculate how much Ca(OH)₂ is present initially, and how much is present at pH 8.0. Calculate change in amount - rest is a simple stoichiometry.

[AL]

I don't fully understand how calculating change in amount (of OH^-?) will help me find amount of acid needed?

Every mole of Ca(OH)₂ will give 2 moles of OH^- so should I calculate when the number of moles of H⁺ equals the number of moles of OH^- at pH 8 using Ca(OH)₂ + 2HCl  CaCl₂ + 2H₂O..

Thanks for your patience with me!

[Borek]

I don't fully understand how calculating change in amount (of OH^-?) will help me find amount of acid needed?

Stoichiometry - if OH^- disappears, that's because it reacted with H⁺.