Morpholine C4H9NO is a weak organic base with pKb = 5.68. Calculate the pH and the concentrations of all species present (C4H9NO, HC4H9NO+, and OH-) in a 0.0100 M morpholine solution.

Verified step by step guidance

1. Step 1: Identify the equilibrium reaction for morpholine in water. Morpholine (C4H9NO) is a weak base, so it will accept a proton from water to form its conjugate acid (HC4H9NO+) and hydroxide ions (OH-). The reaction is: C4H9NO + H2O \rightleftharpoons HC4H9NO^+ + OH^-.
2. Step 2: Write the expression for the base dissociation constant (Kb) using the given pKb value. The relationship between pKb and Kb is given by: pKb = -\log(Kb). Use this to find Kb.
3. Step 3: Set up an ICE (Initial, Change, Equilibrium) table to determine the concentrations of the species at equilibrium. Initially, the concentration of C4H9NO is 0.0100 M, and the concentrations of HC4H9NO+ and OH- are 0 M. Define the change in concentration of C4H9NO as -x, and the change in concentrations of HC4H9NO+ and OH- as +x.
4. Step 4: Substitute the equilibrium concentrations into the Kb expression. The expression for Kb is: Kb = [HC4H9NO^+][OH^-] / [C4H9NO]. Substitute the equilibrium concentrations from the ICE table into this expression.
5. Step 5: Solve for x, which represents the concentration of OH- at equilibrium. Use the value of x to find the pOH of the solution, and then calculate the pH using the relationship: pH + pOH = 14. Also, use x to find the concentrations of HC4H9NO+ and C4H9NO at equilibrium.

Key Concepts

Weak Bases and pKb

Weak bases are substances that partially ionize in solution to produce hydroxide ions (OH-) and their conjugate acids. The strength of a weak base is often expressed using the pKb value, which is the negative logarithm of the base dissociation constant (Kb). A higher pKb indicates a weaker base. In this case, morpholine has a pKb of 5.68, indicating it does not fully dissociate in solution.

Equilibrium and ICE Tables

In chemical reactions, especially in weak acid-base equilibria, the concept of equilibrium is crucial. An ICE (Initial, Change, Equilibrium) table helps organize the concentrations of reactants and products at different stages of the reaction. For morpholine, we can set up an ICE table to track the initial concentration of morpholine, the change as it ionizes, and the equilibrium concentrations of morpholine, its conjugate acid, and hydroxide ions.

pH and pOH Calculations

pH is a measure of the acidity or basicity of a solution, calculated as the negative logarithm of the hydrogen ion concentration. For basic solutions, pOH can also be calculated, which is related to pH by the equation pH + pOH = 14. In this problem, after determining the concentration of hydroxide ions (OH-) from the equilibrium expression, we can calculate the pOH and subsequently the pH of the morpholine solution.