Problem 2 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Aspirin is acetylsalicylic acid which has a \(\mathrm{pK}_{\mathrm{a}}\) of 3.49 (Section 7.2) (a) Calculate the pH of a \(0.10 \mathrm{moldm}^{-3}\) solution of this acid. (b) Would you expect the sodium salt of acetylsalicylic acid to be acidic, neutral, or basic in solution? Explain your reasoning.

Step-by-Step Solution

Answer

(a) The pH of the solution is approximately 2.25. (b) The sodium salt of acetylsalicylic acid would be basic in solution.

Step 1: Recognize the relevant formula for calculating pH

To find the pH of a weak acid solution, we use the expression for pH of a weak acid \[ \text{pH} = -\log[H^+] \] where the concentration of hydrogen ions \([H^+]\) can be determined using the expression for the acid dissociation constant \(K_a\).

Step 2: Calculate the acid dissociation constant \(K_a\)

The relation between pK\(_a\) and \(K_a\) is given by \[ K_a = 10^{-\text{pK}_a} \] Substituting the given pK\(_a\) value of 3.49, we calculate\[ K_a = 10^{-3.49} = 3.24 \times 10^{-4} \]

Step 3: Set up the expression for \(K_a\)

For the dissociation of a weak acid \(HA \leftrightarrow H^+ + A^-\), the expression for \(K_a\) is\[ K_a = \frac{[H^+][A^-]}{[HA]} \] Assuming \([H^+] = [A^-] = x\) and \([HA] = 0.10 - x \approx 0.10\), substitute these into the \(K_a\) expression:\[ 3.24 \times 10^{-4} = \frac{x^2}{0.10} \]

Step 4: Solve for \(x\) to find \([H^+]\)

Rearrange the equation from Step 3 and solve for \(x\):\[ x^2 = 3.24 \times 10^{-5} \] \[ x = \sqrt{3.24 \times 10^{-5}} = 5.69 \times 10^{-3} \] Thus, \([H^+] = 5.69 \times 10^{-3}\) mol/L.

Step 5: Calculate the pH

The pH can now be found by taking the negative log of \([H^+]\):\[ \text{pH} = -\log(5.69 \times 10^{-3}) \approx 2.25 \]

Step 6: Assess the nature of the sodium salt in solution

The sodium salt of acetylsalicylic acid would dissociate in water to form acetate ions \((CH_3COO^- )\) and sodium ions \((Na^+)\). The acetate ion, being the conjugate base of a weak acid, will react with water to a small extent, generating hydroxide ions \((OH^-)\), thus making the solution basic.

Key Concepts

pH Calculation

Calculating pH is an essential part of understanding acid-base chemistry. The pH scale measures how acidic or basic a solution is on a scale from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution.
To find the pH of a substance, especially for a weak acid like acetic acid, we first need to determine the concentration of hydrogen ions in the solution. This is calculated using the equilibrium expression for the acid dissociation constant, denoted as \( K_a \). By knowing the \( K_a \), we can use the formula:

• \( K_a = \frac{[H^+][A^-]}{[HA]} \)

Here, \([H^+]\) represents the concentration of hydrogen ions that appear as the acid dissociates.
Once we have solved for \([H^+]\), we calculate the pH using the formula \( \text{pH} = -\log[H^+] \). This logarithmic function helps translate small changes in hydrogen ion concentration into broader changes in pH, capturing the scale of acidity effectively.

Acetic Acid Dissociation

Acetic acid, being a weak acid, partially dissociates in water.This means not all acetic acid molecules donate their hydrogen ions to the solution; only a small fraction do.
The process is represented by the equation:\[HA \leftrightarrow H^+ + A^- \]In this equation, \( HA \) is the undissociated acetic acid, \( H^+ \) is the hydrogen ion, and \( A^- \) is the acetate ion.
This equilibrium is characterized by the acid dissociation constant \( K_a \). A lower \( K_a \) value indicates weaker acidity, implying less dissociation. For acetic acid with a known \( \text{pK}_a \), calculating \( K_a \) involves the formula \( K_a = 10^{-\text{pK}_a} \).
The extent to which an acid dissociates, i.e., how much it ionizes, affects the resulting pH of the solution, determining its acidity.

Sodium Salt Hydrolysis

When a sodium salt of a weak acid, such as sodium acetate, dissolves in water, it undergoes hydrolysis.Hydrolysis is the reaction of a salt with water to form an acidic or basic solution.
The equation for this process is:\[CH_3COO^- + H_2O \rightarrow CH_3COOH + OH^-\]Here, acetate ions \((CH_3COO^-)\) react with water to form acetic acid \((CH_3COOH)\) and hydroxide ions \((OH^-)\).
Since \( OH^- \) ions make the solution basic, the solution of sodium acetate is basic.This behavior is typical for salts derived from weak acids and strong bases.They tend to produce slightly basic solutions upon dissolving in water.