About this time, you may be wishing you had an aspirin....

About this time, you may be wishing you had an aspirin. Aspirin is an organic acid (page 507 ) with a $K_{\mathrm{a}}$ of $3.27 \times$ $10^{-4}$ for the reaction $\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{C}_{9} \mathrm{H}_{7} \mathrm{O}_{4}^{-}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})$ If you have two tablets, each containing $0.325 \mathrm{g}$ of aspirin (mixed with a neutral "binder" to hold the tablet together), and you dissolve them in a glass of water to give 225 mL of solution, what is the pH of the solution?

Key Concepts

Acid Dissociation Constant (Ka)

The acid dissociation constant, Ka, quantifies the strength of an acid in solution. It is defined as the equilibrium constant for the reaction in which the acid donates a proton to water, producing its conjugate base and hydronium ions. This constant is critical in determining how much an acid will dissociate in a given environment, which directly affects the pH of the solution.

Weak Acid Equilibrium

Weak acids do not completely dissociate in solution; instead, they establish an equilibrium between the undissociated acid and its dissociation products. Understanding this equilibrium is essential for calculating the concentrations of the species present after dissociation, which is foundational for determining the pH of solutions containing weak acids.

pH and its Calculation

The pH of a solution is a measure of its acidity or basicity, defined as the negative base-10 logarithm of the hydronium ion concentration. In the context of acid-base equilibria, calculating the pH involves determining the concentration of hydronium ions that result from the dissociation of the acid, and then applying the logarithmic formula to find the pH.

Molarity and Stoichiometry

Molarity is the measure of the concentration of a solute in a solution, expressed as moles per liter. Accurately converting the mass of a substance into moles using its molar mass, and then dividing by the volume of the solution, is a crucial step in setting up equilibrium calculations and determining the extent of acid dissociation.

Equilibrium Approximation Methods

When dealing with weak acids, simplifying assumptions or approximations such as the neglect of the change in concentration (x) relative to the initial concentration are often applied to solve the equilibrium equations. These methods enable easier calculation of the degree of dissociation, hydronium ion concentration, and ultimately the pH of the solution.

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