91Ó°ÊÓ

The Acid Dissociation Constant, known as \(K_a\), is a value that reflects the strength of an acid in solution. In simpler terms, it's an indicator of how well the acid can donate its hydrogen ions \(H^+\). For aspirin, the \(K_a\) value at body temperature \(37^{\circ} \mathrm{C}\) is given as \(3 \times 10^{-5}\). This relatively small number indicates that aspirin is a weak acid.
To understand aspirin's dissociation in water, consider the equilibrium:

• \(HA \rightleftharpoons H^+ + A^-\)

The equation shows that the acid \(HA\) (in this case, aspirin) partially dissociates into hydrogen ions \(H^+\) and its conjugate base \(A^-\).
At equilibrium, the ratio of concentrations of the products (\([H^+]\) and \([A^-]\)) to the reactant \([HA]\) is constant:

• \(K_a = \frac{[H^+][A^-]}{[HA]}\)

This expression helps determine how much of the aspirin remains undissociated in its neutral form, known as \([HA]\). A large \(K_a\) implies more dissociation, while a small \(K_a\) (our case) indicates limited dissociation.

The term pH is a measure of the acidity of a solution. It specifically reflects the concentration of hydrogen ions \([H^+]\). pH is calculated using the formula:

• \(\text{pH} = -\log_{10}([H^+])\)

In your stomach, a pH of 2 means \([H^+] = 10^{-2} \text{ M}\). This is a highly acidic environment. As aspirin dissolves in the stomach with this pH, we're interested in how the amount of \([H^+]\) affects the dissociation equilibrium.
Because the pH value is low, the concentration of hydrogen ions is high, leading to the assumption that the initial \([H^+]\) stays nearly constant through the reaction. This aids us in simplifying the equilibrium calculations, as the equilibrium concentration of \(H^+\) does not drastically change from its initial concentration of \(10^{-2} \text{ M}\).
Understanding this concept allows calculation of how much aspirin exists in its ionized form \(A^-\) versus its neutral form \(HA\), aiding in determining the medical effectiveness of the aspirin.

Molarity is a way to express the concentration of a solute in a given volume of solution. It is defined as the number of moles of solute per liter of solution.
In our scenario, two aspirin tablets with a total mass of 0.650 g dissolve in a 1 L solution. The molar mass of aspirin \(C_9H_8O_4\) is approximately 180 g/mol, allowing us to calculate moles of aspirin:

• \(\text{Moles of aspirin} = \frac{0.65 \text{ g}}{180 \text{ g/mol}} \approx 0.00361 \text{ mol}\)

Given that the solution's volume is 1 L, the molarity \([HA]\) is computed as:

• \([HA] = \frac{0.00361 \text{ mol}}{1 \text{ L}} = 0.00361 \text{ M}\)

Molarity is vital because it frames our understanding of how concentrated the aspirin is in the stomach solution. It sets the initial condition for the equilibrium and influences the calculations of \([HA]\) and \([A^-]\) to assess how much aspirin remains undissociated.