Calculating Molality from Mole Fraction: NaCl in Water Solutions
Introduction
Solutions of sodium chloride (NaCl) in water are widely used in various applications, from food preservation to industrial processes. Understanding the relationship between mole fraction and molality is crucial for accurate concentration calculations. This article explains how to calculate the molality of an aqueous solution of NaCl given its mole fraction.
Definitions and Given Data
Let's start by defining two key terms: Mole Fraction (X): The ratio of the number of moles of NaCl to the total number of moles in the solution. Molality (m): The number of moles of solute per kilogram of solvent. Given that the mole fraction of NaCl (XNaCl) is 0.1, our goal is to determine the molality of the solution. We know that the sum of the mole fractions of all components in a solution must equal 1. Therefore, the mole fraction of water (Xwater) is 1 - 0.1 0.9.
Step-by-Step Calculation
Here are the steps to calculate the molality of the solution:
Determine the Mole Fraction of Water:Given the mole fraction of NaCl (XNaCl 0.1), the mole fraction of water (Xwater) is:
Xwater 1 - XNaCl 1 - 0.1 0.9Assume a Total Number of Moles: For simplicity, assume there are 1 mole of solute in the solution. This means: Moles of NaCl: 0.1 mole Moles of Water: 0.9 mole Calculate the Mass of the Solvent Water: The molar mass of water (H2O) is approximately 18 g/mol. Thus, the mass of water is: Mass of water moles of water × molar mass of water Mass of water 0.9 mol × 18 g/mol 16.2 g 0.0162 kg Calculate the Molality: Molality (m) is defined as the number of moles of solute per kilogram of solvent. Therefore: Molality (m) moles of NaCl / mass of solvent in kg Molality (m) 0.1 mol / 0.0162 kg ≈ 6.17 mol/kg Conclusion: The molality of the NaCl solution with a mole fraction of 0.1 is approximately 6.17 mol/kg.
Verification and Solubility Considerations
To verify the calculation, we can derive the same result using another approach. We know that the solution consists of 1/10 NaCl and 9/10 water. This means for every 1 mole of NaCl, there are 9 moles of water. The mass of the water can be calculated as:
Mass of water 9 moles × 18 g/mol 162 g 0.162 kg
Therefore, the molality can be calculated as:
Molality (1 mole NaCl / 0.162 kg water) ≈ 6.17 mol/kg
Additionally, it's important to note that the solubility of NaCl in water is approximately 360 g/liter at 20°C. A 6.17 molal solution of NaCl would contain 361.1 g of NaCl in 1000 g of water. Such a highly concentrated solution is highly unlikely to form due to the solubility constraints.
Conclusion
In summary, by understanding the relationship between mole fraction and molality, we can accurately calculate the molality of an aqueous solution of NaCl. Using the provided step-by-step approach, the calculated molality of a NaCl solution with a mole fraction of 0.1 is approximately 6.17 mol/kg. This understanding is vital for practical applications in chemistry and engineering.