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A weak base is a substance that does not completely ionize in solution. Unlike strong bases, which fully dissociate, weak bases only partially dissociate into ions. This incomplete dissociation is what defines a base as "weak" and impacts its ability to raise the pH of a solution significantly.

Examples of common weak bases include ammonia ( \( \text{NH}_3 \)), and some organic compounds such as amines.

• Weak bases only partially dissociate, resulting in an equilibrium between the undissociated base and the ions produced in solution.
• This equilibrium relationship is described by the base dissociation constant ( \( K_b \)), which quantifies the extent of the dissociation process.

Understanding this behavior is crucial when calculating variables like hydroxide ion concentration or the base dissociation constant of a weak base solution.

The pH and pOH relationship is central to understanding how acidic or basic a solution is. They are inversely related and their sum is always 14 in a standard aqueous solution at 25°C: \[ \text{pH} + \text{pOH} = 14 \].

In the given exercise, the \( \text{pH} \) of the weak base solution is \( 10.66 \). This implies a basic solution since its \( \text{pH} \) is greater than 7. By re-arranging the relationship, we calculated the \( \text{pOH} \) to be \( 3.34 \) using the expression:

• \( \text{pOH} = 14 - \text{pH} \)
• Results indicate that since \( \text{pH} \) is high (above 7), the concentration of hydroxide ions is relatively significant, affirming the basic nature of the solution.

This step helps connect directly to finding the hydroxide ion concentration, a key in calculating \( K_b \), reinforcing the foundational concept that high \( \text{pH} \) corresponds to basic solutions.

To find the hydroxide ion concentration in a solution, we use the \( \text{pOH} \) value. The relationship between \( \text{pOH} \) and the hydroxide ion concentration \( [\text{OH}^-] \) is given by:

\[ \text{pOH} = -\log [\text{OH}^-] \]

To find \( [\text{OH}^-] \), rearrange to:
\[ [\text{OH}^-] = 10^{- ext{pOH}} \] .

In our problem, the \( \text{pOH} \) is \( 3.34 \), leading us to:

• \( [\text{OH}^-] = 10^{-3.34} \approx 4.57 \times 10^{-4} \, \text{M} \)

Finding this concentration helps us understand the level of basicity in the solution, directly supporting the calculation of \( K_b \). It's also an essential step as it reveals the effectiveness of the base in generating hydroxide ions, advancing us towards analyzing equilibrium dynamics.

The equilibrium expression for a weak base dissociation is represented by the reaction equilibrium of the base in water. For our weak base, the reaction at equilibrium is:
\[ B + \text{H}_2\text{O} \rightleftharpoons \text{BH}^+ + \text{OH}^- \] .

Based on this, the expression for the base dissociation constant \( K_b \) is:

\[ K_b = \frac{[\text{BH}^+][\text{OH}^-]}{[B]} \] .

• The \( [\text{OH}^-] \) and \( [\text{BH}^+] \) are essentially equal at equilibrium since each molecule of the base \( B \) that dissociates forms one hydroxide ion and one conjugate acid ion.
• In this particular exercise, the initial concentration of the base \( [B] \) is \( 0.30 \, \text{M} \).

Consequently, substituting these values into the formula allows for the calculation of \( K_b \), depicting the degree of base ionization and its strength relative to other weak bases.