Acids and Bases: A Brief Review Acids: taste sour and cause dyes to change color. Bases: taste bitter and feel soapy. Arrhenius: acids increase [H+], bases increase [OH-] in solution. Arrhenius: acid + base  salt + water. Problem: the definition confines us to aqueous solution.

Brønsted-Lowry Acids and Bases The H+ Ion in Water The H+(aq) ion is simply a proton with no electrons. (H has one proton, one electron, and no neutrons.) In water, the H+(aq) joins a water molecule to become H3O+(aq). Generally we use H+(aq) and H3O+(aq) interchangeably.

Proton Transfer Reactions Focus on the H+(aq). Brønsted-Lowry: acid donates H+ and base accepts H+. Brønsted-Lowry base does not need to contain OH-. Consider HCl(aq) + H2O(l)  H3O+(aq) + Cl-(aq): HCl donates a proton to water. Therefore, HCl is an acid. H2O accepts a proton from HCl. Therefore, H2O is a base. Water can behave as either an acid or a base. Amphoteric substances can behave as acids and bases.

Conjugate Acid-Base Pairs Whatever is left of the acid after the proton is donated is called its conjugate base. Similarly, whatever remains of the base after it accepts a proton is called a conjugate acid. Consider After HA (acid) loses its proton it is converted into A- (base). Therefore HA and A- are a conjugate acid-base pair. After H2O (base) gains a proton it is converted into H3O+ (acid). Therefore, H2O and H3O+ are a conjugate acid-base pair. Conjugate acid-base pairs differ by only one proton.

Example – Identify the acid and the base in each equation, and identify each acid-base pair. HNO3 + NH3  NO3- + NH4+ CH3COOH + OH-  H2O + CH3COO- Identify the acid and base for the reverse reaction in each example.

Relative Strengths of Acids and Bases The stronger the acid, the weaker the conjugate base. H+ is the strongest acid that can exist in equilibrium in aqueous solution. OH- is the strongest base that can exist in equilibrium in aqueous solution.

The Autoionization of Water The Ion Product of Water In pure water the following equilibrium is established at 25 C The above is called the autoionization of water.

The pH Scale In most solutions [H+(aq)] is quite small. We define In neutral water at 25 C, pH = pOH = 7.00. In acidic solutions, [H+] > 1.0  10-7, so pH < 7.00. In basic solutions, [H+] < 1.0  10-7, so pH > 7.00. The higher the pH, the lower the pOH, the more basic the solution.

Other “p” Scales In general for a number X, For example, pKw = -log Kw.

Most pH and pOH values fall between 0 and 14. There are no theoretical limits on the values of pH or pOH. (e.g. pH of 2.0 M HCl is -0.301.) Examples: Consider a solution with [H+] = 6.2 x 10-3. Calculate the pH, pOH, and [OH-] Is this solution acidic or basic? Consider a solution with pOH = 13.65 Calculate the pH, [H+], and [OH-]

Most pH and pOH values fall between 0 and 14. There are no theoretical limits on the values of pH or pOH. (e.g. pH of 2.0 M HCl is -0.301.) Examples: Consider a solution with [H+] = 6.2 x 10-3. Calculate the pH, pOH, and [OH-] Is this solution acidic or basic? Consider a solution with pOH = 13.65 Calculate the pH, [H+], and [OH-]

Measuring pH Most accurate method to measure pH is to use a pH meter. However, certain dyes change color as pH changes. These are indicators. Indicators are less precise than pH meters. Many indicators do not have a sharp color change as a function of pH.

The strongest common acids are HCl, HBr, HI, HNO3, HClO4, and H2SO4. Strong Acids The strongest common acids are HCl, HBr, HI, HNO3, HClO4, and H2SO4. Strong acids are strong electrolytes. All strong acids ionize completely in solution: HNO3(aq) + H2O(l)  H3O+(aq) + NO3-(aq) Since H+ and H3O+ are used interchangeably, we write HNO3(aq)  H+(aq) + NO3-(aq)

Strong Acids and Bases Strong Acids In solutions the strong acid is usually the only source of H+. (If the molarity of the acid is less than 10-6 M then the autoionization of water needs to be taken into account.) Therefore, the [H+] of the solution is the initial molarity of the acid. (pH = -log [H+]) Strong Bases Group 1 and soluble group 2 hydroxides are strong bases (e.g. NaOH, KOH, and Ca(OH)2).

In order for a hydroxide to be a base, it must be soluble. Strong bases are strong electrolytes and dissociate completely in solution. The pOH of a strong base is given by the initial molarity of the hydroxide ion. Be careful of stoichiometry. In order for a hydroxide to be a base, it must be soluble. Bases do not have to contain the OH- ion: O2-(aq) + H2O(l)  2OH-(aq) H-(aq) + H2O(l)  H2(g) + OH-(aq) N3-(aq) + H2O(l)  NH3(aq) + 3OH-(aq)

Examples: Calculate the pH and pOH of each: 0.25 M NaOH 12.00 M HCl 6.00 M KOH 0.0050 M HNO3 6.5 x 10-12 M RbOH 0.10 M HClO4

Weak Acids Weak acids are only partially ionized (dissociated) in solution. There is a mixture of ions and unionized acid in solution. Therefore, weak acids are in equilibrium:

Ka is the acid dissociation constant. Note [H2O] is omitted from the Ka expression. (H2O is a pure liquid.) The larger the Ka the stronger the acid (i.e. the more ions are present at equilibrium relative to unionized molecules). If Ka >> 1, then the acid is completely ionized and the acid is a strong acid.

Weak acids are simply equilibrium calculations. Calculating Ka from pH Weak acids are simply equilibrium calculations. The pH is used to calculate the equilibrium concentration of H+. Write the balanced chemical equation clearly showing the equilibrium. Write the equilibrium expression. Use an ICE Chart Find the value for Ka.

Examples: Calculate Ka. A 0.25 M solution of a hypothetical acid, HA, has a pH of 4.06. 2. A 0.10 M solution of acetic acid (CH3COOH) has a pH of 2.87.

Percent Ionization Percent ionization is another method to assess acid strength. For the reaction

Using Ka to Calculate pH Percent ionization relates the equilibrium H+ concentration, [H+]eqm, to the initial HA concentration, [HA]0. The higher percent ionization, the stronger the acid. Percent ionization of a weak acid decreases as the molarity of the solution increases. For acetic acid, 0.05 M solution is 2.0 % ionized whereas a 0.15 M solution is 1.0 % ionized. Use ICE Charts to determine [H+] -log [H+] = pH Substitute into the equilibrium constant expression and solve. Remember to turn x into pH if necessary.

Examples – Calculate pH, pOH and percent dissociation for each of the following: 0.35 M HF (Ka = 7.2 x 10-4) 2. 0.62 M NH4+ (from NH4Cl) (Ka = 5.6 x 10-10)

Polyprotic Acids Polyprotic acids have more than one ionizable proton. The protons are removed in steps not all at once: It is always easier to remove the first proton in a polyprotic acid than the second. Therefore, Ka1 > Ka2 > Ka3 etc. For calculations, we will generally only consider the first dissociation (the others contribute very little to [H+]

Polyprotic Acids

Examples: Calculate pH, pOH, and % dissociation 0.15 M H3PO4 0.30 M NaH2PO4 0.61 M H2CO3

Weak Bases Weak bases remove protons from substances. There is an equilibrium between the base and the resulting ions: Example: The base dissociation constant, Kb, is defined as

Types of Weak Bases Bases generally have lone pairs or negative charges in order to attack protons. Most neutral weak bases contain nitrogen. Amines are related to ammonia and have one or more N-H bonds replaced with N-C bonds (e.g., CH3NH2 is methylamine). Anions of weak acids are also weak bases. Example: OCl- is the conjugate base of HOCl (weak acid):

Calculating pH and pOH of Weak Base Solutions Use ICE Chart to determine [OH-]eq Use [OH-] to find pOH, and thus pH Examples – Calculate pOH and pH of each of the following solutions: 0.15 M NH3 (Kb = 1.8 x 10-5) 0.38 M HONH2 (Kb = 1.1 x 10-8)

Relationship Between Ka and Kb We need to quantify the relationship between strength of acid and conjugate base. When two reactions are added to give a third, the equilibrium constant for the third reaction is the product of the equilibrium constants for the first two: Reaction 1 + reaction 2 = reaction 3 has

For a conjugate acid-base pair Therefore, the larger the Ka, the smaller the Kb. That is, the stronger the acid, the weaker the conjugate base. Taking negative logarithms:

Acid-Base Properties of Salt Solutions Nearly all salts are strong electrolytes. Therefore, salts exist entirely of ions in solution. Acid-base properties of salts are a consequence of the reaction of their ions in solution. The reaction in which ions produce H+ or OH- in water is called hydrolysis. Anions from weak acids are basic. Anions from strong acids are neutral.

An Anion’s Ability to React with Water Anions, X-, can be considered conjugate bases from acids, HX. If X- comes from a strong acid, then it is neutral. If X- comes from a weak acid, then The pH of the solution can be calculated using equilibrium!

A Cation’s Ability to React with Water Polyatomic cations with ionizable protons can be considered conjugate acids of weak bases. Some metal ions react in solution to lower pH. Combined Effect of Cation and Anion in Solution An anion from a strong acid has no acid-base properties. An anion that is the conjugate base of a weak acid will cause an increase in pH (basic ion).

A cation that is the conjugate acid of a weak base will cause a decrease in the pH of the solution (acidic ion). Metal ions will cause a decrease in pH except for the alkali metals and alkaline earth metals. When a solution contains both cations and anions from weak acids and bases, use Ka and Kb to determine the final pH of the solution. Use ICE charts to calculate pH and pOH (as for weak acid and weak base solutions)

Amphoteric Substances Determine Ka and Kb for the substance (ion) If Ka > Kb, then the ion is acidic If Ka < Kb, then the ion is basic Use the appropriate constant to calculate pH and pOH

Examples – State whether each will be acidic, basic, or neutral in aqueous solution: NaOCl Fe(NO3)3 KBr LiClO4 NaHCO3 CaCl2 NH4NO3 NiI2

Examples – Calculate pH and pOH for each solution: 0.25 M NH4Cl 0.60 M KBr 0.18 M KC2H3O2 0.50 M NaHCO3

Acid-Base Behavior and Chemical Structure Factors that Affect Acid Strength Consider H-X. For this substance to be an acid we need: H-X bond to be polar with H+ and X- (if X is a metal then the bond polarity is H-, X+ and the substance is a base), the H-X bond must be weak enough to be broken, the conjugate base, X-, must be stable.

Binary Acids Acid strength increases across a period and down a group. Conversely, base strength decreases across a period and down a group. HF is a weak acid because the bond energy is high. The electronegativity difference between C and H is so small that the C-H bond is non-polar and CH4 is neither an acid nor a base.

Binary Acids

Oxyacids contain O-H bonds. All oxyacids have the general structure Y-O-H. The strength of the acid depends on Y and the atoms attached to Y. If Y is a metal (low electronegativity), then the substances are bases. If Y has intermediate electronegativity (e.g. I, EN = 2.5), the electrons are between Y and O and the substance is a weak oxyacid.

If Y has a large electronegativity (e. g. Cl, EN = 3 If Y has a large electronegativity (e.g. Cl, EN = 3.0), the electrons are located closer to Y than O and the O-H bond is polarized to lose H+. The number of O atoms attached to Y increase the O-H bond polarity and the strength of the acid increases (e.g. HOCl is a weaker acid than HClO2 which is weaker than HClO3 which is weaker than HClO4 which is a strong acid).

Oxyacids

Carboxylic Acids Carboxylic acids all contain the COOH group. All carboxylic acids are weak acids. When the carboxylic acid loses a proton, it generate the carboxylate anion, COO-.

Lewis Acids and Bases Brønsted-Lowry acid is a proton donor. Focusing on electrons: a Brønsted-Lowry acid can be considered as an electron pair acceptor. Lewis acid: electron pair acceptor. Lewis base: electron pair donor. Note: Lewis acids and bases do not need to contain protons. Therefore, the Lewis definition is the most general definition of acids and bases.

Lewis acids generally have an incomplete octet (e.g. BF3). Transition metal ions are generally Lewis acids. Lewis acids must have a vacant orbital (into which the electron pairs can be donated). Compounds with p-bonds can act as Lewis acids: H2O(l) + CO2(g)  H2CO3(aq)

The Common Ion Effect The solubility of a partially soluble salt is decreased when a common ion is added. Consider the equilibrium established when acetic acid, HC2H3O2, is added to water. At equilibrium H+ and C2H3O2- are constantly moving into and out of solution, but the concentrations of ions is constant and equal.

Consider the addition of C2H3O2-, which is a common ion Consider the addition of C2H3O2-, which is a common ion. (The source of acetate could be a strong electrolyte such as NaC2H3O2.) Therefore, [C2H3O2-] increases and the system is no longer at equilibrium. So, [H+] must decrease. HC2H3O2 H+ + C2H3O2- The equilibrium will shift to the left.

Composition and Action of Buffered Solutions A buffer consists of a mixture of a weak acid (HX) and its conjugate base (X-): The Ka expression is

A buffer resists a change in pH when a small amount of OH- or H+ is added. When OH- is added to the buffer, the OH- reacts with HX to produce X- and water. But, the [HX]/[X-] ratio remains more or less constant, so the pH is not significantly changed. When H+ is added to the buffer, X- is consumed to produce HX. Once again, the [HX]/[X-] ratio is more or less constant, so the pH does not change significantly.

Example Write the reaction that occurs in a buffer solution containing HF/F- when: H+ is added OH- is added

Buffer Capacity and pH Buffer capacity is the amount of acid or base neutralized by the buffer before there is a significant change in pH. Buffer capacity depends on the composition of the buffer. The greater the amounts of conjugate acid-base pair, the greater the buffer capacity. The pH of the buffer depends on Ka. In general, the effective range of a buffer is within the pH range: pKa-1 to pKa+1.

Addition of Strong Acids or Bases to Buffers We break the calculation into two parts: stoichiometric and equilibrium.

Addition of Strong Acids or Bases to Buffers The amount of strong acid or base added results in a neutralization reaction: X- + H3O+  HX + H2O HX + OH-  X- + H2O. By knowing how much H3O+ or OH- was added (stoichiometry) we know how much HX or X- is formed. With the concentrations of HX and X- (note the change in volume of solution) we can calculate the pH from the Henderson-Hasselbalch equation or the original equilibrium expression (ICE chart).

Examples Consider a buffer prepared by placing 0.60 moles of HF (Ka = 7.2 x 10-4) and 0.48 moles of NaF in a 1.00 L solution. a. Calculate the pH of the buffer b. Calculate the pH after the addition of 0.08 moles of HCl c. Calculate the pH after the addition of 0.10 moles of NaOH.

Strong Acid-Strong Base Titrations Acid-Base Titrations Strong Acid-Strong Base Titrations A plot of pH versus volume of acid (or base) added is called a titration curve. Consider adding a strong base (e.g. NaOH) to a solution of a strong acid (e.g. HCl). Before any base is added, the pH is given by the strong acid solution. Therefore, pH < 7. When base is added, before the equivalence point, the pH is given by the amount of strong acid in excess. Therefore, pH < 7.

The equivalence point in a titration is the point at which the acid and base are present in stoichiometric quantities. The end point in a titration is the observed point (indicator changes color) The difference between equivalence point and end point is called the titration error. Initially, the strong acid is in excess, so the pH < 7. As base is added, the pH increases but is still less than 7. At equivalence point, the pH is given by the salt solution (i.e. pH = 7). After equivalence point, the pH is given by the amount of strong base in excess.

Strong Acid-Strong Base Titrations At equivalence point, the amount of base added is stoichiometrically equivalent to the amount of acid originally present. Therefore, the pH is determined by the salt solution. Therefore, pH = 7. Consider adding a strong base (e.g. NaOH) to a solution of a strong acid (e.g. HCl). We know the pH at equivalent point is 7.00. To detect the equivalent point, we use an indicator that changes color somewhere near 7.00.

Strong Base-Strong Acid Titrations

Weak Acid-Strong Base Titrations Consider the titration of acetic acid, HC2H3O2 and NaOH. Before any base is added, the solution contains only weak acid. Therefore, pH is given by the equilibrium calculation. As strong base is added, the strong base consumes a stoichiometric quantity of weak acid: HC2H3O2(aq) + OH-(aq)  C2H3O2-(aq) + H2O(l)

Weak Acid-Strong Base Titrations There is an excess of acid before the equivalence point. Therefore, we have a mixture of weak acid and its conjugate base. The pH is given by the buffer calculation. First the amount of C2H3O2- generated is calculated, as well as the amount of HC2H3O2 consumed. (Stoichiometry.) Then the pH is calculated using equilibrium conditions. (Henderson-Hasselbalch.)

Weak Acid-Strong Base Titrations At the equivalence point, all the acetic acid has been consumed and all the NaOH has been consumed. However, C2H3O2- has been generated. Therefore, the pH is given by the C2H3O2- solution. This means pH > 7. More importantly, pH  7 for a weak acid-strong base titration. After the equivalence point, the pH is given by the strong base in excess.

pH at Equivalence Point Type of Titration pH at Equivalence Point Strong Acid and Strong Base 7 Strong Acid and Weak Base <7 Strong Base and Weak Acid >7 Weak Base and Weak Acid If Ka>Kb, pH<7 If Ka<Kb, pH>7

Titrations of Polyprotic Acids In polyprotic acids, each ionizable proton dissociates in steps. Therefore, in a titration there are n equivalence points corresponding to each ionizable proton. In the titration of H3PO3 with NaOH. The first proton dissociates to form H2PO3-. Then the second proton dissociates to form HPO32-.

Equations on the board

Solubility Equilibria The Solubility-Product Constant, Ksp Consider for which Ksp is the solubility product. (BaSO4 is ignored because it is a pure solid so its concentration is constant.)

In general: the solubility product is the molar concentration of ions raised to their stoichiometric powers. Solubility is the amount (grams) of substance that dissolves to form a saturated solution. Molar solubility is the number of moles of solute dissolving to form a liter of saturated solution.

Solubility and Ksp To convert solubility to Ksp solubility needs to be converted into molar solubility (via molar mass); molar solubility is converted into the molar concentration of ions at equilibrium (equilibrium calculation), Ksp is the product of equilibrium concentration of ions.

Examples The solubility of calcium carbonate in water at 25°C is 6.7 x 10-3 g/L. Calculate the molar solubility and Ksp. The solubility of manganese (II) hydroxide in water at 25°C is 3.42 x 10-5 mol/L. Calculate the solubility in g/L and calculate Ksp. Ksp for PbF2 at 25°C is 3.6 x 10-8. Calculate the molar solubility and the solubility in g/L. Ksp for Ca3(PO4)2 is 2.0 x 10-29. Calculate the molar solubility and the solubility in g/L.

Factors that Affect Solubility The Common Ion Effect Solubility is decreased when a common ion is added. This is an application of Le Châtelier’s principle: as F- (from NaF, say) is added, the equilibrium shifts away from the increase. Therefore, CaF2(s) is formed and precipitation occurs. As NaF is added to the system, the solubility of CaF2 decreases.

Calculate the solubility of Ag2SO4 (Ksp = 1.5 x 10-5) Examples Calculate the solubility of Ag2SO4 (Ksp = 1.5 x 10-5) In water In 0.25 M AgNO3 solution In 0.20 M K2SO4 solution

Again we apply Le Châtelier’s principle: Solubility and pH Again we apply Le Châtelier’s principle: If the F- is removed, then the equilibrium shifts towards the decrease and CaF2 dissolves. F- can be removed by adding a strong acid: As pH decreases, [H+] increases and solubility increases. The effect of pH on solubility is dramatic. Acidic salts are more soluble in basic solution and less soluble in acidic solution Basic salts are more soluble in acidic solution and less soluble in basic solution.

Formation of Complex Ions A Consider the formation of Ag(NH3)2+: The Ag(NH3)2+ is called a complex ion. NH3 (the attached Lewis base) is called a ligand. The equilibrium constant for the reaction is called the formation constant, Kf:

Formation of Complex Ions Consider the addition of ammonia to AgCl (white precipitate): The overall reaction is Effectively, the Ag+(aq) has been removed from solution. By Le Châtelier’s principle, the forward reaction (the dissolving of AgCl) is favored.