# pH and Water

### pH

The pH of a solution ranges from 1-14, 1-6 are acidic, 7 is neutral, and 8-14 are basic. It is a measure of the amount of hydrogen ion concentration in a solution and any change greater than 0.5 can cause loss of function or death to any organism. Maintaining a constant pH is vital to existence, because pH also deals with the conformation and formation of hydrogen bonding. The change in pH can cause bonds to weaken, break, or not form at all.

### Water and pH

Water is essential for life; and it has unusual physical properties related to the weak
forces that connect atoms
• covalent: strong (142 –O:O- to 946 N:::N, -C:C- 343 kJ/mol; 0.15 nm)
• hydrogen: weak (12-30 kJ/mol ; 0.3 nm; combine two electronegative atoms, O, N, e.g. O...H-O: water, note 10-ps “flickering clusters”)
• ionic: moderate (20 kJ/mol ; 0.25 nm in crystal; but moderated by H2O: F =Q1Q2/εr2 and ε [dielectric constant] = 1 in vacuum, 80 in H2O)
• Vanderwaal’s: weak (0.4-4.0 kJ/mol ; 0.1 nm)
• hydrophobic: moderate (<40 kJ/mol; depend on hydrocarbons disrupting the H-bonds “flickering clusters” of H2O)
Dissociation of H-O bonds in water
H2O + H2O ↔ H3O+ + OH-
[H3O+] = [OH-] = 10-7 in pure H2O
as with hydrogen bonds, note “flickering” as H is traded around H2O molecules
Note the convention:
H2O ↔ H+ + OH- and [H3O+] = [H+]
Keq = [H+][OH-]/[H2O]
Because [H2O] is approx. constant, define Kw = Keq *[H2O]
Kw = [H+][OH-] = (10-7)( 10-7) = 10-14 M2
Define the p function: p[X] = - log10[X]
pKw = pH + pOH = 7 + 7 = 14 (because –log(10-14) = 14)

#### Strong Acids and Bases

pH of 0.1 M HCl = 1, etc.
pOH of 0.1 M NaOH = 1; pH of 0.1 M NaOH = 13; etc
What is the pH of 1 nM HCl? ([H+] = 10-7+ 10-9M)
Can you made a solution of pH 0? (pH 0: - log10(X) = 0, X = exp10(-0) = 1 M)
**Note that a base can be either an OH- donor or an H+ acceptor

#### Weak Acids

HA↔ H+ + A- HA is “conjugate acid”; Ais conjugate base
Ka = [H+][ A-]/[HA] = [H+]*[ A-]/[HA]
pKa = pH – log ([ A-]/[HA])
Example: CH3COOH ↔ H+ + CH3COO- Ka = 1.74 x 10-5; pKa = 4.76
What is the pH of a 0.1 M CH3COOH solution? What is [H+]?
CH3COOH ↔ H+ + CH3COO-
0.1 – X X X
Ka = [H+]*[CH3COO-]/[CH3COOH] = 1.74 x 10-5
X*X = (0.1-X)* 1.74 x 10-5
Assume (0.1-X) = 0.1 if error < 5%
X = sqrt (1.74 x 10-6) = 1.32 x 10-3 = [H+]
pH = - log10[H+] = 2.88

#### Weak Bases

A- + H2O ↔ HA + OH- HA is “conjugate acid”; A is conjugate base
Keq = [HA][OH-]/[ A-] [H2O]
Kb = Keq* [H2O] = [HA][OH-]/[ A-] Show that Kw = Ka * Kb
pKb = pOH – log ([HA]/[ A-]) pKw = pKa + pKb = 14 Useful!
Example: imidazole C3N2H4 + H2O ↔ C3N2H5+ + OH-
Kb = 0.98 x10-7; pKb = 7.01
What is the pH of a 0.1M imidazole solution in water? What is [H+]?
CH3COOH ↔ H+ + CH3COO-
0.1 – X X X
Kb = [C3N2H5+][OH-]/[C3N2H4] = 0.98 x 10-7
X*X = (0.1-X)* 0.98 x 10-7 Assume (0.1-X) = 0.1
X = sqrt (0.98 x 10-8) = 1.0 x 10-4 = [OH-]
pOH = 4; pH = 14 – 4 = 10; [H+] = 10-10 M