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 the concept of colligative properties. These are properties of solutions that depend on the concentration of solute particles, not their identity. Boiling point elevation is a key colligative property; it describes the increase in a solvent's boiling point when a solute is added. This article will delve into the science behind boiling point elevation, provide a step-by-step calculation for a 0.0098 M solution, explore different scenarios, and address frequently asked questions. Understanding this concept is crucial in various fields, including chemistry, engineering, and even cooking.

Understanding Boiling Point Elevation

Pure solvents have specific boiling points at a given pressure. Water, for instance, boils at 100°C at standard atmospheric pressure. However, when you dissolve a solute in a solvent, the boiling point increases. This phenomenon arises because the solute particles interfere with the solvent molecules' ability to escape into the gaseous phase. More energy (and thus a higher temperature) is needed to overcome the intermolecular forces and achieve boiling.

The extent of boiling point elevation depends on several factors:

• The molality (m) of the solution: Molality is defined as the number of moles of solute per kilogram of solvent. While we're given molarity (moles of solute per liter of solution), we'll need to convert this to molality for accurate calculations. This conversion requires knowing the solution's density, which is often not readily available for dilute solutions and is frequently approximated.

• 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 solutes. Water has a Kb of 0.512 °C/m.

• The van't Hoff factor (i): This factor accounts for the dissociation of the solute in the solvent. For non-electrolytes (substances that don't dissociate into ions), i = 1. For electrolytes (substances that dissociate into ions), i is greater than 1 and represents the number of particles the solute dissociates into. For example, NaCl (sodium chloride) dissociates into two ions (Na+ and Cl-), so i = 2. For incomplete dissociation, i will be less than the theoretical value.

Calculating the Boiling Point of a 0.0098 M Solution

Let's assume our 0.0098 M solution is an aqueous solution (dissolved in water) of a non-electrolyte. This simplifies the calculation because the van't Hoff factor (i) will be 1.

Step 1: Approximate Molality

Since we only have the molarity (0.0098 M), we need to approximate the molality. For very dilute solutions, the density of the solution is approximately equal to the density of the pure solvent. The density of water is approximately 1 kg/L. Therefore, we can approximate the molality as equal to the molarity:

m ≈ 0.0098 m

Step 2: Apply the Boiling Point Elevation Equation

The boiling point elevation (ΔTb) is calculated using the following equation:

ΔTb = i * Kb * m

where:

• ΔTb is the boiling point elevation
• i is the van't Hoff factor (1 for our non-electrolyte)
• Kb is the molal boiling point elevation constant for water (0.512 °C/m)
• m is the molality of the solution (approximately 0.0098 m)

Step 3: Calculate ΔTb

Substituting the values into the equation:

ΔTb = 1 * 0.512 °C/m * 0.0098 m ΔTb ≈ 0.00502 °C

Step 4: Determine the New Boiling Point

The new boiling point (Tb) of the solution is the sum of the boiling point of pure water and the boiling point elevation:

Tb = 100 °C + ΔTb Tb ≈ 100.00502 °C

Therefore, the approximate boiling point of a 0.0098 M aqueous solution of a non-electrolyte is approximately 100.00502 °C. It's crucial to remember that this is an approximation due to the assumption that molarity and molality are essentially the same for this dilute solution. A more precise calculation would require the solution's density.

Different Scenarios and Considerations

The calculation above is simplified. Let's consider some other scenarios:

• Electrolyte Solution: If the 0.0098 M solution is an electrolyte, the van't Hoff factor (i) will be greater than 1. For example, if the solute is NaCl, i = 2, and the boiling point elevation would be doubled.

• Different Solvent: If the solvent is not water, the Kb value would change. Each solvent has its own unique Kb value.

• Concentrated Solutions: For concentrated solutions, the assumption that molarity and molality are equal is no longer valid. The density of the solution significantly differs from the density of the pure solvent. You would need the solution's density to accurately convert molarity to molality.

• Non-ideal Solutions: The equations presented here assume ideal solutions, where solute-solute, solvent-solvent, and solute-solvent interactions are similar. In reality, deviations from ideality can occur, especially in concentrated solutions, leading to discrepancies in calculated versus experimentally observed boiling points.

Practical Applications and Importance

Understanding boiling point elevation has numerous practical applications:

• Antifreeze: Antifreeze solutions are used in car radiators to prevent freezing in winter and boiling in summer. The solute added to the water elevates the boiling point and depresses the freezing point.

• Cooking: Adding salt to water increases its boiling point, which can impact cooking times.

• Desalination: Reverse osmosis and other desalination techniques rely on the colligative properties of solutions to separate salts from water.

• Industrial Processes: Many industrial processes involve solutions, and understanding boiling point elevation is crucial for controlling reaction temperatures and optimizing efficiency.

Frequently Asked Questions (FAQ)

Q: Why is the boiling point of a solution higher than that of the pure solvent?

A: The solute particles interfere with the solvent molecules' ability to escape into the gas phase. More energy is needed to overcome the intermolecular forces and achieve boiling.

Q: What is the difference between molarity and molality?

A: Molarity is moles of solute per liter of solution, while molality is moles of solute per kilogram of solvent.

Q: How does the van't Hoff factor affect boiling point elevation?

A: The van't Hoff factor accounts for the dissociation of the solute into ions. A higher van't Hoff factor leads to a greater boiling point elevation.

Q: Can I use this calculation for all types of solutions?

A: This calculation is an approximation and works best for dilute solutions of non-electrolytes where molarity and molality are approximately equal. For concentrated solutions or electrolytes, a more sophisticated approach is needed, considering the solution's density and the van't Hoff factor accurately.

Conclusion

Determining the boiling point of a 0.0098 M solution requires understanding colligative properties, specifically boiling point elevation. While a simplified calculation provides an approximate value, the accuracy depends on factors like the nature of the solute (electrolyte or non-electrolyte), the solvent, the solution's concentration, and potential deviations from ideal behavior. This article provides a foundational understanding of this important concept and highlights its relevance across various scientific and practical applications. Remember that for precise calculations, especially with concentrated solutions or electrolytes, more detailed information, such as the solution's density, is crucial. Always approach such calculations with a consideration for the limitations of the models used.