Boiling Point Of Sugar Solution: Chemistry Explained

Determining the Boiling Point of a Sugar Solution: A Chemistry Breakdown

Hey chemistry enthusiasts! Let's dive into a fun question that tests our understanding of colligative properties. The question is: Which of these is a possible boiling point for a 1.0 M solution of sugar in water? The normal boiling point of water is $100^{\circ} C$.

• $$100.3^{\circ} C$$

• $$-0.3^{\circ} C$$

• $$99.7^{\circ} C$$

To crack this, we need to understand how adding a solute (in this case, sugar) affects the boiling point of a solvent (water). Let's break it down, shall we?

Understanding Colligative Properties

First off, what are colligative properties? Simply put, they are properties of a solution that depend on the concentration of the solute particles, not on the identity of the solute. This means whether you dissolve sugar, salt, or any other non-volatile solute in water, the effect on the boiling point (or freezing point, vapor pressure, etc.) will depend on how many solute particles you have in the solution. This is a key concept, guys!

Now, there are four main colligative properties: boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. For our question, we're focused on boiling point elevation. When you add a solute to a solvent, the boiling point of the solution increases compared to the pure solvent. The extent of this increase depends on the concentration of the solute particles. Higher the concentration, higher the increase. So, if we add sugar to water, the solution will boil at a temperature higher than 100°C.

Boiling point elevation is directly proportional to the molality (m) of the solution, which is defined as moles of solute per kilogram of solvent. The formula is:

$$\Delta T_b = K_b \cdot m$$

Where:

• $\Delta T_b$ is the boiling point elevation (the change in boiling point).
• $K_b$ is the ebullioscopic constant (boiling point elevation constant), which is a property of the solvent. For water, $K_b \approx 0.512 \, ^\circ C/m$.
• $m$ is the molality of the solution.

Keep in mind, molality (m) is used instead of molarity (M) for boiling point elevation calculations because molality is temperature-independent. Since the volume of a solution can change with temperature, molarity (moles of solute per liter of solution) is temperature-dependent. For dilute solutions, the difference between molarity and molality is often negligible. However, for this example, we assume that the given molarity is approximately equal to molality.

Calculating the Boiling Point Elevation for a 1.0 M Sugar Solution

Now, let's use this knowledge to solve the question. We have a 1.0 M solution of sugar in water. Let's use the formula. First, determine the boiling point elevation:

$\Delta T_b = K_b \cdot m$

Since we have a 1.0 M sugar solution and the $K_b$ for water is approximately 0.512°C/m, we can plug in the values:

$\Delta T_b = 0.512 \, ^\circ C/m \cdot 1.0 \, m$

$\Delta T_b = 0.512 \, ^\circ C$

This means the boiling point of the solution will be elevated by 0.512°C compared to the normal boiling point of water.

To find the new boiling point, add the elevation to the normal boiling point of water (100°C):

New Boiling Point = 100°C + 0.512°C = 100.512°C.

So, the boiling point of the 1.0 M sugar solution is approximately 100.512°C. This is a great example of how understanding colligative properties can help predict the physical behavior of solutions. Also, this is why we can eliminate one of the answer choices instantly. That -0.3°C doesn't even make sense, right?

Analyzing the Answer Choices

Let's go back to the original answer options:

• $$100.3^{\circ} C$$

• $$-0.3^{\circ} C$$

• $$99.7^{\circ} C$$

Based on our calculation and understanding of boiling point elevation, we can eliminate the second and third options immediately. Remember, the boiling point of the solution must be higher than that of pure water (100°C). And, the calculated boiling point is 100.512°C. The closest option is 100.3°C. This demonstrates how colligative properties come into play when dealing with solutions, and now you're better equipped to tackle such problems!

Why Sugar? The Role of Intermolecular Forces

Sugar, also known as sucrose, is a non-electrolyte, meaning it doesn't dissociate into ions when dissolved in water. This contrasts with electrolytes like salt (NaCl), which dissociate into Na+ and Cl- ions. Since each sugar molecule remains intact, the number of solute particles is directly proportional to the concentration of sugar molecules. The interactions between sugar molecules and water molecules (hydrogen bonding) are crucial. Water molecules cluster around sugar molecules, disrupting the ability of water molecules to escape into the vapor phase, thereby increasing the boiling point. The stronger the intermolecular forces between the solute and solvent, the greater the boiling point elevation.

Understanding the Assumptions and Limitations

Our calculations are based on several assumptions, including ideal solution behavior, meaning that the solute particles do not interact significantly with each other. In reality, this is an approximation and is more accurate for dilute solutions. The van't Hoff factor, which accounts for the number of particles formed when a solute dissolves, is equal to 1 for sugar because it doesn't dissociate. For strong electrolytes, this factor would be greater than 1. This is another layer of depth for more complex questions. Furthermore, the use of molality in our calculations provides a more accurate representation of the boiling point elevation than molarity, although the difference is negligible for dilute solutions.

Practical Applications of Boiling Point Elevation

Understanding boiling point elevation isn't just a theoretical exercise, guys; it has practical applications too. For example, it's used in antifreeze in car radiators. Adding antifreeze (ethylene glycol) to the water raises the boiling point, preventing the engine from overheating. It also lowers the freezing point, protecting the engine from freezing in cold weather. Another everyday example is the use of salt to melt ice on roads. The salt dissolves in the water, lowering the freezing point, which helps the ice melt even at temperatures below 0°C.

Conclusion: Cracking the Chemistry Code

So, the boiling point of a 1.0 M solution of sugar in water is expected to be around 100.5°C, which is an elevation from the normal boiling point of pure water. Remember, colligative properties are powerful tools for understanding how solutions behave, and the concentration of the solute is the key factor. Keep practicing, and you'll master these concepts in no time! You're now equipped to tackle similar questions and understand the fascinating world of solution chemistry.

Important Points to Remember

• Colligative Properties: Depend on the concentration of solute particles, not their identity.
• Boiling Point Elevation: Adding a solute increases the boiling point of the solvent.
• Formula: $\Delta T_b = K_b \cdot m$ (where m is molality, and Kb is the solvent's constant).
• Real-World Applications: Antifreeze in car radiators and salt on icy roads are prime examples.

Keep learning, keep exploring, and keep asking questions. The world of chemistry is full of amazing discoveries! Also, remember to always double-check your assumptions and units.