Calculate [OH-] and pH for each of the following strong base solutions: (a) 0.182 M KOH, (b) 3.165 g of KOH in 500.0 mL of solution, (c) a solution formed by mixing 20.0 mL of 0.015 M Ba(OH)2 with 40.0 mL of 8.2 x 10^-3 M NaOH.

Verified step by step guidance

1. For part (a), recognize that KOH is a strong base and dissociates completely in water. The concentration of OH^- ions is equal to the concentration of KOH. Therefore, [OH^-] = 0.182 M.
2. To find the pH from the [OH^-], use the relation pOH = -log[OH^-]. Then, use the equation pH + pOH = 14 to find the pH.
3. For part (b), first calculate the number of moles of KOH using the formula: moles = mass (g) / molar mass (g/mol). The molar mass of KOH is approximately 56.11 g/mol.
4. Next, calculate the concentration of KOH in the solution by dividing the number of moles by the volume of the solution in liters (0.500 L). This gives you [OH^-].
5. For part (c), calculate the moles of OH^- from each solution separately. For Ba(OH)₂, remember it dissociates into two OH^- ions per formula unit. Add the moles of OH^- from both solutions, then divide by the total volume of the mixed solution in liters to find the final [OH^-]. Use this to calculate pOH and then pH.

Key Concepts

Strong Bases and Hydroxide Ion Concentration

Strong bases, like KOH and Ba(OH)2, completely dissociate in water to produce hydroxide ions (OH-). The concentration of OH- can be calculated directly from the molarity of the strong base solution. For example, a 0.182 M KOH solution will yield an OH- concentration of 0.182 M, as each mole of KOH produces one mole of OH-.

pH and pOH Relationship

The pH scale measures the acidity or basicity of a solution, while pOH measures the concentration of hydroxide ions. They are related by the equation pH + pOH = 14 at 25°C. To find the pH from the OH- concentration, first calculate pOH using pOH = -log[OH-], then use the relationship to find pH.

Dilution and Mixing Solutions

When mixing solutions, the total volume and the concentrations of the solutes must be considered. For example, when mixing 20.0 mL of 0.015 M Ba(OH)2 with 40.0 mL of 8.2 x 10^-3 M NaOH, the total volume becomes 60.0 mL, and the total OH- concentration can be calculated by finding the moles of OH- from each solution and dividing by the total volume.