8.2.5: Acid–Base Equilibrium Calculations- A Summary

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17.1: The Common-Ion Effect

The common-ion effect argues that the dissociation of a weak electrolyte is decreased by adding a strong electrolyte to the solution that has a common ion with the weak electrolyte.

17.2: Buffered Solutions

Buffers are solutions that resist a change in pH

17.2.1 Composition and Action of Buffered Solutions

buffers have both acidic and basic species to neutralize H⁺ and OH^- ions
acid dissociation equilibrium in buffered solution \[ HX(aq) \rightleftharpoons H^+ (aq) + X^-(aq) \nonumber \] with \[ K_a = \dfrac{[H^+][X^-]}{[HX]} \nonumber \] or \[[H^+]= K_a \dfrac{[HX]}{[X^-]} \nonumber \]
- pH determined by: value of K_a and the ratio of [HX]/[X^-]
- if OH^- added:
  - \[ OH^-(aq) + HX(aq) \rightleftharpoons H_2O(l) + X^-(aq) \nonumber \]
    - Therefore [HX] decreases and [X^-] increases
    - if amounts of HX and X^- present are very much larger than the amount of OH^- added, then the ratio of [HX]/[X^-] will not change much, and so the increase in pH due to the added hydroxide ion is rather small
- when [HX] and [X^-] are about the same, buffers are most effective: i.e., when \([H^+] = K_a\)

17.2.2 Buffer Capacity and pH

buffer capacity – amount of acid or base buffer can neutralize before the pH changes considerably
capacity depends on amount of acid or base in buffer
pH depends on K_a for acid and relative concentrations of the acid and base
Henderson-Hasselbalch Approximation: \[ pH = pK_a + \log_{10} \dfrac{[base]}{[acid]} \nonumber \]
[base] and [acid] = concentrations of conjugate acid-base pair
when [base]=[acid], pH = pK_a
can use initial concentrations of acid and base components of buffer directly into equation

17.2.3 Addition of Strong Acids or Bases to Buffers

reactions between strong acids and bases go to completion

Flowchart illustrating a mathematical process involving addition, intermediate calculations, and the final equation for \( \beta \). — Buffer contain HX and X minus. Add strong acid or strong bass for neutralization. Recalculate the concentrations. Use Ka to calculate the concentration of H plus and use that to get pH.

Either strong base or acid assumed to be completely consumed by reaction with buffer if buffering capacity is not exceeded

17.3: Acid-Base Titrations

solution containing a known [base] added to an acid or acid solution added to base
acid-base indicators used to signal equivalence point
titration curve – pH vs Volume

17.3.1 Strong Acid – Strong base Titrations

pH starts out low ends high
pH before equivalence point is pH of acid not neutralized by base
pH at equivalence point is pH of solution
pH equals 7.00
for strong base titrations, the pH starts high ends low

17.3.2 The Addition of a Strong Base to a Weak Acid

Reactions between weak acid and strong base goes to completion

calculating pH before equivalence point
- stoichiometric calculations: allow strong base to react to completion producing a solution containing a weak acid and its conjugate base

Flowchart illustrating a process involving calculations and evaluations, with labeled steps indicating various stages. — Start with solution contain weak acid and strong base. Go through neutralization. Calculate the concentrations after the reaction. Use Ka to and concentrations to calculate the concentration of H plus. Use H plus to figure out pH.

equilibrium calculation: use K_a and equilibrium expression to find equilibrium concentrations of the weak acid and its conjugate base, and H⁺

17.3.3 Titration Curves for Weak Acids or Weak Bases

Differences between strong acid-strong base titrations

solution of weak acid as higher initial pH than solution of a strong acid with same concentration
solution of weak acid rises more rapidly in early part of titration and more slowly as it reached the equivalence point
pH is not 7.00 at equivalence point

before equivalence point solution has mixture of weak acid and its salt
also called the buffer region of curve
at equivalence point solution contains only salt
weakly basic due to hydrolysis of anion
after equivalence point solution has mixture of salt and excess strong base
pH determined by [base]

17.3.4 Titrations of Polyprotic Acids

reaction occurs in series of steps
titration curve shows multiple equivalence points

17.4: Solubility Equilibria

17.4.1 The Solubility-Product Constant, K_sp

saturated solution – dissolved and undissolved solute are at equilibrium
expressed by g/L
molar solubility – moles of solute dissolved to form a liter of saturated solution (mol/L)
K_sp equilibrium constant for the equilibrium between an ionic solid and its saturated solution
Solubility of compound (g/L) à molar solubility of compound (mol/L) à [molar] of ions à K_sp of ions

17.5: Factors that Affect Solubility

solubility affected by temperature and presence of other solutes. The solubility of ionic compound affected by:

the presence of common ions
pH of solution
presence of complexing agent

17.5.1 Common-Ion Effect

solubility of slightly soluble salt decreases when a second solute has a common ion

17.5.2 Solubility and pH

solubility of any ionic compound affected if solution is acidic or basic
change only noticeable if both ions are moderately acidic or basic
solubility of slightly soluble salts containing basic anions increase as [H⁺] increases (as pH is lowered)
the more basic an anion is, the greater the solubility will be affected by pH

17.5.3 Formation of Complex Ions

metal ions act as Lewis acids in water
complex ion – metal ion and Lewis base bonded together
K_f – formation constant, equilibrium expression for formation of a complex ion
Solubility of metal salts increases in acceptable Lewis bases if metal forms a complex base
Lewis bases: \(NH_3\), \(CN^-\), \(OH^-\)

17.5.4 Amphoterism

amphoteric substances include hydroxides and oxides of: Al³⁺, Cr²⁺, Zn²⁺, and Sn²⁺
dissolve in strongly basic solutions
formation of complex anions containing, typically four, hydroxides bound to metal ion
amphoterism also associated with behavior of water molecules that surround and bond to metal ions by Lewis acid-base interactions

17.6: Precipitation and Separation of Ions

Q = ion product

If Q > K_sp, precipitation occurs until Q = K_sp
If Q = K_sp, equilibrium exists, have a saturated solution
If Q < K_sp, solid dissolves until Q = K_sp

17.6.1 Selective Precipitation of Ions

separation of ions in aqueous solution using a reagent that precipitates only with selected ions

17.7: Qualitative Analysis for Metallic Elements

Qualitative analysis: determines presence or absence of a particular metal ion

ions separated into broad groups on basis of solubility
ions separated by dissolving selected members in group
ions identified by specific tests

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