Acids and Bases Formulas and Equations

Calculating pH and pOH

• pH Calculation:
  • Formula: (-\log[H^+])
  • ([H^+]) is equivalent to the hydronium ion concentration.
• pOH Calculation:
  • Formula: (-\log[OH^-])
• Relationship:
  • (pH + pOH = 14)

Calculating Concentrations

• Hydrogen Ion Concentration:
  • From pH: ([H^+] = 10^{-pH})
• Hydroxide Ion Concentration:
  • From pOH: ([OH^-] = 10^{-pOH})
• Autoionization of Water:
  • ([H^+] \times [OH^-] = 1 \times 10^{-14} = K_w) at 25°C

Weak Acids

• Weak Acid Reaction:
  • Example: HA + H2O → H3O^+ + A^−
• Acid Dissociation Constant (Ka):
  • Formula: (Ka = \frac{[H3O^+][A^-]}{[HA]})
  • Use approximation: ([H^+] \approx \sqrt{[HA] \times Ka}) if (Ka < 1 \times 10^{-4})
• Direct pH Calculation for Weak Acids:
  • Formula: (pH = \frac{1}{2}(pKa - \log[HA]))
• pKa Relation:
  • (pKa = -\log(Ka))

Weak Bases

• Weak Base Reaction:
  • Example: B + H2O → HB^+ + OH^−
• Base Dissociation Constant (Kb):
  • Formula: (Kb = \frac{[HB^+][OH^-]}{[B]})
  • Use approximation: ([OH^-] \approx \sqrt{[B] \times Kb}) if (Kb < 1 \times 10^{-4})
• Direct pH Calculation for Weak Bases:
  • Formula: (pH = 14 - \frac{1}{2}(pKa + \log[B]))
• pKa from Kb:
  • (Ka = \frac{K_w}{Kb})

Buffer Solutions

• pH of Buffer Solution:
  • Formula: (pH = pKa + \log\left(\frac{[Base]}{[Acid]}\right))
  • The ratio can be used in molarity or moles.
• Equal Concentrations:
  • pH = pKa when ([Base] = [Acid])

Quadratic Equation and Special Cases

• Quadratic Formula:
  • Used when (Ka) or (Kb) is not (< 1 \times 10^{-4})
  • Standard form: (ax^2 + bx + c = 0)
  • Solution: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a})

Additional Resources

• Links to formula sheets and videos for further practice are available in the description section of the lecture.

These notes cover essential formulas and concepts needed for understanding reactions and calculations involving acids and bases, including relationships between different constants and methods for calculating pH under varying conditions.