Consider the titration of a 25.0-mL sample of 0.175 M CH₃NH₂ with 0.150 M HBr. Determine each quantity. a. the initial pH

Verified step by step guidance

1. insert step 1> Start by identifying the species present in the solution before any titrant is added. In this case, you have a solution of methylamine (CH_3NH_2), which is a weak base.
2. insert step 2> Write the equilibrium expression for the weak base dissociation: CH_3NH_2 + H_2O \rightleftharpoons CH_3NH_3^+ + OH^-.
3. insert step 3> Use the base dissociation constant (K_b) for methylamine to set up the equilibrium expression: K_b = \frac{[CH_3NH_3^+][OH^-]}{[CH_3NH_2]}.
4. insert step 4> Assume that the initial concentration of OH^- is negligible and that the change in concentration of CH_3NH_2 is small compared to its initial concentration. This allows you to simplify the expression to: K_b = \frac{x^2}{[CH_3NH_2]_{initial}}, where x is the concentration of OH^-.
5. insert step 5> Solve for x, which represents [OH^-], and then calculate the pOH of the solution. Finally, convert pOH to pH using the relation: pH = 14 - pOH.

Key Concepts

Acid-Base Titration

An acid-base titration is a quantitative analytical method used to determine the concentration of an acid or base in a solution. In this process, a solution of known concentration (the titrant) is added to a solution of unknown concentration until the reaction reaches its equivalence point, where the amount of acid equals the amount of base. Understanding this concept is crucial for calculating pH changes during the titration.

pH Calculation

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. For weak bases like CH3NH2, the initial pH can be calculated using the base dissociation constant (Kb) and the concentration of the base. This calculation is essential for determining the starting conditions before any titrant is added.

Weak Base and Strong Acid Interaction

In the titration of a weak base (like CH3NH2) with a strong acid (like HBr), the weak base will partially ionize in solution, establishing an equilibrium. The addition of the strong acid will shift this equilibrium, affecting the pH. Understanding the behavior of weak bases in the presence of strong acids is vital for predicting how the pH will change throughout the titration process.