15.8:
Weak Base Solutions
A weak base, like ammonia, is a Brønsted base that accepts a proton from water to produce the hydroxide ion. Weak bases react partially with water according to their base dissociation constant, Kb, which is 1.76 × 10−5 for ammonia.
The Kb for ammonia can be expressed as the ammonium ion concentration times the hydroxide ion concentration divided by the concentration of ammonia at equilibrium.
Kb can be used to determine the hydroxide ion concentration in a weak base solution and consequently, the pOH and pH of the solution.
The hydroxide ion concentration and pH of 0.23 M of ammonia solution can be determined using its base dissociation constant and by preparing an ICE table containing the initial and equilibrium values of the ammonia, ammonium ions, and hydroxide ions.
Substituting equilibrium concentrations in the Kb expression, Kb equals x times x divided by 0.23 minus x. As weak bases show partial dissociation, 0.23 minus x can be considered to be approximately 0.23.
When the equation is solved, x equals 2 × 10−3 M.
The approximation 0.23 minus x is equal to 0.23 is valid here as the hydroxide ion concentration is only 0.86% of 0.23 molar.
To calculate the pH of this solution, first determine the pOH by taking the negative log of the hydroxide ion concentration, which equals 2.70. The pH can be determined using the formula: pH plus pOH is equal to 14 and calculated to be 11.30.
The Kb for a weak base solution can be calculated if the pH of the weak base solution is known.
Methylamine is a weak base that partially dissociates in water into methylammonium ions and hydroxide ions.
The Kb for methylamine can be expressed as the methylammonium ion concentration times the hydroxide ion concentration divided by the concentration of methylamine at equilibrium.
To calculate the Kb of a 0.040 M methylamine solution with pH 11.6, first the pOH needs to be calculated followed by its hydroxide ion concentration. As the pH is 11.60, the pOH is 2.40, and its hydroxide ion concentration is 4.0 × 10−3.
The ICE table can be constructed from the initial and the equilibrium concentrations of methylamine, methylammonium, and hydroxide.
Substituting equilibrium concentrations in the expression for the Kb yields value for Kb, which is 4.4 × 10−4.
15.8:
Weak Base Solutions
Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other compounds, and an active ingredient in household cleaners. When dissolved in water, ammonia reacts partially to yield hydroxide ions, as shown here:
This is, by definition, an acid-base reaction, in this case involving the transfer of H+ ions from water molecules to ammonia molecules. Under typical conditions, only about 1% of the dissolved ammonia is present as NH4+ ions.
Calculating Hydroxide Ion Concentrations and pOH in a Weak Base Solution
Find the concentration of hydroxide ion, the pOH, and the pH of a 0.25 M solution of trimethylamine, a weak base:
The ICE table for this system is
| (CH3)3N (aq) | (CH3)3NH+ (aq) | OH− (aq) | |
| Initial Concentration (M) | 0.25 | 0 | ~0 |
| Change (M) | −x | +x | +x |
| Equilibrium Concentration (M) | 0.25 − x | 0 + x | ~0 + x |
Substituting the equilibrium concentration terms into the Kb expression gives
Assuming x << 0.25 and solving for x yields
This value is less than 5% of the initial concentration (0.25), so the assumption is justified.
As defined in the ICE table, x is equal to the equilibrium concentration of hydroxide ion:
The pOH is calculated to be
Using the relation;
permits the computation of pH:
Determination of Kb from pH
If the pH of 0.28 M solution of ethylamine (C2H5NH2) is 12.10, what is its Kb?
To calculate the Kb of ethylamine, first the pOH and the hydroxide ion concentration need to be determined. As the pH is 12.10, the pOH can be calculated as follows:
As the pOH is 1.90, the hydroxide ion concentration of the solution can be calculated using the formula
The ICE table can be constructed for this system as follows
| C2H5NH2 (aq) | C2H5NH3+ (aq) | OH− (aq) | |
| Initial Concentration (M) | 0.28 | 0 | ~0 |
| Change (M) | −0.0126 | +0.0126 | +0.0126 |
| Equilibrium Concentration (M) | 0.28 − 0.0126 | 0.0126 | 0.0126 |
As the 0.0126 M is 4.5% of 0.28 M, 0.28 − 0.0126 can be considered as almost equal to 0.28 M by the 5% rule.
After substituting the above values in the expression for the Kb of ethylamine,
This text is adapted from Openstax, Chemistry 2e Section 4.2: Classifying Chemical Reactions and 14.3 Relative Strengths of Acids and Bases.