Calculate the pH of a solution made by combining 10.0 mL of 17.5 M acetic acid with 5.54 g of sodium acetate and diluting to a total volume of 1.50 L.

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Calculate the moles of acetic acid (CH₃COOH) using its concentration and volume: \( \text{moles of CH}_3\text{COOH} = 17.5 \text{ M} \times 0.010 \text{ L} \).

Calculate the moles of sodium acetate (CH₃COONa) using its mass and molar mass: \( \text{moles of CH}_3\text{COONa} = \frac{5.54 \text{ g}}{\text{molar mass of CH}_3\text{COONa}} \).

Determine the concentrations of acetic acid and acetate ion in the final solution by dividing the moles of each by the total volume of the solution (1.50 L).

Use the Henderson-Hasselbalch equation to calculate the pH: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]} \right) \), where \( \text{pK}_a \) is the negative logarithm of the acid dissociation constant of acetic acid.

Substitute the concentrations of acetate ion and acetic acid into the Henderson-Hasselbalch equation to find the pH.

Key Concepts

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

pH and pKa

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. The pKa is the negative logarithm of the acid dissociation constant (Ka) and indicates the strength of an acid. For weak acids like acetic acid, the pH can be calculated using the Henderson-Hasselbalch equation, which relates pH, pKa, and the ratio of the concentrations of the conjugate base and the acid.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a formula used to calculate the pH of a buffer solution. It is expressed as pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. This equation is particularly useful in buffer solutions, where both the acid and its conjugate base are present, allowing for the calculation of pH based on their concentrations.

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this question, the combination of acetic acid and sodium acetate creates a buffer system, which helps maintain a relatively stable pH despite the addition of acids or bases, making it essential for understanding the pH calculation.