Boiling Point Elevation Calculations For NaCl And Sugar Solutions

by ADMIN 66 views

In chemistry, understanding the colligative properties of solutions is crucial, especially when dealing with boiling point elevation. Boiling point elevation, a colligative property, refers to the increase in the boiling point of a solvent upon the addition of a solute. This phenomenon depends solely on the number of solute particles present in the solution, regardless of their identity. We will explore the concept of boiling point elevation and delve into calculating the boiling point of solutions, focusing on two specific scenarios involving sodium chloride (NaCl) and a non-volatile sugar dissolved in water.

Calculating the Boiling Point Elevation of a NaCl Solution

Understanding Boiling Point Elevation

To accurately calculate the boiling point elevation, it's essential to grasp the underlying principles. Boiling point elevation occurs because the presence of solute particles lowers the vapor pressure of the solvent. Vapor pressure is the pressure exerted by the vapor of a liquid when it is in equilibrium with its liquid phase. When a solute is added, it disrupts the solvent's ability to vaporize, leading to a decrease in vapor pressure. Consequently, a higher temperature is required for the solution to reach its boiling point, the temperature at which the vapor pressure equals the external pressure. The extent of boiling point elevation is directly proportional to the molality of the solute, which is the number of moles of solute per kilogram of solvent.

Step-by-Step Calculation for NaCl Solution

Let's start with the first scenario: determining the boiling point of a solution made by dissolving 45.0 g of NaCl in 500 g of water. We are given the ebullioscopic constant (K_b) for water as 0.512 °C/m. The ebullioscopic constant is a solvent-specific constant that reflects the extent to which the boiling point increases for every 1 mol of solute particles added to 1 kg of the solvent.

  1. Calculate the moles of NaCl: First, we need to convert the mass of NaCl to moles using its molar mass. The molar mass of NaCl is approximately 58.44 g/mol. So, moles of NaCl = 45.0 g / 58.44 g/mol ≈ 0.770 mol.
  2. Determine the molality of the solution: Molality (m) is defined as moles of solute per kilogram of solvent. In this case, the solvent is water, and its mass is 500 g, which is 0.500 kg. Therefore, the molality of the solution is m = 0.770 mol / 0.500 kg = 1.54 m.
  3. Account for the van't Hoff factor: NaCl is an ionic compound that dissociates into two ions (Na+ and Cl-) in water. The van't Hoff factor (i) represents the number of particles a solute dissociates into in a solution. For NaCl, i = 2. This factor is crucial because boiling point elevation depends on the total number of solute particles in the solution.
  4. Calculate the boiling point elevation (ΔT_b): The formula for boiling point elevation is ΔT_b = i * K_b * m, where ΔT_b is the change in boiling point, i is the van't Hoff factor, K_b is the ebullioscopic constant, and m is the molality. Plugging in the values, we get ΔT_b = 2 * 0.512 °C/m * 1.54 m ≈ 1.58 °C.
  5. Determine the new boiling point: The normal boiling point of water is 100 °C. The boiling point of the solution is elevated by ΔT_b. Therefore, the new boiling point is 100 °C + 1.58 °C = 101.58 °C.

Summary for NaCl Solution

In summary, the boiling point of a solution made by dissolving 45.0 g of NaCl in 500 g of water is approximately 101.58 °C. This calculation highlights the significance of considering the dissociation of ionic compounds and the resulting increase in solute particles when determining boiling point elevation.

Calculating the Molar Mass Using Boiling Point Elevation

Understanding Molar Mass and Non-Volatile Solutes

Now, let's consider the second scenario, where 39.8 g of a non-volatile, non-dissociating sugar is dissolved in 200.0 g of water, and the boiling point of the water is raised by 0.34 °C. Here, our objective is to determine the molar mass of the sugar. A non-volatile solute is a substance that does not readily evaporate into a gas at normal temperatures, and a non-dissociating solute is one that does not break apart into ions when dissolved in a solvent. Sugars generally fall into this category, making them ideal for illustrating boiling point elevation calculations without the complication of the van't Hoff factor.

Step-by-Step Calculation for Sugar Solution

To find the molar mass, we'll use the boiling point elevation formula in reverse, leveraging the known values to deduce the unknown molar mass.

  1. Identify the knowns: We know the mass of the sugar (39.8 g), the mass of the water (200.0 g or 0.200 kg), the boiling point elevation (ΔT_b = 0.34 °C), and the ebullioscopic constant for water (K_b = 0.512 °C/m). Since the sugar is non-dissociating, the van't Hoff factor (i) is 1.
  2. Use the boiling point elevation formula to find molality: The formula ΔT_b = i * K_b * m can be rearranged to solve for molality: m = ΔT_b / (i * K_b). Plugging in the values, we get m = 0.34 °C / (1 * 0.512 °C/m) ≈ 0.664 m.
  3. Calculate the moles of sugar: Molality is defined as moles of solute per kilogram of solvent. We know the molality and the mass of the solvent (water), so we can calculate the moles of sugar: moles of sugar = molality * kg of water = 0.664 m * 0.200 kg = 0.133 mol.
  4. Determine the molar mass of the sugar: Molar mass is defined as grams of solute per mole of solute. We know the mass of the sugar (39.8 g) and the moles of sugar (0.133 mol), so we can calculate the molar mass: molar mass = 39.8 g / 0.133 mol ≈ 299 g/mol.

Summary for Sugar Solution

Thus, the molar mass of the non-volatile, non-dissociating sugar is approximately 299 g/mol. This calculation demonstrates how boiling point elevation can be used as a tool to determine the molar mass of unknown substances, especially non-volatile solutes.

Conclusion: Significance of Boiling Point Elevation

In conclusion, boiling point elevation is a fundamental colligative property that has significant implications in chemistry and related fields. Through the detailed calculations for both the NaCl solution and the sugar solution, we've illustrated how the addition of solutes affects the boiling point of a solvent. For ionic compounds like NaCl, the dissociation into ions must be considered using the van't Hoff factor, while for non-dissociating solutes like sugar, the calculations are more straightforward. Understanding these principles allows us to predict and calculate the boiling points of various solutions and even determine the molar masses of unknown substances.

Boiling point elevation is not just a theoretical concept; it has practical applications in various industries, including pharmaceuticals, food processing, and chemical manufacturing. For instance, it is used in the formulation of antifreeze solutions, where solutes are added to water to lower its freezing point and raise its boiling point, preventing damage to engines in cold weather. In the food industry, it plays a role in the concentration of solutions, such as in the production of syrups and jams. Therefore, a thorough understanding of boiling point elevation is essential for students and professionals alike in the field of chemistry and beyond.

In summary, by understanding the principles behind boiling point elevation and mastering the calculations involved, we gain valuable insights into the behavior of solutions and their properties. This knowledge is not only crucial for academic success but also for practical applications in various scientific and industrial contexts. As we continue to explore the fascinating world of chemistry, the concepts of colligative properties, such as boiling point elevation, will undoubtedly remain a cornerstone of our understanding.