pH

pH is a measure of the acidity or alkalinity of a solution. Aqueous solutions at 25°C with a pH less than seven are considered acidic, while those with a pH greater than seven are considered basic (alkaline). When a pH level is 7.0, it is defined as ‘neutral’ at 25°C because at this pH the concentration of H₃O⁺ equals the concentration of OH^? in pure water. pH is formally dependent upon the activity of hydronium ions (H₃O⁺), but for very dilute solutions, the molarity of H₃O⁺ may be used as a substitute with little loss of accuracy. (H⁺ is often used as a synonym for H₃O⁺.) Because pH is dependent on ionic activity, a property which cannot be measured easily or fully predicted theoretically, it is difficult to determine an accurate value for the pH of a solution. The pH reading of a solution is usually obtained by comparing unknown solutions to those of known pH, and there are several ways to do so.

The concept of pH was first introduced by Danish chemist S. P. L. Sørensen at the Carlsberg Laboratory in 1909. The name, pH, has claimed to have come from any of several sources including: pondus hydrogenii, potentia hydrogenii (Latin), potentiel hydrogène (French), and potential of hydrogen (English)

Definition

pH (per hydron or per hydrogen, also power of the hydrogen) is defined operationally as follows. For a solution X, first measure the electromotive force E_X of the galvanic cell

where

F is the Faraday constant;

R is the molar gas constant;

T is the thermodynamic temperature.

Defined this way, pH is a dimensionless quantity. Values pH(S) for a range of standard solutions S, along with further details, are given in the relevant IUPAC recommendation^.

pH has no fundamental meaning as a unit; its official definition is a practical one. However in the restricted range of dilute aqueous solutions having an amount-of-dissolved-substance concentrations less than 0.1 mol/L, and being neither strongly alkaline nor strongly acidic (2 < pH < 12), the definition is such that

where [H⁺] denotes the amount-of-substance concentration of hydrogen ion H⁺ and ?₁ denotes the activity coefficient of a typical univalent electrolyte in the solution.

Explanation

In simpler terms, the number arises from a measure of the activity of hydrogen ions (or their equivalent) in the solution. The pH scale is an inverse logarithmic representation of hydrogen proton (H⁺) concentration. Unlike linear scales which have a constant relations between the item being measured (H⁺ concentration in this case) and the value reported, each individual pH unit is a factor of 10 different than the next higher or lower unit. For example, a change in pH from 2 to 3 represents a 10-fold decrease in H⁺ concentration, and a shift from 2 to 4 represents a one-hundred (10 × 10)-fold decrease in H⁺ concentration. The formula for calculating pH is:

Where ?_H⁺ denotes the activity of H⁺ ions, and is dimensionless. In solutions containing other ions, activity and concentration will not generally be the same. Activity is a measure of the effective concentration of hydrogen ions, rather than the actual concentration; it includes the fact that other ions surrounding hydrogen ions will shield them and affect their ability to participate in chemical reactions. These other ions change the effective amount of hydrogen ion concentration in any process that involves H⁺.

In dilute solutions (such as tap water), activity is approximately equal to the numeric value of the concentration of the H⁺ ion, denoted as [H⁺] (or more accurately written, [H₃O⁺]), measured in moles per litre (also known as molarity). Therefore, it is often convenient to define pH as:

For both definitions, log₁₀ denotes the base-10 logarithm, therefore pH defines a logarithmic scale of acidity. For example, if one makes a lemonade with a H⁺ concentration of 0.0050 moles per litre, its pH would be:

A solution of pH = 8.2 will have an [H⁺] concentration of 10^?8.2 mol/L, or about 6.31 × 10^?9 mol/L. Thus, its hydrogen activity ?_H⁺ is around 6.31 × 10^?9. A solution with an [H⁺] concentration of 4.5 × 10^?4 mol/L will have a pH value of 3.35.

In solution at 25 °C, a pH of 7 indicates neutrality (i.e. the pH of pure water) because water naturally dissociates into H⁺ and OH^? ions with equal concentrations of 1×10^?7 mol/L. 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 basicity. Note, however, 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.

Neutral pH at 25 °C is not exactly 7. pH is an experimental value, so it has an associated error. Since the dissociation constant of water is (1.011 ± 0.005) × 10^?14, pH of water at 25 °C would be 6.998 ± 0.001. The value is consistent, however, with neutral pH being 7.00 to two significant figures, which is near enough for most people to assume that it is exactly 7. The pH of water gets smaller with higher temperatures. For example, at 50 °C, pH of water is 6.55 ± 0.01. This means that a diluted solution is neutral at 50 °C when its pH is around 6.55 and that a pH of 7.00 is basic.

Most substances have a pH in the range 0 to 14, although extremely acidic or extremely basic substances may have pH less than 0 or greater than 14. An example is acid mine runoff, with a pH = –3.6. Note that this does not translate to a molar concentration of 3981 M; such high activity values are the result of the extremely high value of the activity coefficient while concentrations are within a “reasonable” range. E.g. a 7.622 molal H₂SO₄ solution has a pH = -3.13, hydrogen activity ?_H⁺ around 1350 and activity coefficient ?_H⁺ = 165.4 when using the MacInnes convention for scaling Pitzer single ion activity coefficient .

Arbitrarily, the pH is ? log₁₀([H ⁺ ]). Therefore,

pH = ? log₁₀[H ⁺ ]

or, by substitution,

.

The “pH” of any other substance may also be found (e.g. the potential of silver ions, or pAg⁺) by deriving a similar equation using the same process. These other equations for potentials will not be the same, however, as the number of moles of electrons transferred (n) will differ for the different reactions.

Substance	pH
Hydrochloric acid, 10M	-1.0
Lead-acid battery	0.5
Gastric acid	1.5 – 2.0
Lemon juice	2.4
Cola	2.5
Vinegar	2.9
Orange or apple juice	3.5
Tomato Juice	4.0
Beer	4.5
Acid Rain	<5.0
Coffee	5.0
Tea or healthy skin	5.5
Urine	6.0
Milk	6.5
Pure Water	7.0
Healthy human saliva	6.5 – 7.4
Blood	7.34 – 7.45
Seawater	7.7 – 8.3
Hand soap	9.0 – 10.0
Household ammonia	11.5
Bleach	12.5
Household lye	13.5

Measurement

pH can be measured:

• by addition of a pH indicator into the solution under study. 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 variability over a wide pH range and quantitative determinations can be made using indicators that have strong color variability over a small pH range. Precise measurements can be made over a wide pH range using indicators that have multiple equilibriums in conjunction with spectrophotometric methods to determine the relative abundance of each pH-dependent component that make up the color of solution, or
• by using a pH meter together with pH-selective electrodes (pH glass electrode, hydrogen electrode, quinhydrone electrode, ion sensitive field effect transistor and others).
• by using pH paper, indicator paper that turns color corresponding to a pH on a color key. pH paper is usually small strips of paper (or a continuous tape that can be torn) that has been soaked in an indicator solution, and is used for approximations.

The lowest and highest ends of the pH scale do not oxidize. The middle of the scale is what oxidizes, such as water and blood.

As the pH scale is logarithmic, it does not start at zero. Thus the most acidic of liquids encountered can have a pH as low as ?5. The most alkaline typically has pH of 14. Measurement of extremely low pH values has various complications. Calibration of the electrode in such cases can be done with standard solutions of concentrated sulphuric acid whose pH values can be calculated with the Pitzer model.

As an example of home application, the measurement of pH value can be used to quantify the amount of acid in a swimming pool.