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# PH

For other uses, see ph.

pH (potential (of) hydrogen) is a measure of the activity of hydrogen ions (H+) in a solution and, therefore, its acidity or alkalinity. The concept was introduced by S.P.L. Sørensen in 1909. The p stands for the German potenz, meaning power or concentration, and the H for the hydrogen ion (H+). Sometimes it is referred as Latin pondus hydrogenii.

The "pH" value is an approximate number usually between 0 and 14 that indicates whether a solution is acidic (pH < 7), neutral (pH = 7), or basic/alkaline (pH > 7).

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## Definition

The formula for calculating pH is:

$\mbox{pH} = -\log_{10} \left[ \mbox{H}^+ \right]$

[H+] indicates the activity of H+ ions (also written [H3O+], the equivalent hydronium ions), measured in moles per litre (also known as molarity). In dilute solutions (like river or tap water) the activity is approximately equal to the concentration of the H+ ion.

In aqueous solution at standard temperature and pressure, a pH of 7 indicates neutrality (i.e. pure water) because water naturally dissociates into H+ and OH ions with equal concentrations of 1×10−7 M. A lower pH number (for example pH 3) indicates increasing strength of acidity, and a higher pH number (for example pH 11) indicates increasing strength of alkalinity.

Most substances have a pH in the range 0 to 14, although extremely acidic or basic substances may have pH < 0, or pH > 14.

In nonaqueous solutions or non-STP conditions, the pH of neutrality may not be 7. Instead it is related to the dissociation constant for the specific solvent used.

Some common pH values
Substance pH
Battery acid <1.0
Gastric acid 2.0
Lemon juice 2.4
Cola 2.5
Vinegar 2.9
Orange or apple juice 3.5
Beer 4.5
Coffee 5.0
Tea 5.5
Acid rain < 5.6
Human Saliva in Cancer patients 4.5-5.7
Milk 6.5
Pure water 7.0
Human Saliva 6.5-7.4
Blood 7.34 - 7.45
Sea water 8.0
Hand soap 9.0 - 10.0
Household ammonia 11.5
Bleach 12.5
Household lye 13.5

## Measuring

pH can be measured:

• by addition of a pH indicator into studying solution. The indicator changes color depending on the pH of the solution. There are different indicators: short range (for precision determination) and universal (qualitative estimation of solution's acidity)
• by using a pH meter together with pH-selective electrodes (pH glass electrode, hydrogen electrode, quinhydrone electrode and other).

## pOH

There is also pOH, in a sense the opposite of pH, which measures the concentration of OH ions. Since water self ionizes, and notating [OH-] as the concentration of hydroxide ions, we have

Kw = [H+][OH]=10−14 (*)

where Kw is the ionization constant of water.

Now, since

log Kw = log [H+] + log [OH]

by logarithmic identities, we then have the relationship

−14 = log [H+] + log [OH] (*)

and thus

pOH = −log [OH] = 14 + log [H+] = 14 − pH (*)

(*) Valid for temperature = 298 K (24.85 °C) only.

## Calculation of pH for weak and strong acids

Values of pH for weak and strong acids can be approximated using certain assumptions.

Under the Brønsted-Lowry theory, stronger or weaker acids are a relative concept. But here we define a strong acid as a species which is a much stronger acid than the hydronium (H3O+) ion. In that case the dissociation reaction (strictly HX+H2O↔H3O++X but simplified as HX↔H++X) goes to completion, i.e. no unreacted acid remains in solution. Dissolving the strong acid HCl in water can therefore be expressed:

HCl(aq) → H+ + Cl

This means that in a 0.01 M solution of HCl it is approximated that there is a concentration of 0.01 M dissolved hydrogen ions. From above, the pH is: pH = −log10 [H+]:

pH = −log(0.01)

which equals 2.

For weak acids, the dissociation reaction does not go to completion. An equilibrium is reached between the hydrogen ions and the conjugate base. The following shows the equilibrium reaction between methanoic acid and its ions:

HCOOH(aq) ↔ H+ + HCOO

It is necessary to know the value of the equilibrium constant of the reaction for each acid in order to calculate its pH. In the context of pH, this is termed the acidity constant of the acid but is worked out in the same way (see chemical equilibrium):

Ka = [hydrogen ions][acid ions] / [acid]

For HCOOH, Ka = 1.6 × 10−4.

When calculating the pH of a weak acid, it is usually assumed that the water does not provide any hydrogen ions. This simplifies the calculation, and the concentration provided by water, 1×10−7 mol, is usually insignificant.

With a 0.1 mol solution of methanoic acid (HCOOH), the acidity constant is equal to:

Ka = [H+][HCOO] / [HCOOH]

Given that an unknown amount of the acid has dissociated, [HCOOH] will be reduced by this amount, while [H+] and [HCOO] will each be increased by this amount. Therefore, [HCOOH] may be replaced by 0.1 −&; x, and [H+] and [HCOO] may each be replaced by x, giving us the following equation:

$1.6\times 10^{-4} = \frac{x^2}{0.1-x}$

Solving this for x yields 3.9×10−3, which is the concentration of hydrogen ions after dissociation. Therefore the pH is −log(3.9×10−3), or about 2.4.

## Neutralization

Neutralization can be summed up by the equation:

H+ + OH ⇒ H2O

(acid + base ⇒ water)

A simple, common example with HCl and NaOH yielding salt water:

HCl + NaOH ⇒ H+ + Cl + Na+ + OH ⇒ H2O + NaCl

## References

• D. K. Nordstrom, C. N. Alpers, C. J. Ptacek, D. W. Blowes (2000). Negative pH and Extremely Acidic Mine Waters from Iron Mountain, California. Environmental Science & Technology 34 (2), 254-258. (Available online: DOI | Abstract | Full text (HTML) | Full text (PDF))