Determine the pH of each two-component solution. a. 0.050 M KOH and 0.015 M Ba(OH)₂ b. 0.265 M NH₄NO₃ and 0.102 M HCN c. 0.075 M RbOH and 0.100 M NaHCO₃ e. 0.115 M NaClO and 0.0500 M KI

Verified step by step guidance

1. Step 1: Identify the nature of each component in the solution. For example, KOH and Ba(OH)_2 are strong bases, NH_4NO_3 is a salt of a weak base (NH_3) and a strong acid (HNO_3), HCN is a weak acid, RbOH is a strong base, NaHCO_3 is a weak base, NaClO is a salt of a weak acid (HClO) and a strong base (NaOH), and KI is a neutral salt.
2. Step 2: For solutions containing strong bases (like KOH and Ba(OH)_2), calculate the total hydroxide ion concentration by adding the contributions from each base. Remember that Ba(OH)_2 dissociates to give two OH^- ions per formula unit.
3. Step 3: For solutions containing weak acids and their salts (like NH_4NO_3 and HCN), use the Henderson-Hasselbalch equation to find the pH. Calculate the pKa of HCN and use the concentrations of NH_4^+ and HCN to find the pH.
4. Step 4: For solutions containing a strong base and a weak base (like RbOH and NaHCO_3), determine the dominant species affecting the pH. Since RbOH is a strong base, it will dominate the pH calculation. Calculate the pH based on the concentration of OH^- from RbOH.
5. Step 5: For solutions containing salts of weak acids (like NaClO and KI), consider the hydrolysis of the anion from the weak acid (ClO^-). Use the Kb of ClO^- to calculate the pH, considering that KI does not affect the pH as it is a neutral salt.

Key Concepts

pH and pOH

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. Conversely, pOH measures the hydroxide ion concentration. The relationship between pH and pOH is given by the equation pH + pOH = 14 at 25°C. Understanding this relationship is crucial for determining the pH of solutions containing acids and bases.

Strong vs. Weak Bases

Strong bases, like KOH and Ba(OH)₂, completely dissociate in water, contributing to a higher concentration of hydroxide ions. In contrast, weak bases, such as NH₄NO₃ and HCN, do not fully dissociate, leading to a more complex equilibrium that affects pH. Recognizing the strength of the base is essential for calculating the resulting pH in mixed solutions.

Buffer Solutions

Buffer solutions resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid. In the context of the question, solutions like NaHCO₃ and NaClO can act as buffers, which is important for understanding how they will affect the overall pH when mixed with strong bases or acids.