What volume of a 15.0% by mass NaOH solution, which has a density of 1.116 g/mL, should be used to make 5.00 L of an NaOH solution with a pH of 10.8?

Verified step by step guidance

1. Calculate the concentration of hydroxide ions \([OH^-]\) in the target solution using the pH value. Use the formula \(pOH = 14 - pH\) and \([OH^-] = 10^{-pOH}\).
2. Determine the molarity of the target NaOH solution using the concentration of \([OH^-]\) calculated in the previous step.
3. Calculate the mass of NaOH required to achieve the desired molarity in 5.00 L of solution using the formula \(\text{mass} = \text{molarity} \times \text{volume} \times \text{molar mass of NaOH}\).
4. Determine the mass of the 15.0% NaOH solution needed by using the formula \(\text{mass of solution} = \frac{\text{mass of NaOH}}{0.15}\).
5. Convert the mass of the 15.0% NaOH solution to volume using the density \(\text{volume} = \frac{\text{mass of solution}}{\text{density}}\).