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Acetylsalicylic acid, commonly known as aspirin, is a widely used medication known for its pain-relieving, anti-inflammatory, and antiplatelet effects. Chemically, it is a weak acid, with the formula \(\mathrm{HC}_{9}\mathrm{H}_{7}\mathrm{O}_{4}\), and it belongs to the category of salicylates. When acetylsalicylic acid dissolves in water, it releases \(\mathrm{H}^{+}\) ions, a process which can be used to calculate the solution's pH. This compound has particular significance in pharmaceuticals, and understanding its properties鈥攊ncluding its behavior in different mediums鈥攊s crucial for pharmaceutical and medical studies. The balance between its un-ionized (acetylsalicylic acid) and ionized (salicylate ion and hydrogen ion) forms in solution can be represented using the acid dissociation constant.

The acid dissociation constant \(K_{a}\) is a quantitative measure of an acid's strength in solution. It represents the equilibrium constant for the dissociation of an acid into an anion and a proton (hydrogen ion). Specifically for acetylsalicylic acid, the chemical reaction can be described as:\[\mathrm{HC}_{9}\mathrm{H}_{7}\mathrm{O}_{4}(aq) \rightleftharpoons \mathrm{H}^{+}(aq) + \mathrm{C}_{9}\mathrm{H}_{7}\mathrm{O}_{4}^{-}(aq)\]The given \(K_{a}\) value of \(3.3 \times 10^{-4}\) indicates how readily acetylsalicylic acid donates its proton in water. The lower the \(K_{a}\), the weaker the acid and the less it dissociates. When solving for pH, \(K_{a}\) is used to establish an equilibrium expression where the concentrations of the reactants and products can be related, allowing us to find the proton concentration and thus determine the solution's acidity.

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance, expressed in grams per mole (g/mol). It can be calculated by summing the atomic masses of all the atoms in a molecule. For acetylsalicylic acid (HC鈧塇鈧嘜鈧�), the molar mass is calculated by adding the weights of 8 carbon atoms, 8 hydrogen atoms, and 4 oxygen atoms, resulting in \(180.16\ g/mol\). The knowledge of the molar mass is critical when converting between the mass of a substance and the number of moles, as shown in the step-by-step solution. This allows us to understand the quantity of the substance in terms of its moles, which is essential for stoichiometry and determining concentration in solutions.

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a balanced chemical equation. It allows for the precise calculation of reactant and product quantities, based on their molar ratios. In the problem at hand, stoichiometry is applied in several steps: \(

\) \(
• \)Calculating the number of moles of acetylsalicylic acid used by considering the molar mass and weight of the substance.\(
• \)Determining the concentration of acetylsalicylic acid by dividing the number of moles by the volume of the solution.\(
• \)Using the equilibrium expression that relates the concentrations of the reactants and products to solve for the concentration of hydronium ions, based on the \(K_{a}\).\(
• \)Finally, calculating the pH from the hydronium ion concentration, which represents the solution's acidity level.\(

\)Through stoichiometry, we can grasp the relationship between mass and moles, and how these concepts interact to solve for other properties, such as pH, in chemical solutions.