Study Notes on Coefficients, Q, K, and Precipitation

Coefficients Become Exponents

• Example: Ag₂CO₃ in Na₂CO₃ solution
  • Chemical equilibrium: Ag₂CO₃(s) ⇌ 2Ag⁺ + CO₃²⁻
  • Solubility product, $K_{sp}$:
    • Defined as:
      $K<em>{sp} = [Ag^+]^2[CO</em>3^{2-}]$
  • Important Note:
    • The coefficient (2) in front of Ag⁺ becomes the exponent in the $K_{sp}$ expression.
    • It does NOT mean to divide by 2 nor does it disappear in the calculations.

Mixing → Dilution

• First Example: Calculating concentrations upon mixing solutions
  • Given:
    • 0.200 L of 0.0045 M AgNO₃
    • 0.100 L of 0.075 M NaBrO₃
  • Total volume:
    • $0.200 L + 0.100 L = 0.300 L$
  • Calculation Needed:
    • Find the concentration:
    • Use moles of solute divided by total volume before calculating the reaction quotient, Q.
  • Common Mistake:
    • Failing to calculate total concentration before proceeding to Q computation.

Q vs K (Will Precipitate Form?)

• Example: Determining precipitation of BaF₂
  • Calculation for $Q$:
    • $Q = [Ba^{2+}][F^-]^2$
  • Comparison with $K_{sp}$:
    • If:
    • Q < K_{sp} → No precipitation occurs.
    • Q > K_{sp} → Precipitation occurs.
    • Note:
    • Do NOT set Q equal to K unless determining a threshold.

Selective Precipitation

• Example: Comparison of Cu⁺ and Pb²⁺ with I⁻
  • Required concentrations of iodide:
    • For CuI, required [I⁻] = $5.3 × 10^{-8}$
    • For PbI₂, required [I⁻] = $2.65 × 10^{-3}$
  • Outcome:
    • The smaller [I⁻] concentration needed means CuI precipitates before PbI₂.
    • Important Note:
    • Avoid comparing $K_{sp}$ values for different ions unless the metal ion concentrations are identical.

Percent Removed

• Example: Removal of Cu⁺ before PbI₂ begins to precipitate
  • Steps to determine percent removed:
  1. Determine [I⁻] at the point when PbI₂ begins to precipitate.
  2. Insert that value into CuI’s $K_{sp}$.
  3. Calculate the remaining concentration of [Cu⁺].
  4. Calculate the percentage removed.
  • Result: Approximately 99.998 ext{%} of Cu⁺ is removed before PbI₂ starts precipitating.
  • Notation: The pattern observed in these calculations is consistent once recognized.

Hydroxide / pH Problems

• Example: Precipitation of Fe(OH)₃
  • Reaction equilibrium:
    • Fe(OH)₃ ⇌ Fe³⁺ + 3OH⁻
  • Solubility product expression:
    • $K_{sp} = [Fe^{3+}][OH^-]^3$
  • Steps for calculation:
    • Set the $K_{sp}$ expression equal to the known concentrations
    • Solve for [OH⁻].
  • Conversion Steps:
    • Convert [OH⁻] to pOH then to pH as needed.
  • Common Mistakes:
    • Be cautious about cube root errors.

Ksp + Complex Ion (Kf)

• Example: AgBr and NH₃ reaction
  • Dissolution reaction:
    • AgBr(s) ⇌ Ag⁺ + Br⁻
  • Formation of complex:
    • Ag⁺ + 2NH₃ ⇌ Ag(NH₃)₂⁺
  • Overall constant:
    • $K<em>{overall} = K</em>{sp} imes K_f$
  • Solubility Concept:
    • The formation of a complex ion increases the solubility of the metal ion in the solution by pulling it out of the solid phase.

Ultra-Fast Recognition Guide

• Questions to consider:
  • If the question states:
    • "Find solubility" → refer to Pure $K_{sp}$.
    • "Will precipitate form?" → compare Q vs K.
    • "Which precipitates first?" → analyze Selective Precipitation.
    • "Percent removed?" → Selective process + calculate remaining.
    • "At what pH?" → apply Ksp along with pOH.
  • For conditions involving NH₃ or CN⁻:
    • Use the formula:
      $K<em>{sp} imes K</em>f$
    • Consider impact on solubility and precipitation dynamics.