Ch.17 - Acids and Bases

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.17 - Acids and Bases

Problem 87

Chapter 17, Problem 87

Determine the pH of a solution that is 3.55% KOH by mass. Assume that the solution has density of 1.01 g/mL.

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Calculate the mass of KOH in 100 g of solution using the percentage by mass: \( \text{mass of KOH} = 3.55\% \times 100 \text{ g} \).

Determine the volume of the solution using its density: \( \text{volume} = \frac{100 \text{ g}}{1.01 \text{ g/mL}} \).

Calculate the molarity of the KOH solution: \( \text{molarity} = \frac{\text{moles of KOH}}{\text{volume of solution in liters}} \).

Since KOH is a strong base, it dissociates completely in water. Therefore, the concentration of OH\(^-\) ions is equal to the molarity of the KOH solution.

Calculate the pH of the solution using the relation: \( \text{pH} = 14 - \text{pOH} \), where \( \text{pOH} = -\log[\text{OH}^-] \).

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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, values below 7 indicate acidity, and values above 7 indicate basicity. The pH is calculated as the negative logarithm of the hydrogen ion concentration in the solution, which is crucial for understanding the solution's chemical behavior.

KOH as a Strong Base

Potassium hydroxide (KOH) is a strong base that completely dissociates in water to produce potassium ions (K+) and hydroxide ions (OH-). The concentration of hydroxide ions directly influences the pH of the solution. Since KOH fully dissociates, the concentration of OH- can be used to calculate the pH through the relationship between pH and pOH.

Density and Concentration Calculations

To determine the pH of the KOH solution, it is essential to convert the mass percentage into molarity. The density of the solution allows for the calculation of the volume of the solution from its mass. By knowing the mass of KOH in the solution and its molar mass, one can find the concentration of hydroxide ions, which is necessary for calculating the pH.

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