15.7

Weak Base Solutions

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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, K_b, which is 1.76 × 10⁻⁵ for ammonia.

The K_b for ammonia can be expressed as the ammonium ion concentration times the hydroxide ion concentration divided by the concentration of ammonia at equilibrium.

K_b 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 K_b expression, K_b 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 K_b 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 K_b 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 K_b 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 K_b yields value for K_b, which is 4.4 × 10⁻⁴.

Overview

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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:

Mass spectrometry process; diagram illustrating fragmentation pathways with labeled ions for analysis.

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:

Levers in static equilibrium diagram; ΣF=0, ΣM=0, force balance analysis; mechanical advantage.

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 K_b expression gives

Chromatography system diagram for compound separation; gas flow path and detector labels.

Assuming x << 0.25 and solving for x yields

Static equilibrium equations, ΣFx=0, ΣFy=0, demonstrating force balance in a diagram.

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:

Static equilibrium diagram; ΣFx=0; ΣFy=0; ΣMA=0; force balance and moments analysis; educational use.

The pOH is calculated to be

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"Damped harmonic oscillator equation, F=ma-mc, motion dynamics diagram, physics concept"

Using the relation;

Chromatography diagram showing column elution process with stationary and mobile phases labeled.

permits the computation of pH:

Quantum harmonic oscillator wave functions diagram; ψ0 to ψ3; energy states; physics education.

Determination of K_b from pH

If the pH of 0.28 M solution of ethylamine (C₂H₅NH₂) is 12.10, what is its K_b?

Static equilibrium diagram with forces labeled ΣFx=0, diagram for mechanical analysis and physics study.

To calculate the K_bof 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:

Chemical reaction mechanism diagram showing electrophilic aromatic substitution of benzene.

As the pOH is 1.90, the hydroxide ion concentration of the solution can be calculated using the formula

Static equilibrium, ΣFx=0 equation, vector forces diagram, mechanical physics, balance analysis.

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 K_bof ethylamine,

Mass-spring-damper model equations, includes F=ma, mx

This text is adapted from Openstax, Chemistry 2e Section 4.2: Classifying Chemical Reactions and 14.3 Relative Strengths of Acids and Bases.

Transcript

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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, K_b, which is 1.76 × 10⁻⁵ for ammonia.

The K_b for ammonia can be expressed as the ammonium ion concentration times the hydroxide ion concentration divided by the concentration of ammonia at equilibrium.

K_b 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 K_b expression, K_b 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 K_b 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 K_b 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 K_b 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 K_b yields value for K_b, which is 4.4 × 10⁻⁴.

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