Acids 16. and Bases
Note : Practice problems in the MSJ textbook Chapter 16.are given in parentheses. 16.1. Brnsted-Lowry Acids and Bases A Brnsted-Lowry acid is a substance that donates protons (hydrogen ions, H+) to another substance. (MSJ QRT 16.12) A Brnsted-Lowry base is a substance that accepts protons from another substance. (MSJ QRT 16.16) An acid-base reaction consists of a proton transfer between an acid and a base. (MSJ QRT 16.28) In a neutralization reaction an acid and base react completely with each other to form a salt. Water can act either as an acid or a base. Water can donate a proton and become a hydroxide ion, OH-, or it can accept a proton and form the hydronium ion, H3O+. A substance like water that can both donate and accept protons is called amphiprotic. A substance that can act both as an acid or a base is called amphoteric. All amphiprotic substances also are amphoteric. ZnO is an example of a substance that is amphoteric but not amphiprotic. As a base neutralizing an acid: ZnO + 2HCl ZnCl2 + H2O, (16.1.1) and as an acid neutralizing a base and forming an hydroxide salt: ZnO + 2NaOH Na2[Zn(OH)4]. (16.1.2) A conjugate acid-base pair is a pair of molecules or ions that are related to each other by the transfer of a single proton from one to the other, for example NH4+ and NH3. (MSJ QRT 16.24) 16.2. Acid Base Reaction Equilibria The reaction of acids (16.2.1) and bases (16.2.2) with water is called ionization. (16.2.1) HA + H2O A- + H3O+ B + H2O HB + OH (16.2.2) Water can react with itself. This reaction is called autoionization. H2O + H2O H3O+ + OH(16.2.3) All ionization reactions are characterized by equilibrium constants: Ka for acid ionization, Kb for base ionization, and Kw for water autoionization. The equilibrium constant expressions for reactions 16.2.1 16.2.3 are in order (MSJ QRT 16.49)
H 3O A Ka HA
(16.2.4) (16.2.5) (16.2.6)
HB OH Kb B
K w H 3O OH
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At 298 K, Kw = 1.00 x 10-14. Pure water is called neutral because the hydronium ion concentration equals the hydroxide ion concentration, which follows from the stoichiometry in Equation 16.2.3. An acidic solution has the hydronium ion concentration greater than the hydroxide ion concentration. A basic solution has the hydroxide ion concentration greater than the hydronium ion concentration. For any conjugate acid-base pair, Ka x Kb = Kw. (16.2.7) A p-scale commonly is used to report hydronium ion concentration, hydroxide ion concentration, and Ka and Kb values. (MSJ QRT 16.43) pH = - log [H3O+] (16.2.8) pOH = - log [OH ] (16.2.9) pKa = - log [Ka] (16.2.10) pKb = - log [Kb] (16.2.11) Taking ( log) of both sides of Equation 16.2.7 and using Equations 16.2.10 and 16.2.11 produces pKa + pKb = pKw = 14.0 at 298 K (16.2.12) Taking ( log) of both sides of Equation 16.2.6 and using Equations 16.2.8 and 16.2.9 produces pH + pOH = pKw = 14.0 at 298 K. (16.2.13) The pH of a neutral solution at any temperature can be calculated from the value of pKw at that temperature. Since in a neutral solution the concentrations of hydronium ion and hydroxide ion are equal, pH = pOH, and consequently pH = pKw/2 according to Equation 16.2.13. 16.3. Types of Acids A Brnsted-Lowry acid must have a hydrogen ion to donate. Usually the hydrogen is bonded to an electronegative atom like O, N, S, a halogen, or an electronegative group, e.g. HCN. Strong acids ionize essentially completely. They have Ka values greater than 1. For example, hydrochloric acid, HCl, and nitric acid, HNO3. Weak acids do not ionize completely. They have Ka values less than 1. Carboxylic acids are characterized by the presence of a carboxyl group, - COOH. Polyprotic acids have more than one proton that can be donated. These protons usually are attached to oxygen atoms, e.g. H2CO3, H2SO4, and H3PO4, which are carbonic, sulfuric, and phosphoric acid, respectively. Hydrated metal ions act as acids as shown by the following example. Such reactions affect of the pH of soils and the growth of plants. Fe(H2O)63+ + H2O Fe(H2O)5OH2+ + H3O+ (16.3.1) A salt composed of the conjugate acid of a weak base (NH4Cl) produces an acidic solution because it reacts with water to produce hydronium ion. NH4+ + H2O NH3 + H3O+ (16.3.2)
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Oxides of a nonmetal combine with water to produce an acid. This reaction is the source of acid rain, which a consequence of sulfur dioxide, SO2, being produce by coalfired power plants. SO2 + H2O H2SO3 (sulfurous acid) (16.3.2) 16.4. Types of Bases A Brnsted-Lowry base must have a nonbonding pair of electrons to form a bond with the hydrogen ion. Some strong bases dissociate completely in water to produce hydroxide ion, e.g. NaOH and KOH. Other strong bases ionize essentially completely by reacting with water. They have Kb values greater than 1, e.g. the amide and acetylide ions, NH2- and C2H-. Weak bases do not ionize completely. They have Kb values less than 1. Amines are characterized by the presence of an amino group, a nitrogen atom with 3 single bonds and a non-bonded lone pair of electrons. A salt composed of the conjugate base of a weak acid (NaF) produces a basic solution because reacts it with water to produce hydroxide ion. F- + H2O HF +OH(16.4.1 Metal oxides act as bases because the oxygen combines with hydronium ion to produce water. This reaction commonly is used to extract metals from their oxide ores. MgO + 2H3O+ Mg2+ + 3H2O (16.4.2) (MSJ QRT 16.76) 16.5 Two Types of Calculations Involving Ionization Constants Given the initial concentration of the weak acid or base and the pH of the solution, determine the value of Ka or Kb. (MSJ QRT 16.60) Given the initial concentration of the weak acid or base and the pKa or pKb, value, determine the pH and concentration of other components in the solution. (MSJ QRT 16.66) 16.6. Battle of Acids and Bases When comparing the strength of two acids, the stronger of the pair is the one that ionizes more completely. It has the larger value for the ionization constant, Ka, and the smaller value for the pKa. When comparing the strength of two bases, the stronger of the pair is the one that ionizes more completely. It has the larger value for the ionization constant, Kb, and the smaller value for the pKb. Since Ka and Kb values and pKa and pKb values are related by Equations 16.2.7 and 16.2.12, there is a relationship between the strength of an acid and its conjugate base. If one acid is stronger than another that means it ionizes more completely, and its conjugate base is less able to hang onto the proton. Consequently, the stronger acid has the weaker conjugate base. According to Equations 16.2.7 and 16.2.12, the stronger acid with the larger Ka and smaller pKa has the conjugate base with the smaller Kb and larger pKb, making it the weaker conjugate base.
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16.7. What Determines the Values of Ionization Constants? Chemical reactions occur and concentrations of the reactants and products change to minimize the Gibbs free energy, which is equivalent to maximizing the entropy of the universe. When the Gibbs free energy is at a minimum, then G = 0, and the equilibrium concentrations have been produced. These equilibrium concentrations match the equilibrium constant K, that is determined by the standard Gibbs free energy change. Go = -RT ln K (16.7.1) In terms of the standard Gibbs free energy change, the equilibrium constant is given by Equation 16.7.2, which is obtained from Equation 16.7.1 by dividing through by RT and raising each side to the base e.
K e (16.7.2) o o According to Equation 16.7.2, if G = 0, then K = 1. If G < 0, then K > 1, which is characteristic of a strong acid or base. If Go > 0, then K < 1, which is characteristic of a weak acid or base. Consequently any effect that makes the Go less positive will increase the ionization constant corresponding to an increase in the strength of the acid or base. Go is the difference between the free energy of the products and the free energy of the reactants. Go = Go(products) Go(reactants) (16.7.3) o o For weak acids, G (products) > G (reactants), so any effect that stabilizes (lowers the energy) the products relative to the reactants will increase the ionization constant and strength of the acid. Also any effect that increases the energy of the reactants relative to the products will increase the ionization constant and strength of the acid. When a proton is transferred, a negative charge is left behind. This negative charge is stabilized if it is on an electronegative atom. Consequently acid strength increases in the following order corresponding to the increase in electronegativity of the halogen atom: ClOH > BrOH > IOH. The negative charge also stabilized if it can be spread out over a larger volume on more electronegative atoms. Consequently acid strength increases as more oxygen atoms and resonance structures are provided for the anion: HClO4 > HClO3 > HClO2 > HClO. The conjugate base produced by successive proton transfer in polyprotic acids is destabilized as the negative charge increases. Consequently Go becomes more positive, and the ionization constant and acid strength decrease with each successive ionization: H3PO4 > H2PO4- > HPO42-. Even though fluorine is the most electronegative of all the halogens, HF is a weak acid while all the others (HCl, HBr, and HI) are strong acids. This situation results because of another effect that overwhelms the electronegativity effect. HF has the strongest bond, consequently HF is very stable, so Go for ionization of HF is large, producing a small Ka, and making HF a weak acid.
G o RT
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16.8. Controlling Base/Acid Ratios and pH Starting with Equation 16.2.4 the Henderson-Hasselbalch equation given below can be derived by taking (- log) of both sides and using Equations 16.2.8 and 16.2.10.
B pH = pKa + log HB
(16.8.1)
Given the pKa for an acid and the pH of the solution, equation 16.8.1 provides the ratio of conjugate base to acid concentration present in the solution. Similarly given the pKa and the ratio of conjugate base to acid concentration present in the solution, the pH can be calculated using Equation 16.8.1. (MSJ QRT 16.104).
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