# PH

For other uses, see ph.

pH is a measure of the activity of hydrogen ions (H+) in a solution and, therefore, its acidity or alkalinity. The pH value is a number without units, usually between 0 and 14, that indicates whether a solution is acidic (pH < 7), neutral (pH = 7), or basic/alkaline (pH > 7).

The concept was introduced by S.P.L. Sørensen in 1909. The p stands for the German Potenz, meaning power or potency, and the H for the hydrogen ion (H+). Sometimes it is referred as Latin pondus hydrogenii.

 Contents

## Definition

The formula for calculating pH is:

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

[H+] denotes 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.

Log10 denotes the base-10 logarithm, and pH therefore defines a logarithmic scale of acidity. For example, a solution with pH=8.2 will have an [H+] activity (concentration) of 10−8.2 M, or about 6.31 × 10−9 M; a solution with an [H+] activity of 4.5 × 10−4 M will have a pH value of −log10(4.5 × 10−4), or about 3.35.

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 value (for example pH 3) indicates increasing strength of acidity, and a higher pH value (for example pH 11) indicates increasing strength of alkalinity.

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. (Note also that pure water, when exposed to the atmosphere, will take in carbon dioxide, some of which reacts with water to form carbonic acid and H+, thereby lowering the pH to about 5.7.)

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

Some common pH values
Substance pH
Acid mine runoff -3.6 - 1.0
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
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 the studying solution. The indicator color varies depending on the pH of the solution. Using indicators, qualitative determinations can be made with universal indicators that have broad color variablity over a wide pH range and quantitative determinations can be made using indicators that have strong color variablitiy over a small pH range. Extremely precise measurements can be made over a wide pH range using indicators that have multiple equilibriums (ie H2I) in conjunction with spectrophotometric methods to determine each of components that make up the color of solution.
• 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

[itex]K_{w} = \left[ \mbox{H}^+ \right] \left[ \mbox{OH}^- \right] = 10^{-14}[itex] (*)

where Kw is the ionization constant of water.

Now, since

[itex]\log_{10}K_{w} = \log_{10} \left[ \mbox{H}^+ \right] + \log_{10} \left[ \mbox{OH}^- \right][itex]

by logarithmic identities, we then have the relationship

[itex]-14 = \log_{10} \left[ \mbox{H}^+ \right] + \log_{10} \left[ \mbox{OH}^- \right][itex] (*)

and thus

[itex]\mbox{pOH} = -\log_{10} \left[ \mbox{OH}^- \right] = 14 + \log_{10} \left[ \mbox{H}^+ \right] = 14 - \mbox{pH}[itex] (*)

(*) Valid exactly for temperature = 298 K (24.85 °C) only, acceptable for most lab calculations.

## 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 (some other Ka values (http://www.chembuddy.com/?left=BATE&right=dissociation_constants))

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:

[itex]1.6\times 10^{-4} = \frac{x^2}{0.1-x}[itex]

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.

## Indicators

Missing image
Hydrangea_macrophylla_-_Hortensia_hydrangea.jpg
The Hydrangea macrophylla blossoms in pink or blue, depending on soil pH. In acid soils the flowers will be blue, in alkaline soils the flowers will be pink [1] (http://hgic.clemson.edu/factsheets/HGIC1067.htm)

An indicator is used to measure the pH of a substance. Common indicators are litmus paper, phenolphthalein, methyl orange, and bromophenol blue

## 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 (http://dx.doi.org/10.1021/es990646v) | Abstract (http://pubs.acs.org/cgi-bin/abstract.cgi/esthag/2000/34/i02/abs/es990646v.html) | Full text (HTML) (http://pubs.acs.org/cgi-bin/article.cgi/esthag/2000/34/i02/html/es990646v.html) | Full text (PDF) (http://pubs.acs.org/cgi-bin/article.cgi/esthag/2000/34/i02/pdf/es990646v.pdf))cs:PH

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