The point of inflection (located at the midpoint of the vertical part of the curve) is the equivalence point for the titration. It indicates when equivalent quantities of acid and base are present. For the titration of a strong acid with a strong base, the equivalence point occurs at a pH of 7.00 and the points on the titration curve can be calculated using solution stoichiometry (Table 6.2.16.2.1\PageIndex{1} and Figure 6.2.16.2.1\PageIndex{1}).

where pKa is the negative of the common logarithm of the ionization constant of the weak acid (pKa = −log Ka). This equation relates the pH, the ionization constant of a weak acid, and the concentrations of the weak acid and its salt in a buffered solution. Scientists often use this expression, called the Henderson-Hasselbalch approximation, to calculate the pH of buffer solutions. It is important to note that the “x is small” assumption must be valid to use this equation.

Buffer solutions do not have an unlimited capacity to keep the pH relatively constant (Figure 6.1.36.1.3\PageIndex{3}). If we add so much base to a buffer that the weak acid is exhausted, no more buffering action toward the base is possible. On the other hand, if we add an excess of acid, the weak base would be exhausted, and no more buffering action toward any additional acid would be possible. In fact, we do not even need to exhaust all of the acid or base in a buffer to overwhelm it; its buffering action will diminish rapidly as a given component nears depletion.

Environmental Science Normal rainwater has a pH between 5 and 6 due to the presence of dissolved CO2 which forms carbonic acid: H2O(l)+CO2(g)⟶H2CO3(aq)(5.2.12)(5.2.12)H2O(l)+CO2(g)⟶H2CO3(aq)\ce{H2O (l) + CO2(g) ⟶ H2CO3(aq)} \label{14} H2CO3(aq)⇌H+(aq)+HCO−3(aq)(5.2.13)(5.2.13)H2CO3(aq)⇌H+(aq)+HCO3−(aq)\ce{H2CO3(aq) \rightleftharpoons H^+(aq) + HCO3^- (aq)} \label{15} Acid rain is rainwater that has a pH of less than 5, due to a variety of nonmetal oxides, including CO2, SO2, SO3, NO, and NO2 being dissolved in the water and reacting with it to form not only carbonic acid, but sulfuric acid and nitric acid. The formation and subsequent ionization of sulfuric acid are shown here: H2O(l)+SO3(g)⟶H2SO4(aq)(5.2.14)(5.2.14)H2O(l)+SO3(g)⟶H2SO4(aq)\ce{H2O (l) + SO3(g) ⟶ H2SO4(aq)} \label{16} H2SO4(aq)⟶H+(aq)+HSO−4(aq)(5.2.15)(5.2.15)H2SO4(aq)⟶H+(aq)+HSO4−(aq)\ce{H2SO4(aq) ⟶ H^+(aq) + HSO4^- (aq)} \label{17} Carbon dioxide is naturally present in the atmosphere because we and most other organisms produce it as a waste product of metabolism. Carbon dioxide is also formed when fires release carbon stored in vegetation or when we burn wood or fossil fuels. Sulfur trioxide in the atmosphere is naturally produced by volcanic activity, but it also stems from burning fossil fuels, which have traces of sulfur, and from the process of “roasting” ores of metal sulfides in metal-refining processes. Oxides of nitrogen are formed in internal combustion engines where the high temperatures make it possible for the nitrogen and oxygen in air to chemically combine. Acid rain is a particular problem in industrial areas where the products of combustion and smelting are released into the air without being stripped of sulfur and nitrogen oxides. In North America and Europe until the 1980s, it was responsible for the destruction of forests and freshwater lakes, when the acidity of the rain actually killed trees, damaged soil, and made lakes uninhabitable for all but the most acid-tolerant species. Acid rain also corrodes statuary and building facades that are made of marble and limestone (Figure 5.2.25.2.2\PageIndex{2}). Regulations limiting the amount of sulfur and nitrogen oxides that can be released into the atmosphere by industry and automobiles have reduced the severity of acid damage to both natural and manmade environments in North America and Europe. It is now a growing problem in industrial areas of China and India.

And so, at this temperature, acidic solutions are those with hydronium ion molarities greater than 1.0×10−7M1.0×10−7M 1.0 \times 10^{-7}\; M and hydroxide ion molarities less than 1.0×10−7M1.0×10−7M 1.0 \times 10^{-7}\; M (corresponding to pH values less than 7.00 and pOH values greater than 7.00). Basic solutions are those with hydronium ion molarities less than 1.0×10−7M1.0×10−7M 1.0 \times 10^{-7}\; M and hydroxide ion molarities greater than 1.0×10−7M1.0×10−7M 1.0 \times 10^{-7}\; M (corresponding to pH values greater than 7.00 and pOH values less than 7.00).

The hydronium ion molarity in pure water (or any neutral solution) is 1.0×10−7M1.0×10−7M 1.0 \times 10^{-7}\; M at 25 °C. The pH and pOH of a neutral solution at this temperature are therefore:

Finally, the relation between these two ion concentration expressed as p-functions is easily derived from the KwKwK_w expression:

or

Likewise, the hydroxide ion molarity may be expressed as a p-function, or pOH:

Rearranging this equation to isolate the hydronium ion molarity yields the equivalent expression:

The pH of a solution is therefore defined as shown here, where [H3O+] is the molar concentration of hydronium ion in the solution:

A common means of expressing quantities, the values of which may span many orders of magnitude, is to use a logarithmic scale. One such scale that is very popular for chemical concentrations and equilibrium constants is based on the p-function, defined as shown where “X” is the quantity of interest and “log” is the base-10 logarithm:

This type of reaction, in which a substance ionizes when one molecule of the substance reacts with another molecule of the same substance, is referred to as autoionization. Pure water undergoes autoionization to a very slight extent. Only about two out of every 10910910^9 molecules in a sample of pure water are ionized at 25 °C.

Like water, many molecules and ions may either gain or lose a proton under the appropriate conditions. Such species are said to be amphiprotic.

Another term used to describe such species is amphoteric, which is a more general term for a species that may act either as an acid or a base by any definition (not just the Brønsted-Lowry one).