What volume of 0.855 M KOH solution is required to make 3.55 L of a solution with a pH of 12.4?

• A. 0.300 L
• B. 0.600 L
• C. 0.150 L
• D. 0.450 L

Answer: (C)

Verified step by step guidance

1. First, understand that the pH of a solution is related to the concentration of hydrogen ions (H⁺) in the solution. A pH of 12.4 indicates a basic solution, which means we are dealing with hydroxide ions (OH⁻).
2. Calculate the pOH of the solution using the relationship: \( \text{pOH} = 14 - \text{pH} \). Substitute the given pH value to find the pOH.
3. Once you have the pOH, convert it to the hydroxide ion concentration \([\text{OH}^-]\) using the formula: \([\text{OH}^-] = 10^{-\text{pOH}}\).
4. Now, use the dilution equation \( M_1V_1 = M_2V_2 \), where \( M_1 \) is the initial molarity (0.855 M), \( V_1 \) is the volume of the KOH solution we need to find, \( M_2 \) is the molarity of the diluted solution (which is equal to the \([\text{OH}^-]\) concentration calculated), and \( V_2 \) is the final volume of the solution (3.55 L).
5. Rearrange the dilution equation to solve for \( V_1 \): \( V_1 = \frac{M_2V_2}{M_1} \). Substitute the known values to find the volume of the KOH solution required.