A painful arthritic condition known as gout is caused by an excess of uric acid HUric in the blood. An aqueous solution contains \(4.00 \mathrm{~g}\) of uric acid. A \(0.730 \mathrm{M}\) solution of \(\mathrm{KOH}\) is used for titration. After \(12.00 \mathrm{~mL}\) of KOH is added, the resulting solution has pH 4.12. The equivalence point is reached after a total of \(32.62 \mathrm{~mL}\) of KOH is added. $$\operatorname{HUric}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Uric}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}$$ (a) What is the molar mass of uric acid? (b) What is its \(K_{\mathrm{a}}\) ?

The concept of molar mass is critical when working with chemical substances because it links the mass of a substance to its moles, a foundational concept in chemistry. The molar mass of a compound is the weight in grams of one mole of that compound. In essence, it is the sum of the atomic masses of all the atoms in a molecule. To calculate it, you simply divide the total mass of the compound by the number of moles present.

Let's look at an example from a titration problem involving uric acid (HUric). If we know that 4.00 grams of uric acid corresponds to 0.0238 moles, the molar mass is calculated as follows: \[\text{Molar Mass} = \frac{\text{Mass}}{\text{Moles}} = \frac{4.00\,\text{g}}{0.0238\,\text{mol}} = 168.07\,\text{g/mol}\]

This value is pivotal not only to understand the substance in question but also to make stoichiometric calculations in reactions, which is often the first step in many chemistry problems, such as determining the amount of reactants or products involved.

The acid dissociation constant, usually denoted as Ka, measures the strength of an acid in a solution. It is the equilibrium constant for the dissociation of an acid into its conjugate base and a hydrogen ion (proton) in water. A large Ka value indicates a strong acid that dissociates completely in solution, while a small Ka value implies a weak acid that does not dissociate completely.

In our example with uric acid, we need to consider the pH of the solution, the point in the titration where we measured it, and the molar concentrations of the species in solution to calculate the Ka.

From the pH, we can determine the concentration of hydrogen ions (\[[H3O^+]\]) as follows:
\[[H3O^+] = 10^{-\text{pH}} = 10^{-4.12} = 7.58 \times 10^{-5} M\]

The concentrations of uric acid (HUric) and its conjugate base (Uric-) at specific titration points allow us to use the formula for Ka:
\[Ka = \frac{[\text{Uric}^-][H3O^+]}{[\text{HUric}]}\]
Substituting these values into the formula, we get the acid dissociation constant. The calculated Ka for uric acid is thus an expression of its tendency to lose a proton in aqueous solution.

The pH and pOH are the logarithmic measures of hydrogen and hydroxide ion concentrations respectively. They are crucial for understanding the degree of acidity or basicity of a solution. The pH scale ranges from 0 to 14, with 7 being neutral. Values less than 7 indicate acidity, while values greater than 7 signify basicity.

pH is calculated using the concentration of hydrogen ions (\[[H3O^+]\]) in the solution which is inversely related to the pH value:\[\text{pH} = -\log[H3O^+]\]

Similarly, pOH is related to the hydroxide ions concentration \[[OH^-]\], and together, pH and pOH always add up to 14, a relationship derived from the ion-product constant of water \[K_w\]. To determine pH from a known concentration of a hydroxide ion, you first calculate the pOH and then subtract it from 14 to find the pH.

In a titration problem, the pH is especially significant because it changes markedly at the point where the amount of acid equals the amount of base added - known as the equivalence point. Understanding both pH and pOH is essential for analyzing acid-base titrations and for predicting the behavior of acidic and basic solutions in various chemical processes.