pH

Field of Study: Organic Chemistry, Inorganic Chemistry, Biochemistry

ABSTRACT

The acidity and basicity of aqueous solutions are dependent on the balance of hydronium (H₃O⁺) and hydroxide (OH⁻) ions in the solution. Molar concentrations of both ions are typically low, making calculations unwieldy. The pH scale, based on the logarithmic values of the concentrations, greatly facilitates such calculations.

The Nature of Water

In order to understand the pH scale, one must first understand the nature and properties of water. Water is the most common known solvent. It is unique in terms of its molecular structure, physical and chemical properties, and interaction with other materials.

All atoms consist of a central nucleus containing positively charged protons and neutral neutrons, surrounded by negatively charged electrons. Electrons can be thought of as existing in specific regions called orbitals, which in turn are contained within layers known as electron shells. In neutral atoms and molecules, the protons and electrons are equal in number; when an atom or molecule has an unequal number of electrons and protons, it is known as an ion.

The water molecule consists of two hydrogen atoms bonded to an oxygen atom. As an element in the second period of group 16 of the periodic table of the elements, the oxygen atom has six electrons in its outermost, or valence, shell. When the oxygen atom bonds to the two hydrogen atoms, it shares one electron from each, giving the oxygen atom a filled valence shell. The one 2s and three 2p orbitals that contain those eight electrons, arranged in four pairs, hybridize to form four equivalent sp³ orbitals oriented to the four apexes of a tetrahedron. This orbital arrangement has the effect of minimizing the force of repulsion experienced between the electron pairs. Two of the sp³ orbitals form the bonds to the hydrogen atoms; the other two are not involved in bonds, and each contains a lone pair of electrons (a pair of electrons not shared with a hydrogen atom). This gives the water molecule a high degree of polarity, as the lone pairs create a region of high negative charge, while the placement of the hydrogen electrons within the oxygen-hydrogen bonds exposes the positive charge of the hydrogen nuclei. These areas of positive and negative charge cause water molecules to act somewhat like magnets and stick to each other, resulting in a cohesion between molecules that gives water an unexpectedly high boiling point relative to its molecular weight.

In liquid water, the concentrations of acidic hydronium ions (H₃O⁺) and basic hydroxide ions (OH⁻) are exactly equal; as such, liquid water is neither acidic nor alkaline but neutral. Experimental analysis has determined that the concentration of both types of ions in water is 10⁻⁷ moles per liter, or molars (M). (A mole is the amount of any pure substance that contains as many elementary units—approximately 6.022 × 10²³—as there are atoms in twelve grams of the isotope carbon-12.) The equilibrium constant for the reaction is defined as

K_eq = [H₃O⁺][OH⁻] = (10⁻⁷)(10⁻⁷) = 10⁻¹⁴

where [x] is equal to the concentration of x. When the concentration of one ion increases, the concentration of the other ion must decrease by a corresponding amount. This principle is the foundation of the pH scale.

The pH Scale

The term "pH" can be defined as a numerical value that represents the acidity or basicity of a solution, with 0 being the most acidic, 14 being the most basic, and 7 being neutral. The pH of an aqueous solution is determined using the equation

pH = −log[H₃O⁺]

The notation [H⁺] is often used instead of [H₃O⁺], though both forms are correct. The pH scale is a logarithmic scale, meaning that every increase of one unit of pH corresponds to a tenfold change in the concentration of hydronium ions. The use of logarithmic values greatly simplifies calculations of both acid and base concentrations.

The logarithm of a value, or "log" for short, is the exponent to which a base number, in this case 10, must be raised to produce that value. For example, the log of 10³ is 3, and the log of 10⁻² is −2. The ease of using logs is due to what are known as the power rules of mathematics. When two numbers are multiplied, their respective exponents, or powers, are added together. For example, 100 multiplied by 1,000 is 100,000. In scientific notation, this is written as follows:

10² × 10³ = 10⁵

It is easy to see from this that the exponent values 2 and 3 can be added to equal 5. Similarly, to divide two values expressed with exponents, one can subtract one exponent from the other.

In the case of water, the logarithmic expression of the equation for the equilibrium constant of the process is

log(10⁻¹⁴) = log[(10⁻⁷)(10⁻⁷)] = (−7) + (−7)

Thus,

−log(10⁻¹⁴) = −log(10⁻⁷)(10⁻⁷) = −[(−7) + (−7)]

In modern chemical notation, the p of pH represents the cologarithm, or colog, of the value that follows, which is equal to the logarithm of the reciprocal of the value—or, more simply, the negative logarithm (−log). Therefore,

pK_eq = 14 = p[H₃O⁺] + p[OH⁻] = 7 + 7

The term "pOH" is sometimes used to refer to the concentration of hydroxide ions in the solution. The pH and the pOH must always add up to the neutral value of 14. According to Le Chatelier’s principle, named for the French chemist Henry Louis Le Châtelier (1850–1936), adding any material that changes the concentration of either the hydronium or hydroxide ion causes the other concentration to shift to compensate and restore the equilibrium condition. Thus, adding an acidic material such as hydrogen chloride (HCl) to pure water increases the [H³O⁺] and forces the [OH⁻] to decrease by the same amount to maintain the equilibrium. Similarly, adding a base such as sodium hydroxide (NaOH) increases the [OH⁻] and causes the [H₃O⁺] to decrease by the same amount.

The pH scale is used to indicate an aqueous solution’s acidity or basicity, with acidic solutions falling between 0 and 7 on the scale and basic solutions between 7 and 14. Common acidic substances include vinegar and lemon juice, while well-known basic substances include baking soda and ammonia. Pure water is generally considered to have a neutral pH of 7, but this can change when other substances are added to the water, as in the case of the environmental phenomenon known as acid rain.

pH in Biological Systems

Maintaining a constant pH is particularly important in biological systems, as changes in pH can have harmful effects on living things. Enzymes, like many other chemical systems, can only function within a specific pH range, outside of which they become degraded and lose their enzyme functionality. Very minor changes in blood pH affect the solubility of many of the compounds that are transported in the blood, as well as the function of receptor sites on any cells that come in contact with it. Materials such as uric acid that are normally dissolved in blood may instead precipitate as solids in the blood vessels and sinovial fluids of the joints, causing a variety of often painful and even life-threatening conditions. Biological systems prevent harmful changes in pH through the use of buffer solutions, which are mixtures of acids and bases that have the ability to absorb limited quantities of additional acids or bases without changing their pH.

PRINCIPAL TERMS

• acid: a compound that can relinquish one or more hydrogen ions (Brønsted-Lowry acid-base theory) or that possesses vacant atomic orbitals to interact with electron-rich materials (Lewis acid-base theory).
• alkaline: describes a material that tends to increase the concentration of hydroxide ions in an aqueous solution, as well as conditions produced by the presence of bases.
• base: a compound that can relinquish one or more hydroxide ions (Brønsted-Lowry acid-base theory) or that possesses lone pairs of electrons that can interact with electron-poor materials (Lewis acid-base theory).
• concentration: the amount of a specific component present in a given volume of a mixture.
• logarithm: the exponent, or power, to which a specific base number must be raised to produce a given value; commonly abbreviated "log."
• neutral: describes a chemical solution that has a pH of 7 and thus is neither acidic nor basic.

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