Butyric acid is responsible for the foul smell of rancid butter. The pKa of butyric acid is 4.84. (b) Calculate the pH of a 0.050 M solution of butyric acid.

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Identify that butyric acid is a weak acid and will partially dissociate in water.

Write the dissociation equation for butyric acid: \( \text{HC}_4\text{H}_7\text{O}_2 \rightleftharpoons \text{H}^+ + \text{C}_4\text{H}_7\text{O}_2^- \).

Use the given \( \text{pK}_a \) value to find the \( K_a \) using the formula \( K_a = 10^{-\text{pK}_a} \).

Set up an ICE (Initial, Change, Equilibrium) table to determine the concentrations of the species at equilibrium.

Use the expression for \( K_a \), \( K_a = \frac{[\text{H}^+][\text{C}_4\text{H}_7\text{O}_2^-]}{[\text{HC}_4\text{H}_7\text{O}_2]} \), to solve for \([\text{H}^+]\) and then calculate the pH using \( \text{pH} = -\log[\text{H}^+] \).

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Key Concepts

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

pKa and Acid-Base Equilibrium

The pKa value of an acid indicates its strength and the degree to which it dissociates in solution. A lower pKa value corresponds to a stronger acid, meaning it more readily donates protons (H+). In this case, butyric acid has a pKa of 4.84, which helps determine its behavior in a solution and the resulting pH when dissolved.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of an acid and the concentration of its conjugate base. It is expressed as pH = pKa + log([A-]/[HA]). This equation is particularly useful for calculating the pH of weak acid solutions, such as butyric acid, by considering the ratio of the concentrations of the dissociated and undissociated forms.

Weak Acids and Their Dissociation

Weak acids, like butyric acid, do not completely dissociate in solution. Instead, they establish an equilibrium between the undissociated acid (HA) and its ions (A- and H+). The concentration of the acid and its dissociation constant (Ka) are crucial for calculating the pH, as they determine how much of the acid remains undissociated versus how much has dissociated into ions.

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