Calculating Sugar Solution Concentration Using Vapor Pressure Lowering And Osmotic Pressure

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In the realm of chemistry, understanding the properties of solutions is crucial. Colligative properties, which depend on the concentration of solute particles rather than their identity, play a significant role in various applications. This article delves into calculating the concentration of a sugar solution using vapor pressure lowering and osmotic pressure, two key colligative properties. We will explore the underlying principles and step-by-step calculations to arrive at the solution concentration in grams per liter (g/L).

Vapor Pressure Lowering: A Deep Dive

Vapor pressure lowering is a colligative property that describes the decrease in vapor pressure of a solvent when a non-volatile solute is added. The extent of this lowering is directly proportional to the mole fraction of the solute in the solution. Raoult's Law mathematically expresses this relationship:

P = P₀ * X_solvent

Where:

  • P is the vapor pressure of the solution
  • P₀ is the vapor pressure of the pure solvent
  • X_solvent is the mole fraction of the solvent in the solution

In our scenario, we are given that the vapor pressure of the solution (P) is 23.4 mmHg and the relative lowering of vapor pressure is 0.0168. The relative lowering of vapor pressure is defined as:

(P₀ - P) / P₀

This value is equal to the mole fraction of the solute (X_solute). Therefore, we have:

X_solute = 0.0168

To find the concentration of the sugar solution, we need to relate the mole fraction of the solute to its mass concentration (g/L). This involves considering the molar mass of the solvent (water in this case) and the molar mass of the solute (sugar).

Let's assume we are dealing with a dilute aqueous solution. The mole fraction of the solute is much smaller than the mole fraction of the solvent. In such cases, we can approximate the mole fraction of the solute as:

X_solute ≈ n_solute / n_solvent

Where:

  • n_solute is the number of moles of solute
  • n_solvent is the number of moles of solvent

Knowing the mole fraction of the solute and assuming we are working with water as the solvent, we can calculate the number of moles of solute per mole of water. From this, we can derive the mass of solute per mass of water and eventually convert it to grams per liter.

Osmotic Pressure: Unveiling Solution Concentration

Osmotic pressure is another crucial colligative property. It is the pressure required to prevent the flow of solvent across a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. The van't Hoff equation relates osmotic pressure to the concentration of the solution:

π = i * M * R * T

Where:

  • π is the osmotic pressure
  • i is the van't Hoff factor (number of particles the solute dissociates into)
  • M is the molarity of the solution
  • R is the ideal gas constant (0.0821 L atm / (mol K))
  • T is the temperature in Kelvin

In our problem, we are given that the osmotic pressure (π) is 0.46 atm at a temperature (T) of 300 K. Since we are dealing with a sugar solution, sugar is a non-electrolyte and does not dissociate in water, so the van't Hoff factor (i) is 1.

Using the van't Hoff equation, we can calculate the molarity (M) of the solution:

M = π / (R * T)

Once we have the molarity, we can convert it to grams per liter (g/L) by multiplying the molarity by the molar mass of the sugar. The molar mass of the sugar will depend on the specific sugar used (e.g., sucrose, glucose, fructose). Let's assume we are dealing with sucrose (C₁₂H₂₂O₁₁), which has a molar mass of 342.3 g/mol.

Therefore, the concentration in g/L can be calculated as:

Concentration (g/L) = Molarity (mol/L) * Molar mass (g/mol)

By performing these calculations, we can determine the concentration of the sugar solution using the osmotic pressure data.

Step-by-Step Calculation of Sugar Solution Concentration

Let's break down the calculation into clear steps:

Step 1: Calculate Molarity from Osmotic Pressure

Using the van't Hoff equation:

π = i * M * R * T

We have π = 0.46 atm, i = 1, R = 0.0821 L atm / (mol K), and T = 300 K. Plugging these values into the equation:

0.  46 atm = 1 * M * 0.0821 L atm / (mol K) * 300 K

Solving for M (Molarity):

M = 0.46 atm / (0.0821 L atm / (mol K) * 300 K)
M ≈ 0.0187 mol/L

Step 2: Convert Molarity to Grams per Liter (g/L)

Assuming we are using sucrose (C₁₂H₂₂O₁₁) with a molar mass of 342.3 g/mol:

Concentration (g/L) = Molarity (mol/L) * Molar mass (g/mol)
Concentration (g/L) = 0.0187 mol/L * 342.3 g/mol
Concentration (g/L) ≈ 6.40 g/L

Therefore, the concentration of the sugar solution is approximately 6.40 g/L.

Conclusion: Connecting Colligative Properties to Concentration

This exercise demonstrates how colligative properties, such as vapor pressure lowering and osmotic pressure, can be used to determine the concentration of a solution. Understanding these relationships is essential in various chemical and biological applications, ranging from determining the molar masses of unknown substances to understanding the behavior of cells in different environments. By applying the principles of Raoult's Law and the van't Hoff equation, we can accurately calculate solution concentrations and gain valuable insights into the nature of solutions.

In summary, we successfully calculated the concentration of the sugar solution using the given osmotic pressure. The result highlights the power of colligative properties in quantitative analysis. The combined application of vapor pressure lowering and osmotic pressure provides a comprehensive approach to characterizing solutions and understanding their behavior.

  • Colligative Properties
  • Vapor Pressure Lowering
  • Osmotic Pressure
  • Solution Concentration
  • Raoult's Law
  • van't Hoff Equation
  • Molarity
  • Molar Mass
  • Sugar Solution
  • Chemistry Calculations
  • Relative Lowering of Vapor Pressure
  • Non-volatile solute
  • Semipermeable membrane
  • What is the concentration in g/L of a sugar solution with a vapor pressure of 23.4 mmHg, a relative lowering of vapor pressure of 0.0168, and an osmotic pressure of 0.46 atmosphere at 300 K?