Buffer Intensity g Amount of strong 1 .2 1 .0 0 .8 0 .6 0 - PDF document

CEE 680 Lecture #17 2/24/2020 Print version Updated: 24 February 2020 Lecture #17 Acids/Bases and Buffers: Fundamentals & Buffer Intensity (Benjamin, Chapter 5) (Stumm & Morgan, Chapt. 3 ) David Reckhow CEE 680 #17 1 10 -2 M HAc Buffer Intensity g  Amount of strong 1 .2 1 .0 0 .8 0 .6 0 .4 0 .2 0 .0 -0 .2 1 2 acid or base 1 1 required to cause a M id -p o in t 1 0 specific small shift p H 4 .7 9 in pH S ta rtin g P o in t 8 p H 3 .3 5 E n d P o in t pH 7  p H 8 .3 5 pH dC dC 6     B A  C B 5 dpH dpH  pH  4 C B 3 Slope = 1/  2 -0 .2 0 .0 0 .2 0 .4 0 .6 0 .8 1 .0 1 .2 f David Reckhow CEE 680 #17 2 1

CEE 680 Lecture #17 2/24/2020 Buffers: Acetic Acid with Acid/Base Addition  1. List all species present  (use NaOH and HCl as acid/base) Six total  H + , OH ‐ , HAc, Ac ‐ , Na + , Cl ‐  2. List all independent equations  equilibria 1  K a = [H + ][Ac ‐ ]/[HAc] = 10 ‐ 4.77 2  K w = [H + ][OH ‐ ] = 10 ‐ 14  mass balances 5 C A = [Cl - ]  C T = [HAc]+[Ac ‐ ] 3 C B = [Na + ] 6  electroneutrality:  (positive charges) =  (negative charges)  Note: we can’t use the PBE because we’re essentially adding an acid and its conjugate base  [Na + ] + [H + ] = [OH ‐ ] + [Ac ‐ ] + [Cl ‐ ] 4 David Reckhow CEE 680 #17 3 Acetic Acid with Acid/Base Addition (cont.) 2 K w = [H + ][OH - ]  3. Use ENE, substitute & solve for C B ‐ C A [OH - ] = K w /[H + ] 4  [Na + ] + [H + ] = [OH ‐ ] + [Ac ‐ ] + [Cl ‐ ] 5 1,2,3,4,5,6 C A = [Cl - ]  C B + [H + ] = K w /[H + ] + K a C T /{K a +[H + ]} + C A C B = [Na + ] 6 3 C T = [HAc]+[Ac - ]  C B ‐ C A = K w /[H + ] ‐ [H + ] + K a C T /{K a +[H + ]} [HAc]= C T - [Ac - ] 1 K a = [H + ][Ac - ]/[HAc] K a = [H + ][Ac - ]/ {C T -[Ac - ]}  4. Take derivative K a C-K a [Ac - ]= [H + ][Ac - ] 1+3  with respect to [H + ] K a C=[Ac - ]{K a +[H + ]} [Ac - ]=K a C T /{K a +[H + ]} David Reckhow CEE 680 #17 4 2

CEE 680 Lecture #17 2/24/2020 Acetic Acid with Acid/Base Addition (cont.)  Take the derivative with respect to [H + ] of:  C B = C A + K w /[H + ] ‐ [H + ] + K a C T /{K a +[H + ]} dC K C K     B w 1 T a     2 2 d [ H ] [ H ]   K [ H ] a  But this is not exactly what we want  Factor out  equation  dC dC d [ H ]   B  B *  dpH d [ H ] dpH  and recall:  ln[ H ]      pH log[ H ] 2 . 303   d ln[ H ] d [ H ]    dpH  2 . 303 2 . 303 [ H ]  d [ H ]    2 . 303 [ H ] dpH David Reckhow CEE 680 #17 5 Acetic Acid with Acid/Base Addition (cont.)  so: dC     2 . 303 [ H ] B  d [ H ]  and combining:   K C K          2 . 303 [ H ] w 1 T a      2 2 [ H ]   K [ H ]   a  [ HA ] [ H ]       K C K [ H ] 0   C K [ H ]       2 . 303 w [ H ] T a T a      2  [ H ]   [ A ] K K [ H ]      a a 1   C K [ H ] T a      [ HA ][ A ]             2 . 303 [ OH ] [ H ] C     2 . 303 [ OH ] [ H ] C    T 0 1  T 2   [ HA ] [ A ]   David Reckhow CEE 680 #17 6 3

CEE 680 Lecture #17 2/24/2020 0 Example H + OH - -1 Trichlorophenol Trichlorophenate ion -2 -3 Log C -4 -5  Trichlorophenol -6  pKa = 6.00 -7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14  C T = 10 ‐ 2 pH 0.0 1.0 Mid-point 0.2 0.8 pH 6.0 Starting Point 0.4 0.6 pH 4 g f 0.6 0.4 End Point pH 9 0.8 0.2 1.0 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pH David Reckhow CEE 680 #17 7 0.006  See also Local Maximimum @ g=0.5 S&M fig 0.005 Buffer Intensity, B (M/pH) 3.10 0.004 0.003 0.002 0.001 Local Min. Local Min. @ g=0 @ g=1 0.000 2 3 4 5 6 7 8 9 10 11 12 pH David Reckhow CEE 680 #17 8 4

CEE 680 Lecture #17 2/24/2020 Equations for polyprotic acids  Analogous to the monoprotic systems    monoprotic         2 . 303 [ OH ] [ H ] C T 0 1    diprotic            2 . 303 [ OH ] [ H ] C C T 0 1 T 1 2  triprotic                 2 . 303 [ OH ] [ H ] C C C T 0 1 T 1 2 T 2 3 David Reckhow CEE 680 #17 9 Buffer example  Design a buffer using phosphate that will hold its pH at 7.0  0.05 even when adding 10 ‐ 3 moles per liter of a strong acid or base  first determine the required buffer intensity  10 3 dC B     0 . 02 dpH 0 . 05  Next look at the buffer equation and try to simplify based on pH range of interest                 2 . 303 [ OH ] [ H ] C C C T 0 1 T 1 2 T 2 3 0 0 0 0 David Reckhow CEE 680 #17 10 5

CEE 680 Lecture #17 2/24/2020 Buffer example (cont.)  This gives us the simplified version that can be further simplified   C     2 . 303 T 1 2 0 0 0 0 0 . 02          1 1   2    K  K K    K [ H ] [ H ] [ H ] 2 . 303 1 1 2 2 3 3    K   2 K K K   [ H ] [ H ] [ H ] 1 1 2 2 0 . 02          1 1   K  2 . 303 1 [ H ] 1 2     K  [ H ] 2 0 . 02     1 2 . 303 4 . 22  0 . 037 M David Reckhow CEE 680 #17 11 Acid Neutralizing Capacity  Net deficiency of protons  with respect to a proton reference level  when the reference level is H 2 CO 3 , the ANC=Alkalinity  conservative, not affected by T or P  In a monoprotic system:  f x     [ANC] = [A ‐ ] + [OH ‐ ] ‐ [H + ]   ANC dpH = C T  1 + [OH ‐ ] ‐ [H + ]   f n David Reckhow CEE 680 #17 12 6

CEE 680 Lecture #17 2/24/2020 David Reckhow CEE 680 #17 13 David Reckhow CEE 680 #17 14 7

CEE 680 Lecture #17 2/24/2020  To next lecture David Reckhow CEE 680 #17 15 8