the pH scale, while often taught that it runs from 1 to 14, or sometimes 0 to 14, can actually assume any value. I imagine there are physical limits but certainly negative pH or pH greater than 14 is possible, just not very common. If the concentration of protons is 10 molar, the pH would be -1.

One comment - pH, at least when measured, is an index of proton activity, not proton concentration. Its one of the few chemical parameters where activity can be measured directly.

A mole is the amount of an element quivalent to its atomic weight expressed in grams.

1 mole of H (atomic weight 1) is 1 gram
1 mole of H₂O (molecular weight 18) is 18 grams.

In pure water, the concentration of hydrogen ions is 0.0000001 moles per litre, or 10^-7 moles per litre. The exponent is taken, inversed and indicates its acidity (neutral in this case.) The lower the pH#, the higher the concentration of Hydrogen atoms. A difference of one pH unit represents a tenfold difference in the concentration of Hydrogen ions.

Buffers

• Solutions above and below pH 1-14 are possible, but are almost never encountered.
• Almost all chemistry in living things takes place between pH 6 and 8.
• Maintainance of pH is done by buffers which either accept or donate H+ ions.
  • A major buffer in the human bloodstream is acid-base pair H₂CO₃-HCO₃^-. When H⁺ enters the bloodstream, HCO₃^- absorbs it, forming H₂O and CO₂.
  • When OH^- is added, it combines with H⁺ to form H₂O; more H₂CO₃ tends to ionize to replace the H⁺ as it is used.

I hope this ends the bickering. =)

(Formerly p_H·, p_H+, P_H, PH) The degree of acidity or alkalinity (basicity or baseness) of a solution. The measurement was introduced as p_H· by Danish biochemist Søren Sørensen in 1909 in Biochemische Zeitschrift, the p representing the German potenz, "power" and the H· representing the hydrogen ion. It is the negative of the common logarithm of the concentration of hydrogen ions (or protons) in moles per litre of solution (pH = -log[H⁺]). For example, the common logarithm of .0000001 (1 × 10^-7) mole of hydrogen ion per litre equals -7, the negative of which is 7. Therefore, 7 is the pH.

The pH of an aqueous solution normally lies between 0 and 14. A pH of 7, the value for pure water, is regarded as neutral. pH values from 7 to 0 indicate increasing acidity and from 7 to 14 indicate increasing alkalinity. A decrease of one unit of pH (an increase in acidity) indicates a tenfold increase in hydrogen ion concentration. An increase of one unit of pH (an increase in alkalinity) indicates a tenfold decrease in hydrogen ion concentration.

Litmus can be used as a pH indicator; it is red in acid solutions and blue in alkaline solutions. A pH meter translates into pH readings the difference in electromotive force between suitable electrodes placed in the solution to be tested.

See also: acid, base, buffer

Stop this qualitative technobabble, it's time for quantitative calculations! pH is mathematically simple, if the activity coefficients are about 1, i.e. assuming an ideal-dilute solution. And yes, pH can be negative or over 14. The 'p' is shorthand for "power of", to denote very small concentrations; pH 2 is ten times diluted from pH 1, and so on. That is, pH is -1 times tenth base logarithm of the ionic activity of hydrogen ions: pH = -log₁₀ a_H⁺.

The ionic activity is the "effective concentration" of the protons, which is different from the stoichiometric concentration ("how much we added") since ions tend to cluster in solutions. This actually requires a fair bit of calculations for pH measurement in concentrated or salt-laden solutions, such as volcanic waters. In dilute solutions, we can assume that the activity is the same as the stoichiometric concentration. (In 0.1 to about 0.01 M we have to calculate the activity; see Debye-Hückel.)

So, we're left with this: pH = -log₁₀ a_H⁺. (The square brackets mean "the concentration of" in this case, in mol/l or moles per litre as always; this is essentially the count of ions per litre.)

Water dissociates even on when nothing else is present, although the extent of ionization is very small. Water dissociation is an equilibrium reaction, so we can measure an equilibrium constant, which is called water dissociation constant K_W.

The reaction: H₂O <-> H⁺ + OH^-
K = (a_H⁺ a_OH^-) / a_H2O

The water is a solvent, so its activity is 1, a_H2O = 1. One way of looking at this is that we could say that the water is of a different phase - it's not aqueous ions like H⁺ and OH^- but liquid - and when a reaction has one reactant in a different phase, this reactant is left out of the function for the position of the equilibrium. The environment in an dilute aqueous solution is completely saturated with water, which that means we can assume that [H₂O] is constant. Dissolving small amounts of substances to water will not affect the volume considerably or change the number of water molecules. Thus, [H₂O] is left out, and the constant is approximated such that activities are assumed to be the same as concentrations:

K_W = [H⁺][OH^-]

It can be measured that the constant has the value K_W = 10^-14 at 298 K (room temperature). This is an actual experimental value, not a definition. An implication is that pH is not a "scale" in the same way centigrade is, for example; it is a dimensionless number based on real physical quantities.

Neutral pure water has a pH of 7, as you will learn in a chemistry class. Here is the calculation:

In pure water, [H⁺] = [OH^-], so
[H⁺][OH^-] = [H⁺]² = K_W
==> [H⁺] = (10^-14)^0.5 = 10^-7
By definition, pH = -log₁₀ 10^-7
==> pH = 7.

What happens to hydrochloric acid in water?

an activity of 1 mol HCl to 1 dm³ water
HCl -> H⁺ + Cl^- (dissociation)
1 mol H⁺ ==> pH = -log 1
pH = 0.

In this case, we ignore the original dissociation of water, because the acid gives ten million times more H⁺ ions than the water does. This assumption is valid for (not too dilute) solutions with only acid and water. Of course, when concentrations of ions from the acid and from the water are closer, i.e. at 10^-7 mol dm^-3 of acid, you have to take the original dissociation into account. As you can see, if we put more than 1 mol of active protons, we get a negative pH. The result is not accurate for concentration, though; using the Debye-Hückel formula gives the result that an activity of 1 mol/l corresponds to 2 mol/l stoichiometric concentration, although Debye-Hückel probably doesn't work at this high a concentration.

When we remove or add hydrogen ions to the solution, the reaction shifts, because (surprise surprise!) the dissociation constant stays constant. (See Le Chatelier's principle.) This way we can understand how the pH can be over 7. When we increase the [OH^-] part in the reaction, the [H⁺] part has to decrease.

So when we put, for instance, NaOH into the solution, it dissociates into OH^-, which in turn decreases the number of hydrogen ions in the water. As in adding H⁺, we can neglect the small amount of OH^- from the water in the calculations and assume that all OH^- comes from the base.

K_W = [H⁺][OH^-]
[H⁺] = K_W/[OH^-]

An example:

2 mol dm^-3 of NaOH
[H⁺] = 10^-14/(2 mol dm^-3)
pH = 14.3

There you see how the pH is not always from 0 to 14. As you may have noticed, a handy shortcut for the pH is to take the logarithm of the whole K_W expression. Because the numerical value of K_W is 10^-14, its tenth-base logarithm is -14.

K_W = [H⁺][OH^-] (-log₁₀ both sides)
14 = -log₁₀ [H⁺] - log₁₀ [OH^-] (There's the pH!)
pH = 14 - log₁₀ [OH^-]

pH is simply fourteen minus the logarithm of the concentration of the strong acid or base. In this case, log 2 is about -0.3, so pH = 14 - (-0.3) = 14.3. (Notice that in this concentrated solutions, this analysis breaks down, because activity no longer the same as the concentration. Use the Debye-Hückel theory in these cases.) If you want to apply this to weak bases, calculate the concentration of hydroxide ions first. In general:

pH = 14 - pOH

Not cut-n-paste. No source would have come up with this level of clarity and possibly some highly creative errors.

"PH" or more commonly ".ph" is also the two letter country code for the Philippines.