PH: Difference between revisions

Acids and bases
Acceptor number Acid Acid–base reaction Acid–base homeostasis Acid strength Acidity function Amphoterism Base Buffer solutions Dissociation constant Donor number Equilibrium chemistry Extraction Hammett acidity function pH Proton affinity Self-ionization of water Titration Lewis acid catalysis Frustrated Lewis pair Chiral Lewis acid ECW model
Acid types
Brønsted–Lowry Lewis Mineral Organic Oxide Strong Superacids Weak Solid
Base types
Brønsted–Lowry Lewis Organic Oxide Strong Superbases Non-nucleophilic Weak
v t e

pH is a measure of the activity of hydrogen ions (H⁺) in a solution and, therefore, its acidity or alkalinity. In aqueous systems, the hydrogen ion activity is dictated by the dissociation constant of water (K_w = 1.011 × 10⁻¹⁴ at 25 °C) and interactions with other ions in solution. Due to this dissociation constant a neutral solution (hydrogen ion activity equals hydroxide ion activity) has a pH of approximately 7. Aqueous solutions with pH values lower than 7 are considered acidic, while pH values higher than 7 are considered alkaline.

The concept was introduced by S.P.L. Sørensen in 1909.

Though a pH value has no unit, it is not an arbitrary scale; the number arises from a definition based on the activity of hydrogen ions in the solution.

The formula for calculating pH is:

${\displaystyle {\mbox{pH}}=-\log _{10}\left({\frac {\left[{\mbox{H}}^{+}\right]}{\mathrm {mol} \cdot \mathrm {dm} ^{-3}}}\right)}$

or

${\displaystyle {\mbox{pH}}={\frac {\epsilon }{0.059~\mathrm {V} }}}$,

where epsilon (${\displaystyle \epsilon }$) is the electromotive force (EMF) or cell potential of a galvanic cell.

[H⁺] denotes the activity of H⁺ ions (or more accurately 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 mol/L, or about 6.31 × 10⁻⁹ mol/L; a solution with an [H⁺] activity of 4.5 × 10⁻⁴ mol/L will have a pH value of −log₁₀(4.5 × 10⁻⁴), or about 3.35.

In aqueous solution at standard ambient temperature and pressure (SATP), 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 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 alkalinity.

Neutral pH is not exactly 7; this would imply that the H⁺ ion concentration is exactly 1×10⁻⁷ mol/L, which is not the case. The value is close enough, however, for neutral pH to be 7.00 to three significant figures, which is near enough for most people to assume it is exactly 7. In nonaqueous solutions or non-SATP conditions, the pH of neutrality may not even be close to 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 less than 0 or greater than 14. The fact that this is possible follows from the definition. A concentration bigger than 1.0mol/L will make a pH negative.

The formula for pH was derived from the application of the Nernst Equation to concentration cells, or galvanic cells where the half cells are at different concentrations. In the Nernst Equation,

${\displaystyle \epsilon =\epsilon ^{o}-{\frac {0.059}{n}}\times {\log(Q)}}$.

However, in a concentration cell both ε^o are equal so the equation becomes

${\displaystyle \epsilon =-{\frac {0.059}{n}}\times {\log(Q)}}$.

By using the standard hydrogen electrode, with H₂ gas at 1 atm and an unknown molarity of H⁺ ions, and in which 2 moles of electrons are transfered for every mole of reaction, the equation may be set up as follows:

${\displaystyle \epsilon =-{\frac {0.059}{2}}\times {\log \left({\frac {[{\mbox{H}}^{+}]^{2}}{1^{2}}}\right)}}$

${\displaystyle \epsilon =-{\frac {0.059}{2}}\times {2}\times {\log([{\mbox{H}}^{+}])}}$

${\displaystyle \epsilon =0.059\times {-\log([{\mbox{H}}^{+}])}}$

Arbitrarily, the potential of hydrogen, or pH, is defined as -\log ([\mbox{H}⁺]). Therefore,

${\displaystyle {\mbox{pH}}=-\log _{10}[{{\mbox{H}}^{+}}]}$

or, by substitution,

${\displaystyle {\mbox{pH}}={\frac {\epsilon }{0.059}}}$.

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.

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 the relative abundance of each pH dependent component that make up the color of solution.
• by using a pH meter together with pH-selective electrodes (pH glass electrode, hydrogen electrode, quinhydrone electrode, ion sensitive field effect transistor and other).

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

${\displaystyle K_{w}=a_{{\rm {H}}^{\ }}a_{{\rm {OH}}^{-}}=10^{-14}}$ (*)

where K_w is the ionization constant of water.

Now, since

${\displaystyle \log _{10}K_{w}=\log _{10}a_{{\rm {H}}^{+}}+\log _{10}a_{{\rm {OH}}^{-}}}$

by logarithmic identities, we then have the relationship:

${\displaystyle -14={\rm {log}}_{\rm {10}}\,a_{{\rm {H}}^{\rm {+}}}+\log _{10}\,a_{{\rm {OH}}^{-}}}$

and thus

${\displaystyle {\rm {pOH}}=-\log _{10}\,a_{{\rm {OH}}^{-}}=14+\log _{10}\,a_{{\rm {H}}^{+}}=14-{\rm {pH}}}$ (*)

(*) Valid exactly for temperature = 298.15 K (25 °C) only, acceptable for most lab calculations.

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 mol/L solution of HCl it is approximated that there is a concentration of 0.01 mol/L dissolved hydrogen ions. From above, the pH is: pH = −log₁₀ [H⁺]:

${\displaystyle {\textrm {pH}}=-\lg {0.01}}$

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):

${\displaystyle K_{a}={\frac {\left[{\textrm {hydrogenions}}\right]\cdot {}\left[{\textrm {acidions}}\right]}{\left[{\textrm {acid}}\right]}}}$

For HCOOH, K_a = 1.6 × 10⁻⁴ (some other Ka values)

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/L solution of methanoic acid (HCOOH), the acidity constant is equal to:

K_a = [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:

${\displaystyle 1.6\times 10^{-4}={\frac {x^{2}}{0.1-x}}}$

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.

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

• Acid-base reaction theories
• Acid
• Base
• Alkali
• Soil pH
• Titration

• International standard ISO 31-8: Quantities and units — Part 8: Physical chemistry and molecular physics. Appendix C (normative): pH. International Organization for Standardization, Geneva, 1992.
• "Definitions of pH scales, standard reference values, measurement of pH, and related terminology". Pure Appl. Chem. (1985), 57, pp. 531–542.
• 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 | Abstract | Full text (HTML) | Full text (PDF))