Question

Using the solubility data of a solid in a specified liquid, explain how you would determine the mole fraction of the solid in the liquid at the interface at a specified temperature.

Short answer

Question: Using the given solubility data, determine the mole fraction of a solid at the interface with a liquid at a specific temperature. Answer: To determine the mole fraction of the solid at the interface, follow these steps: 1. Understand the concepts of solubility and mole fraction. 2. Relate solubility to concentration using the formula: Concentration (c) = (solubility of solid (S) × mass of liquid (M)) / (molar mass of solid (M_s)). 3. Calculate the moles of solute and solvent using the formulas: moles of solute (n_s) = Concentration (c) × Volume of liquid (V), and moles of solvent (n_l) = mass of liquid (M) / molar mass of liquid (M_l). 4. Calculate the mole fraction of the solid at the interface using the formula: Mole fraction of solid (X_s) = moles of solute (n_s) / (moles of solute (n_s) + moles of solvent (n_l)). Use the given solubility data and specific temperature to compute the values required in each step, and you'll obtain the mole fraction of the solid at the interface.

Step-by-step solution

Understand the concepts of solubility and mole fraction

Solubility is a measure of the maximum amount of solute (in this case, the solid) that can dissolve in a given amount of solvent (in this case, the liquid) at a specified temperature. In the context of this problem, we're interested in the solute-solvent interactions at the interface between the solid and the liquid. Mole fraction is defined as the ratio of the number of moles of solute to the total number of moles of solute and solvent. It is a useful way of expressing the composition of a solution. In this exercise, we will calculate the mole fraction of the solid at the interface.

Relate solubility to concentration

First, we need to establish a relationship between the given solubility data and the concentration of the solid in the liquid. We can express this relationship as: Concentration (c) = (solubility of solid (S) × mass of liquid (M)) / (molar mass of solid (M_s))

Calculate the moles of solute and solvent

Using the concentration of the solid in liquid, we can calculate the number of moles of solute and solvent: moles of solute (n_s) = Concentration (c) × Volume of liquid (V) moles of solvent (n_l) = mass of liquid (M) / molar mass of liquid (M_l)

Calculate the mole fraction of the solid at the interface

Now that we have the number of moles of solute (solid) and solvent (liquid), we can compute the mole fraction of the solid at the interface using the following formula: Mole fraction of solid (X_s) = moles of solute (n_s) / (moles of solute (n_s) + moles of solvent (n_l)) By plugging in the values obtained in the previous steps, we can determine the mole fraction of the solid at the interface for the specified temperature.

Key concepts

Solubility

Solubility is a key concept in chemistry that refers to the ability of a substance, known as the solute, to dissolve in a solvent to form a homogeneous mixture or solution. At a given temperature and pressure, solubility quantifies the maximum amount of solute that can be dissolved in a solvent. When a substance dissolves, its molecules or ions interact with the solvent molecules, which leads to the formation of a solution.

Solubility can vary widely depending on the substances involved and external conditions. For instance, the solubility of solids typically increases with temperature, allowing more solid to dissolve in the liquid at higher temperatures. However, the opposite trend is often true for gases. Temperature and solubility are thus directly related variables in most solid-liquid systems, and understanding this relationship is essential in calculating the mole fraction of the solid in the liquid at any given temperature.

In our exercise, knowing the solubility of a solid at the specified temperature enables us to predict how much of the solid can be present at the interface between the solid and the solvent—this interface is key in determining the concentration of the solid within the liquid part of the solution.

Concentration of Solid in Liquid

Concentration is a measure of how much solute is present in a given quantity of solvent or overall solution. There are various ways to express the concentration of a solution, such as molarity, molality, and mole fraction. In the context of our problem, concentration refers to the amount of solid solute that is dissolved in a specific amount of liquid solvent.

To determine the concentration from solubility information, one generally requires the solubility data expressed in terms of mass per volume (e.g., grams per liter), which then needs to be converted into moles using the molar mass of the solute. This information can be represented by the formula:

Concentration Formula:

\[ \text{Concentration (c)} = \frac{\text{solubility of solid (S)} \times \text{mass of liquid (M)}}{\text{molar mass of solid (M_s)}} \]Calculating the concentration of the solid in the liquid correctly is a crucial step in determining the mole fraction, which will ultimately allow us to understand the ratio of solid solute to the total amount of solute and solvent in the solution.

Solute-Solvent Interaction

Solute-solvent interaction is fundamental to the solution process and directly influences solubility. These interactions involve various forces, including hydrogen bonds, ionic bonds, and Van der Waals forces. The nature and strength of these interactions determine how well a solute can dissolve in a solvent.

When a solute dissolves, it must overcome the forces holding its own particles together, and at the same time, the solvent molecules must move apart to accommodate the solute particles. The process of solvation involves these solute particles being surrounded by solvent molecules, a step that is critical to the creation of a stable solution.

Strong solute-solvent interactions can enhance solubility, as seen with salt (NaCl) in water (H2O), where the positive sodium ions and negative chloride ions are attracted to the polar water molecules. Conversely, weak interactions can result in poor solubility. This is the principle used to explain why oil (non-polar) does not mix well with water (polar).

In the exercise, we consider the interactions at the interface of the solid and liquid, where the solute particles are in direct contact with the solvent. Understanding these interactions is pivotal in accurately calculating the mole fraction based on the changes in concentration due to the increased amount of solute particles at this interface.