Morphine is a weak base. A 0.150 M solution of morphine has a pH of 10.7. What is K_b for morphine?

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Identify the relationship between pH and pOH: \( \text{pH} + \text{pOH} = 14 \). Use this to find pOH from the given pH.

Calculate the hydroxide ion concentration \([\text{OH}^-]\) using the formula \([\text{OH}^-] = 10^{-\text{pOH}}\).

Set up the expression for the base dissociation constant \(K_b\) for morphine: \(K_b = \frac{[\text{OH}^-][\text{BH}^+]}{[\text{B}]}\), where \([\text{B}]=0.150\,\text{M}\) and \([\text{OH}^-] = [\text{BH}^+]\).

Assume that the change in concentration of morphine due to dissociation is negligible, so \([\text{B}]\) remains approximately 0.150 M.

Substitute the values into the \(K_b\) expression and solve for \(K_b\).

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주요 개념

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Weak Bases

Weak bases are substances that partially ionize in solution, establishing an equilibrium between the un-ionized base and its ions. Unlike strong bases, which completely dissociate, weak bases have a lower tendency to accept protons (H+), resulting in a less significant increase in pH. Understanding the behavior of weak bases is crucial for calculating their dissociation constants.

pH and pOH

pH is a measure of the hydrogen ion concentration in a solution, indicating its acidity or basicity. The pH scale ranges from 0 to 14, with values below 7 being acidic, 7 neutral, and above 7 basic. The relationship between pH and pOH is given by the equation pH + pOH = 14, which is essential for determining the hydroxide ion concentration in basic solutions.

Base Dissociation Constant (Kb)

The base dissociation constant (Kb) quantifies the strength of a weak base in solution, representing the equilibrium constant for its ionization. It is calculated using the concentrations of the products and reactants at equilibrium. For a weak base like morphine, Kb can be derived from the pH of the solution, allowing for the determination of its ionization extent and strength.

Morphine is a weak base. A 0.150 M solution of morphine has a pH of 10.7. What is Kb for morphine?