SOLUTION EQUILIBRIA BUFFER – A solution of about equal amounts of a weak acid and its weak conjugate base A buffer is resistant to changes in pH because it can neutralize any strong acid or base added to it 2A-1 (of 16) A solution contains both HF and FWeak acid: HF Weak conjugate base: FIf a strong acid is added to the buffer: 1 HCl molecule 2A-2 (of 16) A solution contains both HF and FWeak acid: HF Weak conjugate base: FIf a strong acid is added to the buffer: H3O+ + F- → HF + H2O The STRONG ACID (H3O+) is reacted away completely by the WEAK CONJUGATE BASE (F-) The original [H3O+] is virtually unchanged 2A-3 (of 16) 1 HCl molecule A solution contains both HF and FWeak acid: HF Weak conjugate base: FIf a strong base is added to the buffer: OH- + HF → H2O + FThe STRONG BASE (OH-) is reacted away completely by the WEAK ACID (HF) The original [H3O+] is virtually unchanged 2A-4 (of 16) 1 OH- ion The higher the concentrations of the weak acid and weak conjugate base in the buffer, the more strong acid or strong base it can neutralize This buffer can neutralize 2 H3O+’s and 2 OH-’s 2A-5 (of 16) CALCULATING THE pH OF A BUFFER SOLUTION Calculate the pH of a solution 0.25 M in hydrofluoric acid (Ka = 7.2 x 10-4) and 0.50 M in sodium fluoride A buffer: contains a weak acid (HF) and its weak conjugate base (F-) HF (aq) + H2O (l) ⇆ Initial M’s Change in M’s Equilibrium M’s 0.25 - x Ka = [H3O+][F-] 7.2 x 10-4 = x(0.50 + x) _____________ 0.25 -x ______________ (0.25 – x) [HF] 3.6 x 10-4 = x = 2A-6 (of 16) [H3O+] 3.44 = pH H3O+ (aq) + F- (aq) ~0 +x 0.50 +x x 0.50 + x 7.2 x 10-4 = x(0.50) _________ 0.25 CALCULATING THE pH OF A BUFFER SOLUTION Calculate the pH of a solution 0.25 M in hydrofluoric acid (Ka = 7.2 x 10-4) and 0.50 M in sodium fluoride [H3O+][F-] _____________ = Ka [HF] [H3O+] x [F-] ______ log [H3O+] + log [F-] ______ = log Ka [HF] = Ka [HF] - log [H3O+] - log [F-] ______ = - log Ka [HF] log [H3O+] x [F-] ______ [HF] = Ka pH - log [F-] ______ = pKa [HF] pH = pKa + log [F-] ______ [HF] 2A-7 (of 16) CALCULATING THE pH OF A BUFFER SOLUTION Calculate the pH of a solution 0.25 M in hydrofluoric acid (Ka = 7.2 x 10-4) and 0.50 M in sodium fluoride pH = pKa + log [A-] _____ [HA] HENDERSON-HASSELBALCH EQUATION 2A-8 (of 16) CALCULATING THE pH OF A BUFFER SOLUTION Calculate the pH of a solution 0.25 M in hydrofluoric acid (Ka = 7.2 x 10-4) and 0.50 M in sodium fluoride pH = pKa + log [A-] _____ [HA] DAVID HASSELHOFF EQUATION This can be used when a solution contains both a weak acid and its weak conjugate base 2A-9 (of 16) CALCULATING THE pH OF A BUFFER SOLUTION Calculate the pH of a solution 0.25 M in hydrofluoric acid (Ka = 7.2 x 10-4) and 0.50 M in sodium fluoride Determine the pKa of the weak acid pKa = -log Ka = -log (7.2 x 10-4) = 3.143 Use the David Hasselholf Equation pH = pKa + log [F-] = 3.143 + log (0.50 M) [HF] (0.25 M) ______ 2A-10 (of 16) ___________ = 3.44 CALCULATING THE pH OF A BUFFER SOLUTION pH = pKa + log [weak conj base] ______________________ [weak acid] pH = pKa + log (nweak conj base) / vol ________________________ (nweak ccid) / vol pH = pKa + log (nweak conj base) _________________ (nweak acid) Useful when buffers are produced from mixing different solutions together 2A-10 (of 16) Find the pH of a buffer solution that is prepared by mixing 300. mL of 2.50 M acetic acid (Ka = 1.8 x 10-5) and 200. mL of 2.50 M sodium acetate. HC2H3O2 : Weak Acid NaC2H3O2 : Salt w/ Weak Conj. Base Solutions are mixed calculate the moles of all species present 2.50 mol HC2H3O2 x 0.300 L solution _______________________ = 0.750 mol HC2H3O2 L solution 2.50 M NaC2H3O2 2.50 M Na+ and 2.50 M C2H3O2- 2.50 mol C2H3O2- x 0.200 L solution _______________________ L solution 2A-12 (of 16) = 0.500 mol C2H3O2- Find the pH of a buffer solution that is prepared by mixing 300. mL of 2.50 M acetic acid (Ka = 1.8 x 10-5) and 200. mL of 2.50 M sodium acetate. HC2H3O2 : Weak Acid NaC2H3O2 : Salt w/ Weak Conj. Base Determine the pKa of the weak acid pKa = -log Ka = -log (1.8 x 10-5) = 4.745 Use the David Hasselholf Equation pH = pKa + log nC2H3O2- = 4.745 + log (0.500 mol) nHC2H3O2 (0.750 mol) _________ 2A-13 (of 16) ______________ = 4.57 Find the pH of a solution that is prepared by mixing 150. mL of 0.300 M nitrous acid (Ka = 4.0 x 10-4) and 100. mL of 0.200 M sodium nitrite. HNO2 : Weak Acid NaNO2 : Salt w/ Weak Conj. Base Solutions are mixed calculate the moles of all species present 0.300 mol HNO2 _____________________ x 0.150 L solution = 0.0450 mol HNO2 L solution 0.200 M NaNO2 0.200 M Na+ and 0.200 M NO2- 0.200 mol NO2- x 0.100 L solution ____________________ L solution 2A-14 (of 16) = 0.0200 mol NO2- Find the pH of a solution that is prepared by mixing 150. mL of 0.300 M nitrous acid (Ka = 4.0 x 10-4) and 100. mL of 0.200 M sodium nitrite. HNO2 : Weak Acid NaNO2 : Salt w/ Weak Conj. Base Determine the pKa of the weak acid pKa = -log Ka = -log (4.0 x 10-4) = 3.398 Use the David Hasselholf Equation pH = pKa + log nNO2- = 3.398 + log (0.0200 mol) nHNO2 (0.0450 mol) _______ 2A-15 (of 16) ________________ = 3.05 What must be the [NO2-]/[HNO2] to make a buffer with a pH = 3.00? HNO2 : Weak Acid 3.00 = 3.398 + NO2- : Weak Conjugate Base log [NO2-] _________ [HNO2] -0.398 = log [NO2-] _________ [HNO2] 0.40 = [NO2-] _________ [HNO2] = 0.40 ______ 1.0 When the pKa of the weak acid is within 1 pH unit of the desired pH, then the weak acid / weak conjugate base combination is a good choice for preparing the buffer 2A-16 (of 16) Find the pH of 500. mL of a buffer solution that is 1.50 M in acetic acid and 1.00 M in sodium acetate if 0.100 moles of sodium hydroxide are added. HC2H3O2 : Weak Acid NaOH NaC2H3O2 : Salt w/ Weak Conj. Base : Strong Base Look up the Ka of the weak acid and determine its pKa pKa = -log Ka 2B-1 (of 18) = -log (1.8 x 10-5) = 4.745 Find the pH of 500. mL of a buffer solution that is 1.50 M in acetic acid and 1.00 M in sodium acetate if 0.100 moles of sodium hydroxide are added. HC2H3O2 : Weak Acid NaOH NaC2H3O2 : Salt w/ Weak Conj. Base : Strong Base Calculate the moles of all species present 1.50 mol HC2H3O2 x 0.500 L solution _______________________ = 0.750 mol HC2H3O2 L solution 1.00 M NaC2H3O2 1.00 M Na+ and 1.00 M C2H3O2- 1.00 mol C2H3O2- x 0.500 L solution _______________________ = 0.500 mol C2H3O2- L solution 0.100 mol NaOH 2B-2 (of 18) 0.100 mol Na+ and 0.100 mol OH- Find the pH of 500. mL of a buffer solution that is 1.50 M in acetic acid and 1.00 M in sodium acetate if 0.100 moles of sodium hydroxide are added. HC2H3O2 : Weak Acid NaOH NaC2H3O2 : Salt w/ Weak Conj. Base : Strong Base Strong bases react completely with acids OH- (aq) + HC2H3O2 (aq) → the weak acid is reacted away by the strong base 2B-3 (of 18) H2O (l) + C2H3O2- (aq) the weak conjugate base is produced Find the pH of 500. mL of a buffer solution that is 1.50 M in acetic acid and 1.00 M in sodium acetate if 0.100 moles of sodium hydroxide are added. HC2H3O2 : Weak Acid NaOH NaC2H3O2 : Salt w/ Weak Conj. Base : Strong Base Strong bases react completely with acids OH- (aq) + HC2H3O2 (aq) → Initial moles 0.100 Reacting moles – 0.100 0 Final moles 2B-4 (of 18) 0.750 – 0.100 0.650 H2O (l) + C2H3O2- (aq) 0.500 + 0.100 0.600 Find the pH of 500. mL of a buffer solution that is 1.50 M in acetic acid and 1.00 M in sodium acetate if 0.100 moles of sodium hydroxide are added. HC2H3O2 : Weak Acid NaOH NaC2H3O2 : Salt w/ Weak Conj. Base : Strong Base David Hasselholf Equation pH = pKa + log nC2H3O2_________ nHC2H3O2 = 4.745 + log 0.600 mol _____________ 0.650 mol 2B-5 (of 18) = 4.71 Find the pH of 500. mL of a buffer solution that is 1.50 M in acetic acid and 1.00 M in sodium acetate if 0.100 moles of sodium hydroxide are added. HC2H3O2 : Weak Acid NaOH NaC2H3O2 : Salt w/ Weak Conj. Base : Strong Base Amend the David Hasselholf Equation pH = pKa + log nC2H3O2- + nOH_________ __________ nHC2H3O2 – nOH- = 4.745 + log (0.500 mol + 0.100 mol) ______________________________ (0.750 mol – 0.100 mol) 2B-6 (of 18) = 4.71 200. mL of a solution 0.40 M in ammonia and 0.30 M in ammonium chloride are mixed with 100. mL of 0.45 M hydrochloric acid. Find the pH. NH3 : Weak Base NH4Cl : Salt w/ Weak Conj. Acid HCl : Strong Acid Look up the Ka of the weak acid and determine its pKa pKa = -log Ka 2B-7 (of 18) = -log (5.6 x 10-10) = 9.252 200. mL of a solution 0.40 M in ammonia and 0.30 M in ammonium chloride are mixed with 100. mL of 0.45 M hydrochloric acid. Find the pH. NH3 : Weak Base NH4Cl : Salt w/ Weak Conj. Acid HCl : Strong Acid Calculate the moles of all species present 0.40 mol NH3 _________________ x 0.200 L solution = 0.080 mol NH3 L solution 0.30 mol NH4+ x 0.200 L solution __________________ = 0.060 mol NH4+ L solution 0.45 mol H3O+ x 0.100 L solution __________________ L solution 2B-8 (of 18) = 0.045 mol H3O+ 200. mL of a solution 0.40 M in ammonia and 0.30 M in ammonium chloride are mixed with 100. mL of 0.45 M hydrochloric acid. Find the pH. NH3 : Weak Base NH4Cl : Salt w/ Weak Conj. Acid HCl : Strong Acid Strong acids react completely with bases 2B-9 (of 18) 200. mL of a solution 0.40 M in ammonia and 0.30 M in ammonium chloride are mixed with 100. mL of 0.45 M hydrochloric acid. Find the pH. NH3 : Weak Base NH4Cl : Salt w/ Weak Conj. Acid HCl : Strong Acid Amend the David Hasselholf Equation pH = pKa + log nNH3 – nH3O+ ___________ ______ nNH4+ + nH3O+ = 9.255 + log (0.080 mol – 0.045 mol) _______________________________ (0.060 mol + 0.045 mol) 2B-10 (of 18) = 8.78 A buffer can be made by mixing solutions of: (1) a weak acid and a salt containing its weak conjugate base (2) a weak acid and a lesser amount of a strong base (3) a weak base and a lesser amount of a strong acid 2B-11 (of 18) (1) If 600. mL of 0.50 M nitrous acid and 400. mL of 0.50 M sodium nitrite are mixed, a buffer is produced. Find the pH. HNO2 : Weak Acid NaNO2 : Salt containing the Conjugate Base the solution is a buffer Look up the Ka of the weak acid and determine its pKa pKa = -log Ka 2B-12 (of 18) = -log (4.0 x 10-4) = 3.398 (1) If 600. mL of 0.50 M nitrous acid and 400. mL of 0.50 M sodium nitrite are mixed, a buffer is produced. Find the pH. HNO2 : Weak Acid NaNO2 : Salt containing the Conjugate Base the solution is a buffer Calculate the moles of all species present 0.50 mol HNO2 x 0.600 L solution ____________________ = 0.30 mol HNO2 L solution 0.50 mol NO2- __________________ L solution 2B-13 (of 18) x 0.400 L solution = 0.20 mol NO2- (1) If 600. mL of 0.50 M nitrous acid and 400. mL of 0.50 M sodium nitrite are mixed, a buffer is produced. Find the pH. HNO2 : Weak Acid NaNO2 : Salt containing the Conjugate Base the solution is a buffer Use the David Hasselholf Equation pH = pKa + log nNO2- = 3.398 + log (0.20 mol) nHNO2 (0.30 mol) _______ 2B-14 (of 18) _____________ = 3.22 (2) If 600. mL of 0.50 M nitrous acid and 400. mL of 0.50 M sodium hydroxide are mixed, a buffer is produced. Find the pH. HNO2 : Weak Acid NaOH : Strong Base Calculate the moles of all species 0.50 mol HNO2 x 0.600 L solution ____________________ = 0.30 mol HNO2 L solution 0.50 mol OH- _________________ L solution 2B-15 (of 18) x 0.400 L solution = 0.20 mol OH- (2) If 600. mL of 0.50 M nitrous acid and 400. mL of 0.50 M sodium hydroxide are mixed, a buffer is produced. Find the pH. HNO2 : Weak Acid NaOH : Strong Base Use the Amended David Hasselholf Equation pH = pKa + log nNO2- + nOH- _________ __________ nHNO2 – nOH= 3.398 + log (0 mol + 0.20 mol) ___________________________ (0.30 mol – 0.20 mol) 2B-16 (of 18) = 3.70 (3) If 500. mL of 0.60 M sodium nitrite and 250. mL of 0.80 M hydrochloric acid are mixed, a buffer is produced. Find the pH. NaNO2 : Salt containing a Weak Base HCl : Strong Acid Calculate the moles of all species 0.60 mol NO2- ___________________ x 0.500 L solution = 0.30 mol NO2- x 0.250 L solution = 0.20 mol H3O+ L solution 0.80 mol H3O+ _________________ L solution 2B-17 (of 18) (3) If 500. mL of 0.60 M sodium nitrite and 250. mL of 0.80 M hydrochloric acid are mixed, a buffer is produced. Find the pH. NaNO2 : Salt containing a Weak Base HCl : Strong Acid Use the Amended David Hasselholf Equation pH = pKa + log nNO2- – nH3O+ _________ ___________ nHNO2 + nH3O+ = 3.398 + log (0.30 mol – 0.20 mol) _____________________________ (0 mol + 0.20 mol) 2B-18 (of 18) = 3.10 ACID-BASE TITRATIONS Acid-base reactions with either a strong base or strong acid run to completion Determinations of volumes or molarities are stoichiometric calculations 2C-1 (of 18) If a 10.0 mL sample of an acetic acid solution is titrated with 24.5 mL of a 0.250 M lithium hydroxide solution, find the molarity of the acetic acid This is a stoichiometric calculation HC2H3O2 xM 10.0 mL 1 mol + → LiOH H(OH) LiC2H3O2 0.250 M 24.5 mL 1 mol 0.250 mol LiOH x 0.0245 L __________________ L x 1 mol HC2H3O2 ___________________ 1 mol LiOH = 0.613 M HC2H3O2 2C-2 (of 18) + x 1 ____________ 0.0100 L 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (a) Calculate the volume of NaOH solution needed to neutralize the HZ solution. NaOH 0.400 M x mL 1 mol + HZ x 1 mol NaOH ________________ L = 0.0500 L NaOH solution 2C-3 (of 18) NaZ + H(OH) 1.00 M 20.0 mL 1 mol 1.00 mol HZ x 0.0200 L __________________ → 1 mol HZ x L _____________________ 0.400 mol NaOH = 50.0 mL NaOH solution 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (b) Calculate the pH of the HZ solution before the titration if the Ka of HZ is 1.0 x 10-5. The pH of a weak acid is determined from an ICE table for the ionization reaction of the weak acid HZ (aq) Initial M’s Change in M’s Equilibrium M’s Ka = [H3O+][Z-] ____________ + H3O+ (aq) + Z- (aq) 1.00 -x 0 +x 0 +x 1.00 - x x x 1.00 x 10-5 = [HZ] pH = -log (3.162 x 10-3) = 2.50 2C-4 (of 18) ⇆ H2O (l) x2 ____________ (1.00 – x) x = 3.162 x 10-3 M 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (c) Calculate the pH of the solution after 10.0 mL of the NaOH was added. This solution will contain both a weak acid and its conjugate base Calculate moles of all species 1.00 mol HZ ________________ x 0.0200 L solution = 0.0200 mol HZ L solution 0.400 mol OH- x 0.0100 L solution = 0.00400 mol OH__________________ L solution 2C-5 (of 18) 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (c) Calculate the pH of the solution after 10.0 mL of the NaOH was added. Use the Amended David Hasselholf Equation pH = pKa + log nZ- + nOH_________ __________ nHZ – nOH- = 5.00 + log (0 mol + 0.00400 mol) ___________________________________ (0.0200 mol – 0.00400 mol) 2C-6 (of 18) = 4.40 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (d) Calculate the pH of the solution after 25.0 mL of the NaOH was added. Calculate moles of all species 1.00 mol HZ ________________ x 0.0200 L solution = 0.0200 mol HZ L solution 0.400 mol OH- x 0.0250 L solution = 0.0100 mol NaOH __________________ L solution = 0.0100 mol OH- 2C-7 (of 18) 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (d) Calculate the pH of the solution after 25.0 mL of the NaOH was added. Use the Amended David Hasselholf Equation pH = pKa + log nZ- + nOH- _________ __________ nHZ – nOH= 5.00 + log (0 mol + 0.0100 mol) _________________________________ = 5.00 (0.0200 mol – 0.0100 mol) At the half equivalence point, pH = pKa 2C-8 (of 18) 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (e) Calculate the pH of the solution at the equivalence point. (remembering 50.0 mL of base needed) Calculate moles of all species 1.00 mol HZ ________________ x 0.0200 L solution = 0.0200 mol HZ L solution 0.400 mol OH- x 0.0500 L solution = 0.0200 mol NaOH __________________ L solution = 0.0200 mol OH- 2C-9 (of 18) 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (e) Calculate the pH of the solution at the equivalence point. Use the Amended David Hasselholf Equation pH = pKa + log nZ- + nOH- _______ __________ nHZ – nOH= 5.00 + log (0 mol + 0.0200 mol) _________________________________ = ??? (0.0200 mol – 0.0200 mol) At the equivalence point, the solution contains only the conjugate base, Z- 2C-10 (of 18) 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (e) Calculate the pH of the solution at the equivalence point. The pH of a weak base is determined from an ICE table for the ionization reaction of the weak base Z- (aq) + H2O (l) ⇆ HZ (aq) + OH- (aq) Calculate the molarity of the Z- in the solution at the equivalence point 0.0200 mol Z- __________________ = 0.2857 M mol Z- 0.0700 L Calculate the Kb of the weak base ZKb = Kw = 1.00 x 10-14 ____ ______________ Ka 1.0 x 10-5 2C-11 (of 18) = 1.0 x 10-9 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (e) Calculate the pH of the solution at the equivalence point. Z- (aq) Initial M’s Change in M’s Equilibrium M’s Kb = [HZ][OH-] _____________ 2C-12 (of 18) H2O (l) ⇆ 0.2857 -x 0.2857 - x 1.0 x 10-9 = HZ (aq) + OH- (aq) 0 +x x 0 +x x x2 _______________ (0.2857 – x) [Z-] 1.69 x 10-5 = + x = [OH-] 4.77 = pOH 1.0 x 10-9 = x2 __________ (0.2857) 9.23 = pH 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (f) Calculate the pH of the solution after 60.0 mL of the NaOH was added. Calculate moles of all species 1.00 mol HZ ________________ x 0.0200 L solution = 0.0200 mol HZ L solution 0.400 mol OH- x 0.0600 L solution = 0.0240 mol NaOH __________________ L solution = 0.0240 mol OH- 2C-13 (of 18) 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (f) Calculate the pH of the solution after 60.0 mL of the NaOH was added. Use the Amended David Hasselholf Equation pH = pKa + log nZ- + nOH______ __________ nHZ – nOH= 5.00 + log (0 mol + 0.0200 mol) _________________________________ = ??? (0.0200 mol – 0.0240 mol) Impossible – the strong base did not all react away There are 0.0040 moles of excess OH- in the solution 2C-14 (of 18) 20.0 mL of a 1.00 M HZ solution is titrated with a 0.400 M NaOH solution. (f) Calculate the pH of the solution after 60.0 mL of the NaOH was added. Calculate the molarity of the OH- in the solution 0.0040 mol OH- ____________________ 0.0800 L pOH = pH 1.30 = 12.70 2C-15 (of 18) = 0.050 M mol OH- Weak Acid-Strong Base Titration (HZ and NaOH) At the start of the titration : pure HZ At the half-neutralization point, half HZ, half Z- pH = pKa At the equivalence point : pure ZA weak acid-strong base titration produces an equivalence point pH > 7 because at the equivalence point the solution contains a weak base (Z-) 2C-16 (of 18) INDICATORS Phenolphthalein is a weak organic acid (pKa = 9.75) HInd (aq) + H2O (l) ⇆ H3O+ (aq) + Ind- (aq) colorless pink colorless if more HInd, pink if more IndKa = [H3O+][Ind-] _______________ [Hind] Color change occurs when [Ind-] = [Hind] , so when Ka = [H3O+] or pKa = pH Phenolphthalein will change color at pH = 9.75 good for titrations in which the equivalence point pH is slightly basic 2C-17 (of 18) Strong Acid-Strong Base Titration (HA and NaOH) A strong acid-strong base titration produces an equivalence point pH = 7 because at the equivalence point the solution contains a non base (A-) An indicator with a pKa = 7 should be used for this titration 2C-18 (of 18)