What Is 0.0098 Boiling Point

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

The question "What is the boiling point of a 0.0098 molar solution?" can't be answered directly without knowing the solute and the solvent. The boiling point elevation is a colligative property, meaning it depends on the concentration of solute particles, not their identity. This article will delve into the science behind boiling point elevation, explain how to calculate it, and address common misconceptions. We'll also explore the factors influencing the accuracy of the calculation and provide a step-by-step guide to determine the boiling point of a 0.0098 molar solution.

Understanding Boiling Point Elevation

Boiling occurs when the vapor pressure of a liquid equals the atmospheric pressure. Adding a non-volatile solute to a solvent lowers its vapor pressure. This means you need to increase the temperature to reach the point where the vapor pressure of the solution equals atmospheric pressure. This increase in boiling point is called boiling point elevation.

The magnitude of the boiling point elevation depends on several factors:

• The molality (m) of the solution: This represents the moles of solute per kilogram of solvent. While the problem provides molarity (M), which is moles of solute per liter of solution, we'll need to convert to molality for accurate calculations. Molarity and molality are approximately equal for dilute solutions, but the difference becomes significant in concentrated solutions.

• The molal boiling point elevation constant (Kb) of the solvent: This constant is a characteristic property of the solvent and reflects its sensitivity to the presence of solute particles. Each solvent has its own unique Kb value. For example, water has a Kb of 0.512 °C/m.

• The van't Hoff factor (i): This factor accounts for the number of particles a solute dissociates into when dissolved in the solvent. For non-electrolytes (substances that don't dissociate into ions), i = 1. For strong electrolytes (substances that completely dissociate into ions), i is equal to the number of ions produced per formula unit. For example, NaCl (sodium chloride) has i = 2 (Na⁺ and Cl⁻), while CaCl₂ (calcium chloride) has i = 3 (Ca²⁺ and 2Cl⁻). Weak electrolytes have an i value between 1 and the theoretical maximum, depending on the degree of dissociation.

Calculating Boiling Point Elevation: A Step-by-Step Guide

Let's outline the steps to calculate the boiling point elevation for a 0.0098 molar solution, assuming we're dealing with an aqueous solution (water as the solvent) and a non-electrolyte solute (i = 1):

Step 1: Identify the solvent and solute. We need to know the identity of the solvent and solute to determine the Kb value and the van't Hoff factor (i). The problem only specifies the molarity, and we must assume the solvent. For this example, we will assume water as the solvent.

Step 2: Convert molarity to molality. This is crucial because boiling point elevation is dependent on molality, not molarity. To convert, we need the density of the solution. However, for dilute solutions, molarity and molality are approximately equal. For a 0.0098 M solution, the approximation is reasonable. Therefore, we can assume molality (m) ≈ 0.0098 m.

Step 3: Determine the van't Hoff factor (i). Since we are assuming a non-electrolyte solute, the van't Hoff factor (i) is 1.

Step 4: Find the molal boiling point elevation constant (Kb) for the solvent. For water, Kb = 0.512 °C/m.

Step 5: Calculate the boiling point elevation (ΔTb). We use the following formula:

ΔTb = i * Kb * m

Where:

• ΔTb = boiling point elevation (°C)
• i = van't Hoff factor
• Kb = molal boiling point elevation constant (°C/m)
• m = molality (m)

In our example:

ΔTb = 1 * 0.512 °C/m * 0.0098 m ≈ 0.005 °C

Step 6: Calculate the new boiling point. The boiling point of pure water at 1 atm is 100 °C. Therefore, the boiling point of the 0.0098 m solution is approximately:

New boiling point = 100 °C + ΔTb = 100 °C + 0.005 °C = 100.005 °C

The Importance of Accurate Molality Calculation

It is crucial to understand that the above calculation relies on the approximation that molarity and molality are roughly equal for dilute solutions. For more precise calculations, especially for concentrated solutions, we need the density of the solution to accurately convert molarity to molality. The density allows us to determine the mass of the solvent in a given volume of solution.

The formula for converting molarity (M) to molality (m) is:

m = (M * 1000) / (1000 * ρ - M * Mw)

where:

• M = molarity
• ρ = density of the solution (g/mL)
• Mw = molar mass of the solute (g/mol)

The Influence of Electrolytes

The presence of electrolytes significantly alters the boiling point elevation. Electrolytes dissociate into ions in solution, increasing the total number of solute particles. This leads to a greater decrease in vapor pressure and a higher boiling point elevation. The van't Hoff factor (i) accounts for this effect. For instance, a 0.0098 m solution of NaCl (i ≈ 2) would exhibit approximately double the boiling point elevation compared to a 0.0098 m solution of a non-electrolyte.

Factors Affecting Accuracy

Several factors can affect the accuracy of boiling point elevation calculations:

• Non-ideality of solutions: The formulas assume ideal behavior, meaning there are no significant interactions between solute and solvent molecules. In real solutions, these interactions can affect vapor pressure and boiling point.

• Experimental error: Measurements of temperature, mass, and volume are subject to experimental error, which can propagate through the calculations.

• Dissociation of weak electrolytes: Weak electrolytes don't fully dissociate, making it challenging to determine the precise van't Hoff factor. The degree of dissociation depends on factors like concentration and temperature.

Frequently Asked Questions (FAQ)

Q1: Can I use molarity instead of molality in boiling point elevation calculations?

A1: While molarity and molality are approximately equal for very dilute solutions, using molarity directly can lead to significant errors, especially for concentrated solutions. Molality is the correct concentration unit for colligative properties calculations.

Q2: What happens if the solute is volatile?

A2: If the solute is volatile (meaning it has a significant vapor pressure), it will contribute to the total vapor pressure of the solution. This complicates the calculation because the reduction in vapor pressure caused by the solute is counteracted by the vapor pressure of the solute itself. Boiling point elevation calculations are typically only applicable to non-volatile solutes.

Q3: Why is the boiling point elevation so small in this example?

A3: The boiling point elevation is small because the concentration of the solution (0.0098 m) is very low. Colligative properties are directly proportional to concentration; a higher concentration will result in a larger boiling point elevation.

Q4: What are some real-world applications of boiling point elevation?

A4: Boiling point elevation is used in many applications, including antifreeze solutions (preventing car radiators from freezing in winter), and in the food industry to control boiling temperatures.

Conclusion

Determining the boiling point of a 0.0098 molar solution requires understanding the principles of colligative properties, particularly boiling point elevation. The calculation necessitates knowing the identity of the solvent and solute to accurately determine the molal boiling point elevation constant (Kb) and the van't Hoff factor (i). Converting molarity to molality is crucial for precise results, especially in concentrated solutions. While the approximation of molarity and molality for dilute solutions provides a reasonable estimate, precise calculations require consideration of solution density and non-ideal behavior. Understanding these factors ensures more accurate predictions of boiling points in various solutions. Remember, this article provides a foundational understanding; for complex solutions or high precision, further investigation might be required.