Graphical Approach Independent Variable pH: the master variable - PDF document

CEE 680 Lecture #11 2/7/2020 Print version Updated: 7 February 2020 Lecture #11 Acids & Bases: Graphical Solutions I (Stumm & Morgan, Chapt.3 ) (Benjamin, Chapt. 4) David Reckhow CEE 680 #11 1 Graphical Approach  Independent Variable  pH: “the master variable”  Two types of graphs  Distribution diagrams  alpha values, independent of concentration  Log concentration diagrams  pC ‐ pH diagrams David Reckhow CEE 680 #11 2 1

CEE 680 Lecture #11 2/7/2020 Monoprotic acids: calculations Note:  0 +  1 = 1  Start with C and K a equations 3    C [ HA ] [ A ]    [ A ] C [ HA ]    1 [ HA ] C [ A ] 1+3   [ H ][ A ] 1+3  K a [ HA ]     [ H ][ A ]   [ H ] C [ HA ] K a  K a    C [ A ] [ HA ]           K C K [ A ] [ A ][ H ] K a [ HA ] [ HA ][ H ] C [ H ] a a For LogC vs pH K C  C [ H ]    [ A ] a [ HA ] diagrams     K [ H ] K [ H ] a a  [ A ] 1  1 [ HA ] 1  0  For distribution    C 1 [ H ] K a  C 1 diagrams K  [ H ] a David Reckhow CEE 680 #11 3 Distribution Diagram for Ammonia 1.0  [ A ] 1 [ HA ] 1 0.9     K a  C 1 [ H ] C 1  K [ H ] a 0.8  0 =NH 4  1 =NH 3 /C + /C 0.7 0.6 pH  0  1  0.5 6 1 0 0.4 8.3 0.91 0.09 9.3 0.5 0.5 0.3 10.3 0.09 0.91 0.2 12 0 1 0.1 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pH David Reckhow CEE 680 #11 4 2

CEE 680 Lecture #11 2/7/2020 Preparing log C vs. pH Diagrams  1. Draw [H + ] line  pH  ‐ log[H + ]  log[H + ] = ‐ pH  2. Draw [OH ‐ ] line 2  K w =[H + ][OH ‐ ]  log K w = log[H + ] + log[OH ‐ ]  log [OH ‐ ] = ‐ log [H + ] + log K w  log [OH ‐ ] = pH ‐ pK w  3. Draw [HA] and [A ‐ ] lines  see next slide David Reckhow CEE 680 #11 5 Calculations for log [HA] and log [A ‐ ] lines  K C C [ H ]    [ HA ] [ A ] a     K [ H ] K [ H ] a a 1+3 1+3  If pH << pK a , or [H + ] >> K a Log [A - ]=log C + pH - pK a Log [HA]=log C  If pH >> pK a , or [H + ] << K a Log [HA]=log C - pH + pK a Log [A - ]=log C  If pH = pK a , or [H + ] = K a Log [A - ]=log C - 0.3 Log [HA]=log C - 0.3 David Reckhow CEE 680 #11 6 3

CEE 680 Lecture #11 2/7/2020 0 -1 -2 Blank Axes -3 -4 -5 -6 Log C -7 -8 -9 -10 -11 -12 -13 -14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pH David Reckhow CEE 680 #11 7 0 -1 OH - H + -2 -3 -4 -5 -6 Log C -7 -8 -9 -10 -11 -12 -13 -14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pH David Reckhow CEE 680 #11 8 4

CEE 680 Lecture #11 2/7/2020 0 -1 OH - H + -2 1+3 Log C vs. pH for 10 ‐ 3 HOCl HOCl OCl - -3 -4 -5 -6 Log C -7 -8 -9 -10 2 -11 -12 4? -13 -14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pH David Reckhow CEE 680 #11 9  To next lecture David Reckhow CEE 680 #11 10 5