What Is 0.0098 Boiling Point

What is the Boiling Point of 0.0098 Molar Solution? Understanding Colligative Properties

Determining the boiling point of a 0.0098 molar (M) solution requires understanding colligative properties, specifically boiling point elevation. This article will delve into the concept of boiling point elevation, the factors that influence it, and how to calculate the boiling point of a 0.0098 M solution, considering the need for additional information to provide a precise answer. We will explore the underlying chemistry and provide practical examples to make this complex topic easier to understand.

Introduction to Colligative Properties

Colligative properties are properties of solutions that depend on the concentration of solute particles, not their identity. This means that the properties are affected by the number of solute particles present, regardless of what those particles are. Four main colligative properties exist:

Vapor pressure lowering: The presence of a non-volatile solute lowers the vapor pressure of the solvent.
Boiling point elevation: The boiling point of a solution is higher than that of the pure solvent.
Freezing point depression: The freezing point of a solution is lower than that of the pure solvent.
Osmotic pressure: The pressure required to prevent the flow of solvent across a semipermeable membrane.

In this case, we are focusing on boiling point elevation, which is crucial for understanding the boiling point of a 0.0098 M solution.

Boiling Point Elevation: The Science Behind It

The boiling point of a liquid is the temperature at which its vapor pressure equals the atmospheric pressure. When a non-volatile solute is added to a solvent, the vapor pressure of the solvent is lowered. Consequently, a higher temperature is required to reach the point where the vapor pressure of the solution equals atmospheric pressure. This increase in boiling point is directly proportional to the molal concentration of the solute.

The relationship is described by the following equation:

ΔTb = Kb * m * i

Where:

ΔTb is the boiling point elevation (the difference between the boiling point of the solution and the boiling point of the pure solvent).
Kb is the ebullioscopic constant (a constant that depends on the solvent).
m is the molality of the solution (moles of solute per kilogram of solvent). Note the distinction between molarity (moles of solute per liter of solution) and molality (moles of solute per kilogram of solvent).
i is the van't Hoff factor, which accounts for the dissociation of the solute into ions in solution. For non-electrolytes (substances that do not dissociate into ions), i = 1. For strong electrolytes, i is equal to the number of ions produced per formula unit.

Calculating the Boiling Point: The Missing Pieces

To calculate the boiling point of a 0.0098 M solution, we need more information:

The identity of the solvent: The ebullioscopic constant (Kb) is specific to each solvent. For example, water has a Kb of 0.512 °C/m, while benzene has a Kb of 2.53 °C/m. Different solvents will have drastically different boiling point elevations for the same molal concentration.
The identity of the solute: This is crucial for determining the van't Hoff factor (i). If the solute is a non-electrolyte like glucose (C6H12O6), i = 1. However, if it's a strong electrolyte like NaCl, it dissociates into Na+ and Cl− ions, making i = 2. Weak electrolytes will have an i value between 1 and the theoretical maximum based on complete dissociation, and this value can be experimentally determined or estimated based on the weak electrolyte's dissociation constant.
The mass of the solvent: We need the mass of the solvent (in kilograms) to calculate the molality (m) of the solution. The molarity (M) only tells us the concentration in moles per liter of solution, not per kilogram of solvent. To convert from molarity to molality, we would need the density of the solution and a bit of stoichiometry.

Let's illustrate with an example:

Example: Suppose our 0.0098 M solution is composed of glucose (a non-electrolyte, i = 1) dissolved in water. We will assume, for simplicity's sake, that the molarity and molality are approximately equal for such a dilute solution. This is a reasonable approximation, but not always accurate.

Kb (water) = 0.512 °C/m
m ≈ 0.0098 m (approximating molarity as molality)
i = 1

Then, ΔTb = 0.512 °C/m * 0.0098 m * 1 = 0.0050176 °C

The boiling point elevation is approximately 0.005 °C. Since the boiling point of pure water is 100 °C at standard pressure, the boiling point of this approximate 0.0098 m glucose solution in water would be approximately 100.005 °C.

Importance of Molality over Molarity

It's crucial to understand why molality is used in colligative properties calculations, rather than molarity. Molality is based on the mass of the solvent, which remains constant regardless of temperature or pressure changes. Molarity, on the other hand, is based on the volume of the solution, which can change with temperature. This temperature dependence would introduce unnecessary complications in the boiling point elevation calculation.

Advanced Considerations and Further Research

The simple equation presented above provides a good approximation for dilute solutions. However, for more concentrated solutions, deviations from this ideal behavior can occur due to intermolecular interactions between solute and solvent particles. More sophisticated models might be required to accurately predict boiling points in such scenarios.

Furthermore, the van't Hoff factor (i) for strong electrolytes is often not exactly equal to the theoretical value because of ion pairing—the attraction between oppositely charged ions, which reduces their effective concentration.

Frequently Asked Questions (FAQ)

Q: Can I use this equation for any solution?

A: While this equation is a good starting point, it works best for dilute solutions of non-volatile solutes. For concentrated solutions or volatile solutes, more complex models accounting for intermolecular interactions are necessary.

Q: What is the difference between molarity and molality?

A: Molarity is the number of moles of solute per liter of solution, while molality is the number of moles of solute per kilogram of solvent. Molality is preferred in colligative properties calculations because it is temperature-independent.

Q: Why is the boiling point elevated?

A: The solute particles disrupt the solvent's intermolecular forces, making it harder for the solvent molecules to escape into the gaseous phase. This requires a higher temperature to overcome the reduced vapor pressure.

Q: What if the solute is a volatile substance?

A: The equation doesn't directly apply to volatile solutes because their vapor pressure contributes to the overall vapor pressure of the solution, complicating the calculation.

Conclusion

Determining the precise boiling point of a 0.0098 M solution requires knowing the identity of both the solvent and the solute and the mass of the solvent. While the equation ΔTb = Kb * m * i provides a fundamental understanding of boiling point elevation, it’s vital to remember the assumptions made and the limitations of this simplified model, particularly for concentrated solutions and volatile solutes. Understanding the concept of colligative properties and the factors influencing them is crucial for accurate calculations and a comprehensive understanding of solution behavior. This detailed explanation offers a solid foundation for further exploration into the fascinating world of physical chemistry.