H Chemical Principles: The Quest for Insight, 3rd Ed., New York: W.H. K {\displaystyle pH=pK_{w}-pOH} An example of a weak base is ammonia. w ]\!\!\text{ }=\sqrt{K_{b}c_{b}} \\ \text{ }=\sqrt{\text{1}\text{.8 }\times \text{ 10}^{-\text{5}}\text{ mol L}^{-\text{1}}\text{ }\times \text{ 0}\text{.100 mol L}^{-\text{1}}} \\\text{ }=\sqrt{\text{1}\text{.8 }\times \text{ 10}^{-\text{6}}\text{ mol}^{\text{2}}\text{ L}^{-2}}=\text{1}\text{.34 }\times \text{ 10}^{-\text{3}}\text{ mol L}^{-\text{1}} \\\end{align}\), Checking the accuracy of the approximation, we find, $$\dfrac{\text{ }\!\! [\!\!\text{ OH}^{-}\text{ }\!\! H A list of Kb values for selected bases arranged in order of strength is given in the table below. The pH of a solution of a weak base can be calculated in a way which is very similar to that used for a weak acid. − , where pKw = 14.00. Have questions or comments? Missed the LibreFest? (3) and reads, [OH–] ≈ \(\sqrt{K_{b}\text{(}c_{b}-\text{ }\!\! [\!\!\text{ OH}^{-}\text{ }\!\! 4) They have a small value for Kb. This calculated value checks well with our initial guess. [1], As seen above, the strength of a base depends primarily on pH. w The Kb for C5H5N is 1.8 x 10−9.[3]. [\!\!\text{ OH}^{-}\text{ }\!\! For example, when ammonia is put in water, the following equilibrium is set up: A base that has a large Kb will ionize more completely and is thus a stronger base. [\!\!\text{ OH}^{-}\text{ }\!\! This page was last edited on 7 June 2020, at 00:23. If a weak base B accepts protons from water according to the equation, $\text{B} + \text{ H}_{\text{2}}\text{O}\rightleftharpoons\text{BH}^{+} + \text{OH}^{-} \label{1}$, then the base constant is defined by the expression, $K_{b}=\dfrac{\text{ }\!\! p which is identical to the expression obtained in the acid case (approximation shown in equation 6 in the section on the pH of weak acids) except that OH– replaces H3O+ and b replaces a. "Strong and Weak Bases."N.p.,2002. K [ "article:topic", "pH", "pH of Solutions of Weak Bases", "weak base", "authorname:chemprime", "showtoc:no", "license:ccbyncsa" ], Ed Vitz, John W. Moore, Justin Shorb, Xavier Prat-Resina, Tim Wendorff, & Adam Hahn, Chemical Education Digital Library (ChemEd DL), equation 4 in the section on the pH of weak acids, equation 6 in the section on the pH of weak acids, \(NH_3 + H_2O \rightleftharpoons NH^+_4 + OH^–$$, $$C_6H_5NH_2 + H_2O \rightleftharpoons C_6H_5NH^+_3 + OH^–$$, $$CO_3^{2–} + H_2O \rightleftharpoons HCO^-_3 + OH^–$$, $$N_2H_4 + H_2O \rightleftharpoons N_2H^+_5 + OH^–$$, $$PO_4^{3–} + H_2O \rightleftharpoons HPO^{2-}_4 + OH^–$$, $$C_5H_5N + H_2O \rightleftharpoons C_5H_5NH^+ + OH^–$$, Taken from Hogfelt, E. Perrin, D. D. Stability Constants of Metal Ion Complexes, 1. [\!\!\text{ OH}^{-}\text{ }\!\! The appropriate formula can be derived from Eq. A weak base is a base that, upon dissolution in water, does not dissociate completely, so that the resulting aqueous solution contains only a small proportion of hydroxide ions and the concerned basic radical, and a large proportion of undissociated molecules of the base. is just the self-ionization constant of water, we have The further to the left it is, the weaker the base. Web. {\displaystyle {K_{w}}=[H_{3}O^{+}][OH^{-}]} p Using Eq. If a weak base B accepts protons from water according to the equation. ]\!\!\text{ )}}\) (5). K As the bases get weaker, the smaller the Kb values become. As shown above, the pH of the solution, which depends on the H+ concentration, increases with increasing OH− concentration; a greater OH− concentration means a smaller H+ concentration, therefore a greater pH. NaOH (s) (sodium hydroxide) is a stronger base than (CH3CH2)2NH (l) (diethylamine) which is a stronger base than NH3 (g) (ammonia). The position of equilibrium varies from base to base when a weak base reacts with water. The pOH is defined as: If we multiply the equilibrium constants of a conjugate acid (such as NH4+) and a conjugate base (such as NH3) we obtain: As For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. [\!\!\text{ BH}^{\text{+}}\text{ }\!\! ] K b. Ammonia. Clark, Jim. 3) The acquire H + in aqueous solutions. A weak base persists in chemical equilibrium in much the same way as a weak acid does, with a base dissociation constant (Kb) indicating the strength of the base. [\!\!\text{ OH}^{-}\text{ }\!\! Atkins, Peter, and Loretta Jones. K Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Freeman, 2005. However, pH of bases is usually calculated in terms of the OH− concentration. ] Bases yield solutions in which the hydrogen ion activity is lower than it is in pure water, i.e., the solution is said to have a pH greater than 7.0 at standard conditions, potentially as high as 14 (and even greater than 14 for some bases). A pH of 10 or 11 seems reasonable. Watch the recordings here on Youtube! Formula. To help describe the strengths of weak bases, it is helpful to know the percentage protonated-the percentage of base molecules that have been protonated. The pH of a weak base falls somewhere between 7 and 10. It is not a bad idea to guess an approximate pH before embarking on the calculation. This is done because the H+ concentration is not a part of the reaction, whereas the OH− concentration is. Name. Using the value for Kb listed in the table, find the pH of 0.100 M NH3. × ]\!\!\text{ }}{\text{mol L}^{-\text{1}}}=-\text{log(1}\text{.34 }\times \text{ 10}^{-\text{3}}\text{)}=\text{2}\text{.87}\). From the equation for percentage protonated with [HB. If the stoichiometric concentration of the base is indicated by cb, the result is entirely analogous to equation 4 in the section on the pH of weak acids; namely, \[K_{b}=\dfrac{\text{ }\!\! A weak base will have a higher H+ concentration than a stronger base because it is less completely protonated than a stronger base and, therefore, more hydrogen ions remain in its solution. This table is part of our larger collection of acid-base resources. The formula for pH is: Bases are proton acceptors; a base will receive a hydrogen ion from water, H2O, and the remaining H+ concentration in the solution determines pH. The pH of a solution of a weak base can be calculated in a way which is very similar to that used for a weak acid. Like weak acids, weak bases do not undergo complete dissociation; instead, their ionization is a two-way reaction with a definite equilibrium point. Basic Information . 3 A base dissociation constant, K b , mathematically represents the base’s relative strength and is analogous to the acid dissociation constant; weaker bases have smaller K b values. 1) Weak bases are less than 100% ionized in solution. It does not contain hydroxide ions, but it reacts with water to produce ammonium ions and hydroxide ions. ]\!\!\text{ }} \label{2}$. Taking the logarithm of both sides of the equation yields: Finally, multiplying both sides by -1, we obtain: With pOH obtained from the pOH formula given above, the pH of the base can then be calculated from Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn. We can assume that x is so small that it will be meaningless by the time we use significant figures. The formula for pH is: pH Calculation for Weak Bases : WEAK BASES. 5) weak bases acquire hydrogen ions from water leaving hydroxide . To find the pH we follow the same general procedure as in the case of a weak acid. H Instead of an acid constant Ka, a base constant Kb must be used. [ NH 3. a = Guide to Weak Bases from Georgetown course notes, Article on Acidity of Solutions of Weak Bases, https://en.wikipedia.org/w/index.php?title=Weak_base&oldid=961170760, Creative Commons Attribution-ShareAlike License, Substitute the equilibrium molarities into the basicity constant. {\displaystyle K_{a}\times K_{b}=K_{w}}. A pH of 13 or 14 would be too basic, while a pH of 8 or 9 is too close to neutral. Calculate the pH and percentage protonation of a .20 M aqueous solution of pyridine, C5H5N. [\!\!\text{ OH}^{-}\text{ }\!\! ]\!\!\text{ }^{\text{2}}}{c_{b}-\text{ }\!\! ]\!\!\text{ }\!\! = ]\!\!\text{ }}{c_{\text{b}}}=\dfrac{\text{1}\text{.34 }\times \text{ 10}^{-\text{3}}}{\text{0}\text{.1}}\approx \text{1 percent}\). Strong bases have smaller H+ concentrations because they are more fully protonated, leaving fewer hydrogen ions in the solution. Bases yield solutions in which the hydrogen ion activity is lower than it is in pure water, i.e., the solution is said to have a pH greater than 7.0 at standard conditions, potentially as high as 14 (and even greater than 14 for some bases).