Acid-Base Chemistry Extremely important in the environment Examples • Acid rain • Biological systems - cells buffer (i.e., stabilize) their internal pH - biological processes in nature and in engineered processes need stable pH • Air-water interactions CO2 in atmosphere ↑↓ CO2 in surface waters ↑↓ + H2O H2CO3 ↑↓ - H+ HCO3- bicarbonate ion ↑↓ - H+ CO32- carbonate ion Thus, adding CO2 lowers the pH (makes system more acidic) • Acid mine drainage – Coal contains reduced sulfur and acid mine drainage has long been an environmental problem. Much of this sulfur is contained in pyrite, FeS2, a common mineral. On exposure to the air it oxidizes giving ferric, sulfate and hydrogen ions: FeS2 + 15/4 O2 + 1/2 H2O ↔ Fe3+ + 2 SO42- + 2 H+ The ferric ions undergo a hydrolysis reaction with water liberating more protons (thus making the system even more acidic) and precipitating ferric hydroxide (“rust”) on the stream bottom and banks. Fe3+ + 3 H2O ↔ Fe(OH)3 (s) + 3 H+ • A treatment question – Most metals (e.g., Fe, Cu, Zn etc) come from open-pit mines using large equipment for processing. After removal of the metals from the finely crushed rock the residual “tailings” are disposed in piles or disposal areas. The residual sulfide will, over time, oxidize causing the material to become acidic and thus leaching metals into surface and ground water. To prevent this potential contamination, limestone (CaCO3) is added to neutralize the released hydrogen ions. Can you calculate the amount of limestone that would have to be added if, for instance, the waste material had been found to contain 4% S? Consider the reaction H2O ↔ H+ + OHBased on the definition of K K= {H }{OH } + {H 2 O} - 1000 g L = 55.5 mol/L ⇒ concentration of H2O: 18 g/mol ~ But Define {H2O} = 1 In a dilute system { } = [ ] Kw = [H+] [OH-] at 25°C, Kw = 1.0 × 10-14 [H+] [OH-] = 10-14 When are they equal? [H+] = [OH-] = (10-14)1/2 = 10-7 But in an acidified lake [H+] = 10-4; [OH-] = 10-14/[H+] = 10-14/10-4 = 10-10 Range of concentrations is orders of magnitude. So – define “p” = “-log10” pH = -log10 [H+] pOH = -log10 [OH-] So we don’t always have to deal with negative values - if we just use logs Note the – sign: as [H+] increases, pH decreases pH 7 pH 4 [H+] = 10-7 [H+] = 10-4 [OH-] = 10-7 [OH-] = 10-10 Convert the equilibrium expression -log10 ([H+] [OH-]) = -log10 [H+] + -log10 [OH-] = -log10 Kw = pKw = -log10 10-14 = 14 and -log10 [H+] + -log10 [OH-] = 14 so pH + pOH =14 It is useful to consider log – log plots of concentration 0 + log [H ] 2 10 4 - log C = pC - log [OH ] -4 6 pH 7 8 + - [H ] = [OH ] 10 10 -10 12 14 0 2 4 6 8 10 12 14 pH --- "M aste r Variable " We can treat acids and bases in a similar manner Definitions Acid can donate H+ (proton) Base can accept H+ Generic acid “HA” HA ↔ H+ + A- (dissociation) A strong acid (HCl – hydrochloric, HNO3 – nitric, H2SO4 – sulfuric, but only first proton) is one for which the dissociation is complete in water If the dissociation is <100%, it is a weak acid Generic base “BOH” BOH ↔ B+ + OH- If the dissociation is <100%, it is a weak base Strong bases dissociate completely in water (NaOH – sodium hydroxide, KOH – potassium hydroxide) (How does this involve H+? generate 1 OH-, this accepts 1 H+ OH- + H+ → H2O net: BOH + H+ → B+ + H2O The extent of these reactions may be determined using dissociation constants. We can so the same thing we did for H2O: HA ↔ H+ + AH+ AKa = = " acidity constant" [HA] [ ][ ] (eqn 1) Example acetic acid CH3COOH = “HA” and acetate ion CH3COO- = “A-” pKa = 4.7, Ka = 10-4.7 = 2.0 × 10-5 Put 10-4 mol CH3COOH in 1 L solution. What is the pH? Is this a strong acid? From equation 1: 2 × 10 [H ][CH COO ] = + −5 3 - [CH 3COOH ] 2 × 10 −5 [CH 3 COOH ] + [ ] and H = [CH COO ] - 3 we could solve for [CH 3COOH ] but we would still need another equation. [CH COO ] 3 - What else do we know? 10-4 M! [CH3COOH] + [CH3COO-] = 10-4 = CT (eqn 2) Combining eqn 1 and eqn 2 gives [HA] = CT and [A ] = - [H ] K + [H ] + + a Ka (eqn 3) (eqn 4) CT Ka + H+ We will use these instead of solving directly for [H+]. The two equations generate a useful graph (see Appendix p 9 for mathematical details). [ ] 0 -log C = pC 2 log C T CH COO3 4 6 CH COOH 3 8 10 0 2 4 pKa 6 pH 8 10 12 14 This graph shows the concentration of the CH3COOH (protonated) species and CH3COO- (dissociated) species at any pH. Note that at a low pH, the protonated species is predominant, but at higher pH, the dissociated species predominates. Notice that when the pH equals the pKa, the CH3COOH and CH3COOconcentrations are equal. Because a strong acid completely dissociates to A-, the pKa would have to be very low. At any pH below 4.7, acetic acid is less than 50% dissociated. It is a weak acid. A strong acid would have to have a very small pKa. Actually, their values are negative! So now we know that acetic acid is a weak acid. But we never figured out where we were on the log C – pH diagram (i.e., the pH after adding 10-4 M acetic acid to the H2O). We need another equation. There are two that can be used, either a charge balance or a proton condition. In this course we’ll just use the charge balance which simply says that the total negative charge in the system must equal the overall positive chare (“electroneutrality”). We add the concentrations of all anions on one side of the equation, cations on the other. In our example [H+] = [H3CCOO-] + [OH-] We finish our problem by combining our acetic acid graph with our previous graph for [H+] and [OH-], and look for a pH where the [H+], [H3CCOO-], and [OH-] lines satisfy the above condition. 0 H+ 2 CH3COO -log C = pC 4 - OH - 6 8 CH COOH 3 10 12 14 0 2 4 6 pH 8 10 12 14 You could have plotted -log C as is frequently done. The graph would have been identical except for the sign of the values on the y-axis. If you draw the graph by hand, you must use graph paper. Preferable is 10 × 10 to the centimeter (10 × 10 to the inch may also be used). The solution to the charge balance equation is found by inspection being careful to consider only the lines of species that are represented in the electroneutrality equation and remembering that the graph shows logarithmic, not linear, values. The charge balance is fulfilled when pH ≅ 4.5, where [CH3COO-] ≅ 10-4.5, [H+] ≅ 10-4.5, and [OH-] is so small that it can be neglected (~10-9.5). So the pH of the acetic acid solution will be 4.5. So the overall approach is this: 1. Get the pKa. It’s –log10 Ka if you have Ka. If you have Kb or pKb (the base dissociation constant), use Kb = 10-14/ Ka, or p Kb = 14 – p Ka. 2. Get CT and –log10CT (pCT). CT is the sum of [HA] and [A-] already in the solution plus the amount added. It must be in moles/L. 3. Draw the graph in the following steps: a. Draw axes as shown in the example. b. Draw a vertical line at pH = pKa. c. Draw a horizontal line at –log10CT. d. Locate the intersection from (b) and (c) and from it, draw lines downward in each direction at 45°. Also locate a point (x) 0.3 units below this intersection. e. Draw a line that connects the lower portion of each 45° with point x and then over onto the horizontal CT line. The one that’s higher at low pH is protonate; the one that is higher at high pH is dissociated. f. Now draw the H+ and OH- lines. These are 45° lines that cross at pH = 7 4. Write the charge balance (electroneutrality) equation*. Find the location on your graph where it is satisfied. Usually only one negatively charged species and one positively charged species will be significant, and the others will be low enough to neglect. 5. Once you have this point, it gives you the pH and the concentration (-log10 concentrations) for all species. We will stop with this application. But this type of graph can be used to analyze titrations, precipitation, equilibria with the atmosphere or other gas phases, and mineral equilibria. * Any species with more than one + or – charge must include this coefficient in the equation. Remember, it is moles of charge not moles of compound that is being considered. For example, adding Ca(OH)2 to H2O, we would write 2 [Ca2+] + [H+] = [OH-] Appendix: How the pC-pH graph is obtained from the equilibrium equations (eqn. 3 and eqn. 4). 1. First consider the low pH region, where pH<< pKa. Then –log10[H+] << -log10 Ka, and [H+] >> Ka. Equation 4 was CT K a A- = Ka + H+ The denominator can now be approximated by [H+], so taking logs gives log10 [A-] = log10 CT + log10 Ka – log [H+] p[A-] = pCT + log10 Ka + pH which is the 45° line upward*. Also using [H+] >> Ka, eqn. 3 gives p[HA] = pCT, the horizontal line. [ ] [ ] 2. Now at high pH, we have [H+] << Ka. Equation 3 gives p[HA] = pCT + pH - pKa, thedownward* sloping 45° line. Equation 4 gives [A-] = CT, horizontal line. 3. At the intersection, where the [HA] and [A-] lines cross, [HA] = [A-] and equation 1 then gives Ka = [H+] or the pH where the lines cross must be where pH = pKa. Then, since [A-] = [HA], both of these must be CT/2. Then p[A-] = p[HA] = -log10(CT/2) = -log10CT – log (1/2) = -log10CT + 0.3 So, the lines cross at 0.3 units below* the CT line. * If “upward” and “downward” seem inconsistent, note that the pC axis increases going downward.