Why does pH vary only between 0 to 14. What is the pH of 100 Molar HCL (-2??)?

Question

>>>Water dissociates into H+ and OH- each having conc of 10^-7 but acid adds more H+ ions. Even if the reaction proceeds in reverse direction there cannot be a limit to added H+ ions as they are being added externally.
>>>If h+ ion conc refers only to the ions produced by pure water when acid is mixed then why is it that for solving numericals we use conc of acid with no reference to water. Eg pH of 10^-3 Molar HCl is 3.

Answer 1

The pH scale actually ranges from -infinity to +infinity. There is no reason, in principle, that you cannot have negative pH values or values > 14.

Although it is common to define the pH as the negative of the logarithm of the hydrogen ion activity, it's real definition is in terms of the log of the thermodynamic activity of the hydrogen ion. For dilute solutions, the activity is approximately equal to the activity, but this is not true for concentrated solutions. In order to get to pH's below 0 or above 14, one would need rather concentrated acid or base solutions (e.g., ~>1M H+ for a pH< 0, and ~> 1M OH- for pH >14), so the equivalence between concentration and activity does not hold, and the pH is different from what one would calculate naively by using the concentration. In addition, although we typically assume that strong acids and strong bases are completely dissociated, this is not true at high concentrations, so again, the pH will not be as extreme as one might think simply from a consideration of the solution concentration of an acid or base.

All this having been said, a saturated solution of NaOH (a strong base) has a pH of about 15, and a 12 M HCL solution has a pH < -1, so pH values outside the range of 0-14 do occur.

Answer 2

hfshaw has already addressed the issue of concentration vs activity and has provided some very good links.

I just want to clarify that the pH scale was introduced by Soerensen for expressing the H+ concentration of dilute aqueous solutions.

The ionization of water is H2O <=> H(+) + OH(-)
with an equilibrium constant Kw=[H+][OH-]= 10^-14 at 25 C

so pH=pKw -pOH.= 14-pOH

pH=0 or 14 corresponds to concentration (or activity to be more precise) 1M H+ and 1M OH- respectively, which is already not very dilute.

For more concentrated solutions, the pH will be out of this scale, but then you start having problems with the accuracy of the measurement and also there are no chemical indicators for those regions.

HCl is a gas that is dissolved in water, so you can't get higher concentration than 12M.

As for your last question...
pH measures the activity of H+ in a solution. H+ comes both from water and the acid that you add.
At equilibrium however you must have Kw=[H+][OH-]= 10^-14
so if you add an acid, fewer molecules of water will self-dissociate, in order to meet this requirement.

When you add significant amounts of strong acids, you assume that the contribution of the self-dissociation of water is insignificant and you don't take it into account. However for very dilute solutions you have to consider both sources

For example let's assume you have a solution 10^-8M HCl

Then if you don't consider the self-dissociation of water you would have pH=8 which is impossible for an acid. The correct calculation would be solving Kw=[H+][OH-]= (x+10^-8)*x =10^-14
where x is the amount that comes from the self-dissociation of water and then pH= -log(x+10^-8)

(or solve (10^-8+10^-7-x)* (10^-7-x)=10^-14 if you treat the problem as an established equilibrium for water with initial concentrations of 10^-7M H+ and OH- that is forced to shift by the addition of external H+; then x is the amount of H+ and OH- that reacted to give water during the shift of the equilibrium. This way is closer to what happens in reality, but both are correct and the first one is more straightforward. Now pH=-log(10^-8+10^-7-x))

Answer 3

pH in water is always between 0 to 14 because an effect that is called "water's equalizing effect" which means no mater how much acid you add to the water, it won't produce more H+ if it reaches 1molar concentration. and since pH is -log[H+] so it won't go lower than 0. in other solvents however you can reach higher or lower pHs(for example in ethanol the ph rate is approximately between 0 to 40) that's why then we need a very powerful acidic solution we;ll use alcohol rather than water.