Problem 102 - Chemistry: The Central Science

Question

A \(40.0 \%\) by weight solution of \(\mathrm{KSCN}\) in water at \(20^{\circ} \mathrm{C}\) has a density of \(1.22 \mathrm{~g} / \mathrm{mL}\). (a) What is the mole fraction of \(\mathrm{KSCN}\) in the solution, and what are the molarity and molality? (b) Given the calculated mole fraction of salt in the solution, comment on the total number of water molecules available to hydrate each anion and cation. What ion pairing (if any) would you expect to find in the solution? Would you expect the colligative properties of such a solution to be those predicted by the formulas given in this chapter? Explain.

Step-by-Step Solution

Answer

The mole fraction of KSCN in the solution is 0.110, the molarity is 5.02 M, and the molality is 6.863 mol/kg. There are approximately 4 water molecules available to hydrate each ion (K+ and SCN-). Since the solution is concentrated, ion pairing is expected, which would affect the colligative properties and make the observed values differ from those predicted by theoretical formulas.

Step 1: Calculate the mass of KSCN and Water

Given, we have a 40.0% by weight solution of KSCN in water. Therefore, we can assume we have 100 g of the solution (as it simplifies calculations). Hence, we have 40 g of KSCN and 60 g of water.

Step 2: Calculate moles of KSCN and water

To find the moles, divide the mass by molar mass. Molar mass of KSCN = 97.18 g/mol Moles of KSCN = mass / molar mass = 40 g / 97.18 g/mol = 0.4118 mol Molar mass of water = 18.015 g/mol Moles of water = mass / molar mass = 60 g / 18.015 g/mol = 3.3316 mol

Step 3: Determine the mole fraction, molarity, and molality of KSCN

Mole fraction of KSCN: Mole fraction = moles of KSCN / (moles of KSCN + moles of water) = 0.4118 mol / (0.4118 mol + 3.3316 mol) = 0.110 Molarity: Given density of solution = 1.22 g/mL Volume of 100 g solution = mass / density = 100 g / 1.22 g/mL = 81.97 mL Now, molarity of a solution is defined as: moles of solute / liters of solution Molarity of KSCN = 0.4118 mol / 0.08197 L = 5.02 M Molality: Molality is defined as the moles of solute per kilogram of solvent. Molality of KSCN = 0.4118 mol / 0.060 kg = 6.863 mol/kg So, the mole fraction of KSCN in the solution is 0.110, the molarity is 5.02 M, and the molality is 6.863 mol/kg. #b) Hydration, ion pairing, and colligative properties#

Step 4: Determine the total number of water molecules available to hydrate ions

We have 3.3316 moles of water and 0.4118 moles of KSCN (0.4118 moles each for K+ and SCN- ions). Now we will find the ratio of water molecules per ion. Total ions = 0.4118 * 2 = 0.8236 mol Ratio of water molecules per ion = moles of water / total ions = 3.3316 / 0.8236 = 4.04 There are approximately 4 water molecules available to hydrate each ion (K+ and SCN-).

Step 5: Analyze ion pairing and colligative properties

As there are only 4 water molecules per ion, the solution is concentrated and the chances of ion pairing are higher. Ion pairs can form due to the proximity of the ions, which reduce the effective number of solute particles available for interactions. Colligative properties like boiling point elevation, freezing point depression, and osmotic pressure are directly related to the concentration of solute particles in the solution. The presence of ion pairs can affect the values of these properties, making the observed values differ from those predicted by the theoretical formulas. Therefore, we can expect the colligative properties of such a solution to be not accurately predicted by the formulas provided in this chapter.

Key Concepts

Molarity

Molarity is a key concept in chemistry, describing the concentration of a solute in a solution. It is denoted by the symbol M and defined as the number of moles of solute per liter of solution.
The formula for calculating molarity is: \( \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \).
This concept is particularly useful in reactions occurring in liquid solutions since it directly relates the amount of reactant to the volume of the solution.
In the given problem, the molarity of KSCN was found to be 5.02 M, indicating that there are 5.02 moles of KSCN in every liter of solution.
This high molarity suggests a concentrated solution, which has several implications for the behavior of the solution, including how it interacts with water and other solutes.

Molality

Molality is another measure of concentration, but unlike molarity, it is based on the mass of the solvent rather than the volume of the solution. It is represented by the symbol m and defined as the moles of solute per kilogram of solvent.
The formula for molality is: \( \text{Molality (m)} = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \).
One advantage of using molality over molarity is that molality does not change with temperature, as it relies on mass rather than volume.
In the context of the exercise, the molality of the solution was determined to be 6.863 mol/kg, indicating a high concentration of KSCN relative to the amount of water.
This concentration is crucial when considering properties that depend on the amount of solute versus solvent, such as boiling point elevation.

Ion Pairing

Ion pairing occurs when oppositely charged ions in a solution come close enough to each other to form a neutral pair.
This phenomenon is more common in concentrated solutions where ions have less space to disperse and are more likely to interact with each other rather than staying completely dissociated.
In the exercise, with only about 4 water molecules available to hydrate each ion, ion pairing becomes probable.
These pairs can reduce the effective number of particles in the solution, impacting how the solution behaves and reacts.
The formation of ion pairs can lead to deviations in the expected behavior of the solution, affecting properties like boiling point and osmotic pressure.

Colligative Properties

Colligative properties are those properties of solutions that depend on the number of solute particles rather than their identity. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.
In simple terms, adding solute particles disrupts the structure and interaction among solvent molecules, altering physical properties.
For example, the freezing point of a solution is lower than that of the pure solvent because the solute particles inhibit the formation of a solid structure.
In this exercise, due to ion pairing, the expected colligative properties do not match the theoretical values, as ion pairs decrease the effective concentration of particles.
This results in smaller changes to these properties than predicted, demonstrating why understanding concentration and particle interaction is critical in advanced chemistry.

• Boiling point elevation
• Freezing point depression
• Osmotic pressure
• Vapor pressure lowering