What is pH ?

pouvoir hydrogène

pH was originally acronym for French clause "pouvoir hydrogène," which can be translated into the English as "power of hydrogen," "hydrogen power," or "potential of hydrogen." pH is used to quantify acidic or alkaline nature of a chemical which is measured in terms of H+ ions concentration. Hence the name pH.

In chemistry, pH  (potential of hydrogen) is a numeric scale used to specify the acidity or basicity of an aqueous solution. It is approximately the negative of the base 10 logarithm of the molar concentration, measured in units of moles per liter, of hydrogen ions. More precisely it is the negative of the base 10 logarithm of the activity of the hydrogen ion. Solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic. Pure water is neutral, at pH 7 (25 °C), being neither an acid nor a base. Contrary to popular belief, the pH value can be less than 0 or greater than 14 for very strong acids and bases respectively.

Measurements of pH are important in agronomy, medicine, biology, chemistry, agriculture, forestry, food science, environmental science, oceanography, civil engineering, chemical engineering, nutrition, water treatment and water purification, and many other applications.

The pH scale is traceable to a set of standard solutions whose pH is established by international agreement. Primary pH standard values are determined using a concentration cell with transference, by measuring the potential difference between a hydrogen electrode and a standard electrode such as the silver chloride electrode. The pH of aqueous solutions can be measured with a glass electrode and a pH meter, or an indicator.

pH

pH is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, a_H+, in a solution.

{\displaystyle \mathrm {pH} =-\log _{10}(a_{{\textrm {H}}^{+}})=\log _{10}\left({\frac {1}{a_{{\textrm {H}}^{+}}}}\right)}

For example, a solution with a hydrogen ion activity of 5×10⁻⁶ = 1/(2×10⁵) (at that level essentially the number of moles of hydrogen ions per liter of solution) has a pH of log₁₀(2×10⁵) = 5.3. For a commonplace example based on the facts that the masses of a mole of water, a mole of hydrogen ions, and a mole of hydroxide ions are respectively 18 g, 1 g, and 17 g, a quantity of 10⁷ moles of pure (pH 7) water, or 180 tonnes (18×10⁷ g), contains close to 1 g of dissociated hydrogen ions (or rather 19 g of H₃O⁺ hydronium ions) and 17 g of hydroxide ions.

Note that pH depends on temperature. For instance at 0 °C the pH of pure water is 7.47. At 25 °C it's 7.00, and at 100 °C it's 6.14.

This definition was adopted because ion-selective electrodes, which are used to measure pH, respond to activity. Ideally, electrode potential, E, follows the Nernst equation, which, for the hydrogen ion can be written as

{\displaystyle E=E^{0}+{\frac {RT}{F}}\ln(a_{{\textrm {H}}^{+}})=E^{0}-{\frac {2.303RT}{F}}\mathrm {pH} }

where E is a measured potential, E⁰ is the standard electrode potential, R is the gas constant, T is the temperature in kelvins, F is the Faraday constant. For H⁺ number of electrons transferred is one. It follows that electrode potential is proportional to pH when pH is defined in terms of activity.

pOH is sometimes used as a measure of the concentration of hydroxide ions. OH⁻. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by

{\displaystyle [\mathrm {OH} ^{-}]={\frac {K_{W}}{[\mathrm {H} ^{+}]}}}

where K_W is the self-ionisation constant of water. Taking logarithms

{\displaystyle \mathrm {pOH} =\mathrm {pK_{W}} -\mathrm {pH} }

So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of soil alkalinity.

Calculations of pH

The calculation of the pH of a solution containing acids and/or bases is an example of a chemical speciation calculation, that is, a mathematical procedure for calculating the concentrations of all chemical species that are present in the solution. The complexity of the procedure depends on the nature of the solution. For strong acids and bases no calculations are necessary except in extreme situations. The pH of a solution containing a weak acid requires the solution of a quadratic equation. The pH of a solution containing a weak base may require the solution of a cubic equation. The general case requires the solution of a set of non-linear simultaneous equations.

A complicating factor is that water itself is a weak acid and a weak base (see amphoterism). It dissociates according to the equilibrium

{\displaystyle {\ce {2H2O<=>{H3O+(aq)}+{OH^{-}(aq)}}}}

with a dissociation constant, K_w defined as

{\displaystyle K_{w}={\ce {[H+][OH^-]}}}

where [H⁺] stands for the concentration of the aqueous hydronium ion and [OH⁻] represents the concentration of the hydroxide ion. This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.

Strong acids and bases

Strong acids and bases are compounds that, for practical purposes, are completely dissociated in water. Under normal circumstances this means that the concentration of hydrogen ions in acidic solution can be taken to be equal to the concentration of the acid. The pH is then equal to minus the logarithm of the concentration value. Hydrochloric acid (HCl) is an example of a strong acid. The pH of a 0.01M solution of HCl is equal to −log₁₀(0.01), that is, pH = 2. Sodium hydroxide, NaOH, is an example of a strong base. The p[OH] value of a 0.01M solution of NaOH is equal to −log₁₀(0.01), that is, p[OH] = 2. From the definition of p[OH] above, this means that the pH is equal to about 12. For solutions of sodium hydroxide at higher concentrations the self-ionization equilibrium must be taken into account.

Self-ionization must also be considered when concentrations are extremely low. Consider, for example, a solution of hydrochloric acid at a concentration of 5×10⁻⁸M. The simple procedure given above would suggest that it has a pH of 7.3. This is clearly wrong as an acid solution should have a pH of less than 7. Treating the system as a mixture of hydrochloric acid and the amphotericsubstance water, a pH of 6.89 results.^[26]

Weak acids and bases

A weak acid or the conjugate acid of a weak base can be treated using the same formalism.

Acid: {\displaystyle {\ce {HA<=>{H+}+{A^{-}}}}}

Base: {\displaystyle {\ce {HA+ <=> {H+}+ A}}}

First, an acid dissociation constant is defined as follows. Electrical charges are omitted from subsequent equations for the sake of generality

{\displaystyle K_{a}={\frac {{\ce {[H] [A]}}}{{\ce {[HA]}}}}}

and its value is assumed to have been determined by experiment. This being so, there are three unknown concentrations, [HA], [H⁺] and [A⁻] to determine by calculation. Two additional equations are needed. One way to provide them is to apply the law of mass conservation in terms of the two "reagents" H and A.

{\displaystyle C_{{\ce {A}}}={\ce {[A]}}+{\ce {[HA]}}}

{\displaystyle C_{{\ce {H}}}={\ce {[H]}}+{\ce {[HA]}}}

C stands for analytical concentration. In some texts one mass balance equation is replaced by an equation of charge balance. This is satisfactory for simple cases like this one, but is more difficult to apply to more complicated cases as those below. Together with the equation defining K_a, there are now three equations in three unknowns. When an acid is dissolved in water C_A = C_H = C_a, the concentration of the acid, so [A] = [H]. After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained.

{\displaystyle [{\ce {H}}]^{2}+K_{a}[{\ce {H}}]-K_{a}C_{a}=0}

Solution of this quadratic equation gives the hydrogen ion concentration and hence p[H] or, more loosely, pH. This procedure is illustrated in an ICE table which can also be used to calculate the pH when some additional (strong) acid or alkaline has been added to the system, that is, when C_A ≠ C_H.

For example, what is the pH of a 0.01M solution of benzoic acid, pK_a = 4.19?

• Step 1: {\displaystyle K_{a}=10^{-4.19}=6.46\times 10^{-5}}
• Step 2: Set up the quadratic equation. {\displaystyle {\ce {{[H]^{2}}+{6.46\times 10^{-5}[H]}-6.46\times 10^{-7}=0}}}
• Step 3: Solve the quadratic equation. {\displaystyle {\ce {{[H+]}=7.74\times 10^{-4}}}} ; pH = 3.11

For alkaline solutions an additional term is added to the mass-balance equation for hydrogen. Since addition of hydroxide reduces the hydrogen ion concentration, and the hydroxide ion concentration is constrained by the self-ionization equilibrium to be equal to {\displaystyle {\frac {K_{w}}{{\ce {[H+]}}}}}

{\displaystyle C_{\ce {H}}={\frac {[{\ce {H}}]+[{\ce {HA}}]-K_{w}}{\ce {[H]}}}}

In this case the resulting equation in [H] is a cubic equation.

General method

Some systems, such as with polyprotic acids, are amenable to spreadsheet calculations.^[27]With three or more reagents or when many complexes are formed with general formulae such as A_pB_qH_r the following general method can be used to calculate the pH of a solution. For example, with three reagents, each equilibrium is characterized by an equilibrium constant, β.

{\displaystyle [{\ce {A}}_{p}{\ce {B}}_{q}{\ce {H}}_{r}]=\beta _{pqr}[{\ce {A}}]^{p}[{\ce {B}}]^{q}[{\ce {H}}]^{r}}

Next, write down the mass-balance equations for each reagent:

{\displaystyle {\begin{aligned}C_{\ce {A}}&=[{\ce {A}}]+\Sigma p\beta _{pqr}[{\ce {A}}]^{p}[{\ce {B}}]^{q}[{\ce {H}}]^{r}\\C_{\ce {B}}&=[{\ce {B}}]+\Sigma q\beta _{pqr}[{\ce {A}}]^{p}[{\ce {B}}]^{q}[{\ce {H}}]^{r}\\C_{\ce {H}}&=[{\ce {H}}]+\Sigma r\beta _{pqr}[{\ce {A}}]^{p}[{\ce {B}}]^{q}[{\ce {H}}]^{r}-K_{w}[{\ce {H}}]^{-1}\end{aligned}}}

Note that there are no approximations involved in these equations, except that each stability constant is defined as a quotient of concentrations, not activities. Much more complicated expressions are required if activities are to be used.

There are 3 non-linear simultaneous equations in the three unknowns, [A], [B] and [H]. Because the equations are non-linear, and because concentrations may range over many powers of 10, the solution of these equations is not straightforward. However, many computer programs are available which can be used to perform these calculations. There may be more than three reagents. The calculation of hydrogen ion concentrations, using this formalism, is a key element in the determination of equilibrium constants by potentiometric titration.