Calculate the concentration of an aqueous solution of NaOH that has a pH of 11.50.

Verified step by step guidance

Step 1: Understand that pH is a measure of the hydrogen ion concentration in a solution. The pH is related to the pOH by the equation: \( \text{pH} + \text{pOH} = 14 \).

Step 2: Calculate the pOH of the solution using the given pH value: \( \text{pOH} = 14 - \text{pH} \). Substitute the given pH of 11.50 into the equation.

Step 3: Convert the pOH to hydroxide ion concentration \([\text{OH}^-]\) using the formula: \([\text{OH}^-] = 10^{-\text{pOH}}\).

Step 4: Recognize that the concentration of NaOH in the solution is equal to the concentration of \([\text{OH}^-]\) because NaOH dissociates completely in water.

Step 5: Use the calculated \([\text{OH}^-]\) concentration as the concentration of the NaOH solution.

Key Concepts

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

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is neutral, while values below 7 indicate acidity and above 7 indicate basicity. Each unit change in pH represents a tenfold change in hydrogen ion concentration, making it crucial for understanding the behavior of acids and bases in solution.

Concentration of Hydroxide Ions

In basic solutions, the concentration of hydroxide ions (OH-) is significant. The relationship between pH and hydroxide ion concentration can be derived from the equation pOH = 14 - pH. For a pH of 11.50, the pOH can be calculated, allowing for the determination of the hydroxide ion concentration, which is essential for calculating the concentration of NaOH in the solution.

Stoichiometry of NaOH Dissociation

Sodium hydroxide (NaOH) is a strong base that completely dissociates in water into sodium ions (Na+) and hydroxide ions (OH-). The stoichiometry of this dissociation means that the concentration of NaOH is equal to the concentration of OH- produced. Understanding this relationship is vital for calculating the concentration of the NaOH solution based on the hydroxide ion concentration derived from the pH.