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Chemistry · Ch 6 — Equilibrium

Ionization of Weak Bases

6.11.4

Ionization of Weak Bases

The Ionization of Weak Bases

A weak base, like a weak acid, does not fully dissociate in water. When a general weak base MOH is placed in water, an equilibrium is established between the unionized base and its ions:

MOH(aq)⇌M+(aq)+OH−(aq)\text{MOH(aq)} \rightleftharpoons \text{M}^+(aq) + \text{OH}^-(aq)

This is a dynamic equilibrium. At any given time, only a fraction of the MOH molecules have broken apart into M⁺ and OH⁻ ions. The extent of this ionization is described by an equilibrium constant specific to bases, called the base ionization constant, denoted by KbK_b.

The Base Ionization Constant, KbK_b

For the equilibrium above, the law of mass action gives:

Kb=[M+][OH−][MOH]K_b = \frac{[\text{M}^+][\text{OH}^-]}{[\text{MOH}]}

This expression is the direct analogue of the acid dissociation constant KaK_a. The square brackets denote equilibrium concentrations in molarity (mol/L). A very small value of KbK_b (e.g., 10−510^{-5} or smaller) tells you the base is weak — it exists mostly in the unionized form at equilibrium.

Table 6.7The Values of the Ionization Constant of Some Weak Bases at 298 K
BaseKbK_b
Dimethylamine, (CH3)2NH(CH_3)_2NH5.4×10−45.4 \times 10^{-4}
Triethylamine, (C2H5)3N(C_2H_5)_3N6.45×10−56.45 \times 10^{-5}
Ammonia, NH3NH_3 or NH4OHNH_4OH1.77×10−51.77 \times 10^{-5}
Quinine (a plant product)1.10×10−61.10 \times 10^{-6}
Pyridine, C5H5NC_5H_5N1.77×10−91.77 \times 10^{-9}

Relating KbK_b to Degree of Ionization (α\alpha)

Just as with weak acids, we can express KbK_b in terms of the initial concentration and the degree of ionization. Let:

  • cc = initial concentration of the weak base MOH (in M)
  • α\alpha = degree of ionization (the fraction of MOH that has ionized at equilibrium)

The ICE table for the ionization is:

SpeciesMOHM⁺OH⁻
Initial conc. (M)cc00
Change (M)−cα-c\alpha+cα+c\alpha+cα+c\alpha
Equilibrium conc. (M)c(1−α)c(1-\alpha)cαc\alphacαc\alpha

Substituting these equilibrium concentrations into the expression for KbK_b:

Kb=(cα)(cα)c(1−α)=c2α2c(1−α)K_b = \frac{(c\alpha)(c\alpha)}{c(1-\alpha)} = \frac{c^2 \alpha^2}{c(1-\alpha)}

This simplifies to the central relationship:

Kb=cα21−αK_b = \frac{c \alpha^2}{1-\alpha}

This equation is identical in form to the one for weak acids. For a very weak base (KbK_b is very small), α\alpha is also very small, so 1−α≈11-\alpha \approx 1. This gives a useful approximation:

Kb≈cα2orα≈KbcK_b \approx c \alpha^2 \quad \text{or} \quad \alpha \approx \sqrt{\frac{K_b}{c}}

Watch out

The approximation 1−α≈11-\alpha \approx 1 is only valid when α\alpha is less than about 5%. If the base is not extremely weak or the concentration is very low, you must solve the quadratic equation cα2+Kbα−Kb=0c\alpha^2 + K_b\alpha - K_b = 0 for α\alpha.

The pKbpK_b Scale

Just as with KaK_a and pH, the enormous range of KbK_b values is more conveniently handled using a logarithmic scale. The base ionization constant is expressed as pKbpK_b:

pKb=−log⁡(Kb)pK_b = -\log(K_b)

A smaller pKbpK_b corresponds to a stronger weak base (larger KbK_b). A larger pKbpK_b corresponds to a weaker base.

Ammonia and Organic Bases

The most common weak base is ammonia, NH3NH_3. Its ionization in water is:

NH3(aq)+H2O(l)⇌NH4+(aq)+OH−(aq)NH_3(aq) + H_2O(l) \rightleftharpoons NH_4^+(aq) + OH^-(aq)

Here, ammonia acts as a base by accepting a proton from water, leaving behind a hydroxide ion. The equilibrium constant for this reaction is KbK_b. …

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