Calculate [OH-] and pH for (a) 1.5 × 10^-3 M Sr(OH)_2 (b) 2.250 g of LiOH in 250.0 mL of solution (c) 1.00 mL of 0.175 M NaOH diluted to 2.00 L (d) a solution formed by adding 5.00 mL of 0.105 M KOH to 15.0 mL of 9.5 × 10^-2 M Ca(OH)_2.

Verified step by step guidance

1. Step 1: For part (a), determine the concentration of hydroxide ions [OH^-] from Sr(OH)_2. Since Sr(OH)_2 dissociates into one Sr^2+ ion and two OH^- ions, multiply the given concentration of Sr(OH)_2 by 2 to find [OH^-].
2. Step 2: Calculate the pH for part (a) using the formula pH = 14 - pOH. First, find pOH by taking the negative logarithm (base 10) of the [OH^-] concentration.
3. Step 3: For part (b), calculate the moles of LiOH by dividing the mass of LiOH by its molar mass. Then, find the concentration of LiOH by dividing the moles by the volume of the solution in liters. Since LiOH dissociates into one Li^+ and one OH^-, the concentration of LiOH is equal to [OH^-].
4. Step 4: For part (c), use the dilution formula M1V1 = M2V2 to find the new concentration of NaOH after dilution. Here, M1 is the initial concentration, V1 is the initial volume, M2 is the final concentration, and V2 is the final volume. The concentration of NaOH is equal to [OH^-].
5. Step 5: For part (d), calculate the moles of OH^- from both KOH and Ca(OH)_2 separately. Add the moles of OH^- together and divide by the total volume of the solution in liters to find the final [OH^-]. Then, calculate the pH using the formula pH = 14 - pOH, where pOH is found from the [OH^-].

Key Concepts

Strong Bases and Hydroxide Ion Concentration

Strong bases, such as Sr(OH)₂, LiOH, NaOH, and KOH, completely dissociate in water to produce hydroxide ions (OH⁻). The concentration of OH⁻ can be calculated directly from the molarity of the base, taking into account the stoichiometry of the dissociation reaction. For example, Sr(OH)₂ produces two OH⁻ ions per formula unit, which must be factored into the concentration calculation.

pH and pOH Relationship

The pH and pOH of a solution are related through the equation pH + pOH = 14 at 25°C. pH measures the acidity of a solution, while pOH measures its basicity. To find the pH from the hydroxide ion concentration, first calculate the pOH using pOH = -log[OH⁻], and then use the relationship to find pH. This is essential for understanding the overall acidity or basicity of the solution.

Dilution and Concentration Calculations

When diluting a solution, the concentration and volume are related by the equation C₁V₁ = C₂V₂, where C is concentration and V is volume. This principle is crucial for calculating the new concentration of a solution after dilution, such as when 1.00 mL of NaOH is diluted to 2.00 L. Understanding this concept allows for accurate determination of the resulting hydroxide ion concentration and subsequent pH.