Acids and Bases

Acid-Base Calculations

1. pH and pOH

   • pH is a measure of the concentration of hydrogen ions ([H^+]) in a solution.

   • pOH is a measure of the concentration of hydroxide ions ([OH^-]) in a solution.

   • pH = -log_{10}[H^+]

   • pOH = -log_{10}[OH^-]

   • In aqueous solutions at 25^\circ C, pH + pOH = 14

2. Strong Acids and Bases

   • Strong acids and bases completely dissociate in water.

   • For strong acids, the concentration of H^+ is equal to the concentration of the acid.

   • For strong bases, the concentration of OH^- is equal to the concentration of the base.

     • Example: If you have a 0.01 M solution of HCl, then [H^+] = 0.01 M and pH = -log_{10}(0.01) = 2

3. Weak Acids and Bases

   • Weak acids and bases only partially dissociate in water.

   • The acid dissociation constant, K_a, is used to measure the strength of a weak acid.

   • The base dissociation constant, K_b, is used to measure the strength of a weak base.

   • K_a = \frac{[H^+][A^-]}{[HA]}, where HA is the weak acid and A- is its conjugate base.

   • K_b = \frac{[OH^-][HB^+]}{[B]}, where B is the weak base and HB+ is its conjugate acid.

   • The smaller the Ka or Kb, the weaker the acid or base.

4. Calculations with Weak Acids and Bases

   • To calculate the pH of a weak acid or base solution, you typically need to use an ICE table.

   • ICE (Initial, Change, Equilibrium) table helps to organize the concentrations of the species in the equilibrium.

   • Example: Calculate the pH of a 0.1 M solution of acetic acid (CH3COOH, Ka = 1.8 \times 10^{-5})

     • ICE Table:

       	CH_3COOH	H^+	CH_3COO^-
       Initial (I)	0.1	0	0
       Change (C)	-x	+x	+x
       Equilib (E)	0.1 - x	x	x

     • Ka = \frac{[H^+][CH3COO^-]}{[CH_3COOH]} = \frac{x^2}{0.1 - x} = 1.8 \times 10^{-5}

     • Assume x is small, so 0.1 - x ≈ 0.1

     • x^2 = 1.8 \times 10^{-6}

     • x = \sqrt{1.8 \times 10^{-6}} = 0.00134 M = [H^+]

     • pH = -log_{10}(0.00134) = 2.87

5. Acid-Base Titrations

   • Titration is a process used to determine the concentration of an acid or base by neutralizing it with a known concentration of a base or acid.

   • Equivalence point: The point at which the acid and base have completely reacted with each other.

   • Endpoint: The point at which the indicator changes color.

   • For a strong acid-strong base titration, the pH at the equivalence point is 7.

   • For a weak acid-strong base titration, the pH at the equivalence point is greater than 7.

   • For a strong acid-weak base titration, the pH at the equivalence point is less than 7.

6. Buffers

   • A buffer is a solution that resists changes in pH when small amounts of acid or base are added.

   • A buffer typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid.

   • The pH of a buffer can be calculated using the Henderson-Hasselbalch equation:

     • pH = pKa + log{10}(\frac{[A^-]}{[HA]})

     • pOH = pKb + log{10}(\frac{[HB^+]}{[B]})

     • where pKa = -log{10}(Ka) and pKb = -log{10}(Kb)

7. Polyprotic Acids

   • Acids that have more than one ionizable proton are called polyprotic acids (e.g