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Solubility refers to the ability of a substance to dissolve in a solvent to form a homogenous solution. In the context of our exercise, we are considering the solubility of a gaseous amine, \( \mathrm{RNH}_2(\mathrm{~g}) \), in water. The solubility is provided as 22.4 L per unit volume of water under specific conditions (1 atm and 273 K). This value suggests that at full solubility, 22.4 volumes of gaseous amine dissolve in a volume of water. Solubility is crucial in determining how much of the amine can interact with water, which directly influences chemical reactions, such as amine's dissociation into its ionic forms. A high solubility means more \( \mathrm{RNH}_2 \) is available to participate in equilibrium reactions, which relates to the calculation of maximum pOH.

The \( \text{pK}_\mathrm{b} \) represents the basic dissociation constant's negative logarithm. It's a critical parameter in understanding the strength of a base in its ability to generate hydroxide ions (\(\mathrm{OH}^-\)) in solution. For gaseous amine \( \mathrm{RNH}_2 \), a \( \text{pK}_\mathrm{b} = 4 \) indicates a certain level of intrinsic basicity. A lower \( \text{pK}_\mathrm{b} \) means a stronger base because it implies a higher \( K_\mathrm{b} \). Use the formula \( \text{pK}_\mathrm{b} = -\log(K_\mathrm{b}) \) to find \( K_\mathrm{b} \):- Calculate \( K_\mathrm{b} \) as: \[ K_\mathrm{b} = 10^{-4} \]This constant helps us set up the equilibria involving the amine and predict concentrations of produced ions at equilibrium which we use in calculating pOH.

A gaseous amine like \( \mathrm{RNH}_2(\mathrm{~g}) \) is an amine in the gaseous state dissolved in a solvent like water. These compounds can act as weak bases, meaning they accept protons and increase the concentration of hydroxide ions \(\mathrm{OH}^-\) in the solution.When gauging the effects of a gaseous amine, focus on:- Its ability to dissolve (solubility)- Its basic strength (via \( \text{pK}_\mathrm{b} \))Dissolving gaseous amines affects the chemical equilibrium in solution, as they can dissociate and influence the resulting pOH, which measures a solution's alkalinity.

An equilibrium expression helps us understand how species in a chemical reaction dynamically balance. For \( \mathrm{RNH}_2 \) dissolving in water, the equilibrium can be written as:\[ \mathrm{RNH}_2 + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{RNH}_3^+ + \mathrm{OH}^- \]This expression reflects how \( \mathrm{RNH}_2 \), once dissolved, can form \( \mathrm{RNH}_3^+ \) and \(\mathrm{OH}^-.\) Setting up the equilibrium as \( K_\mathrm{b} = \frac{[\mathrm{RNH}_3^+][\mathrm{OH}^-]}{[\mathrm{RNH}_2]} \) emphasizes the concentrations' relationship at equilibrium.At maximum solubility (22.4 M concentration of \( \mathrm{RNH}_2 \)), we assume minimal change in its concentration due to dissociation (small \( x \)). Solving gives us \( x \approx 0.047 \) M for \( \mathrm{OH}^- \). Calculating pOH from this illustrates how equilibrium constants like \( K_\mathrm{b} \) dictate the resulting alkali level in a solution.