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?

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Calculate the concentration of hydroxide ions \([OH^-]\) in the target solution using the pH value. Use the formula \(pOH = 14 - pH\) and \([OH^-] = 10^{-pOH}\).

Determine the molarity of the target NaOH solution using the concentration of \([OH^-]\) calculated in the previous step.

Calculate the mass of NaOH required to achieve the desired molarity in 5.00 L of solution using the formula \(\text{mass} = \text{molarity} \times \text{volume} \times \text{molar mass of NaOH}\).

Determine the mass of the 15.0% NaOH solution needed by using the formula \(\text{mass of solution} = \frac{\text{mass of NaOH}}{0.15}\).

Convert the mass of the 15.0% NaOH solution to volume using the density \(\text{volume} = \frac{\text{mass of solution}}{\text{density}}\).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Concentration and Mass Percent

Mass percent is a way of expressing the concentration of a solution, defined as the mass of solute divided by the total mass of the solution, multiplied by 100. In this case, a 15.0% by mass NaOH solution means that there are 15 grams of NaOH in every 100 grams of the solution. Understanding this concept is crucial for calculating the amount of NaOH needed to achieve the desired pH in the final solution.

pH and pOH Relationship

pH is a measure of the acidity or basicity of a solution, with lower values indicating higher acidity and higher values indicating higher basicity. The pH scale ranges from 0 to 14, where a pH of 7 is neutral. For a solution with a pH of 10.8, it is basic, and the corresponding pOH can be calculated using the formula pOH = 14 - pH. This relationship is essential for determining the concentration of hydroxide ions in the solution.

Density and Volume Calculations

Density is defined as mass per unit volume and is crucial for converting between mass and volume of a solution. In this problem, the density of the NaOH solution is given as 1.116 g/mL, which allows us to calculate the mass of the solution needed to achieve the desired concentration. By using the density, we can convert the mass of NaOH required into the corresponding volume of the 15.0% solution.

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