Biological Chemistry 1B Equilibria - Acid-Base Equilibria

Acid-Base Equilibria

  • Proton transfer is rapid, systems are at equilibrium.

Autoprotolysis of Water

  • H<em>2O+H</em>2O⇌H3O++OH−H<em>2O + H</em>2O \rightleftharpoons H_3O^+ + OH^-
  • K<em>w=[H</em>3O+][OH−]K<em>w = [H</em>3O^+][OH^-]
  • At 25 °C, [H<em>3O+]=[OH−]=10−7M[H<em>3O^+] = [OH^-] = 10^{-7} M and K</em>w=1×10−14K</em>w = 1 \times 10^{-14}
  • H2O(l)H_2O(l) has activity of 1.

The pH Scale

  • pX=−log⁡10XpX = -\log_{10}X
  • pK<em>w=−log⁡</em>10(10−14)=14pK<em>w = -\log</em>{10}(10^{-14}) = 14
  • pH=−log⁡<em>10[H</em>3O+]pH = -\log<em>{10}[H</em>3O^+]

Blood pH Range

  • Normal value: 7.4
  • Death is likely beyond ±0.4 units.
  • pH 7.0 corresponds to [H<em>3O+]=100[H<em>3O^+] = 100 nM, pH 7.8 corresponds to [H</em>3O+]=16[H</em>3O^+] = 16 nM.
  • Each pH unit represents a 10x change in [H3O+][H_3O^+].

Weak Acids

  • HA+H<em>2O⇌H</em>3O++A−HA + H<em>2O \rightleftharpoons H</em>3O^+ + A^-
  • Equilibrium constant: K<em>a=[H</em>3O+][A−][HA]K<em>a = \frac{[H</em>3O^+][A^-]}{[HA]}
  • Larger KaK_a = more acidic.
  • pK<em>a=−log⁡</em>10KapK<em>a = -\log</em>{10}K_a
  • Smaller pKapK_a = more acidic.

Weak Bases

  • B+H2O⇌BH++OH−B + H_2O \rightleftharpoons BH^+ + OH^-
  • Equilibrium constant: Kb=[BH+][OH−][B]K_b = \frac{[BH^+][OH^-]}{[B]}
  • Larger KbK_b = more basic.
  • pK<em>b=−log⁡</em>10KbpK<em>b = -\log</em>{10}K_b
  • Smaller pKbpK_b = more basic.

Conjugate Acid-Base Pairs

  • Strong acid implies a weak conjugate base, and vice versa.
  • K<em>a=[H</em>3O+][A−][HA]K<em>a = \frac{[H</em>3O^+][A^-]}{[HA]}
  • Kb=[HA][OH−][A−]K_b = \frac{[HA][OH^-]}{[A^-]}
  • K<em>aK</em>b=[H<em>3O+][OH−]=K</em>wK<em>a K</em>b = [H<em>3O^+][OH^-] = K</em>w
  • pK<em>w=pK</em>a+pKbpK<em>w = pK</em>a + pK_b

Examples of Weak Acid and Weak Base

  • Weak acid: CH<em>3COOH+H</em>2O⇌H<em>3O++CH</em>3COO−CH<em>3COOH + H</em>2O \rightleftharpoons H<em>3O^+ + CH</em>3COO^-
  • Weak base: R−NH<em>2+H</em>2O⇌R−NH3++OH−R-NH<em>2 + H</em>2O \rightleftharpoons R-NH_3^+ + OH^-

Using pKa

  • Indomethacin (pKa = 4.5).
  • Unionized form is better absorbed.
  • Empty stomach (low pH ~ 2.0) shifts equilibrium to the left.
  • Full stomach (pH ~ 6.0) shifts equilibrium to the right.

pH Dependence on Temperature

  • At 25 °C, K<em>w=1.0×10−14K<em>w = 1.0 \times 10^{-14}, and at 37 °C, K</em>w=2.4×10−14K</em>w = 2.4 \times 10^{-14}.
  • At 25 °C, [H3O+]=1.0×10−7[H_3O^+] = 1.0 \times 10^{-7}, so pH = 7.00.
  • At 37 °C, [H3O+]=2.4×10−14=1.55×10−7[H_3O^+] = \sqrt{2.4 \times 10^{-14}} = 1.55 \times 10^{-7}, so pH = 6.81.

pOH Scale

  • pOH=−log⁡10[OH−]pOH = -\log_{10}[OH^-]
  • [H<em>3O+][OH−]=K</em>w[H<em>3O^+][OH^-] = K</em>w
  • pH+pOH=pKwpH + pOH = pK_w
  • At T = 25 °C, pH+pOH=14pH + pOH = 14

General Terms for Weak Acids & Weak Bases

  • For weak acids: pH=12pK<em>a−12log⁡</em>10([HA]0)pH = \frac{1}{2}pK<em>a - \frac{1}{2}\log</em>{10}([HA]_0)
  • For weak bases: pH=pK<em>w−12pK</em>b+12log⁡<em>10([B]</em>0)pH = pK<em>w - \frac{1}{2}pK</em>b + \frac{1}{2}\log<em>{10}([B]</em>0)

Summary for Weak Acids & Weak Bases

  • For weak acid: pH=12pK<em>a−12log⁡</em>10([HA]0)pH = \frac{1}{2} pK<em>a - \frac{1}{2} \log</em>{10}([HA]_0)
  • For weak base: pH=pK<em>w−12pK</em>b+12log⁡<em>10([B]</em>0)pH = pK<em>w - \frac{1}{2} pK</em>b + \frac{1}{2} \log<em>{10}([B]</em>0)