Ethanol Solution Concentration Calculations Molarity, Molality, And Mole Fraction

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In chemistry, understanding the concentration of solutions is crucial for various applications, from laboratory experiments to industrial processes. Concentration can be expressed in several ways, including molarity, molality, and mole fraction. This article delves into calculating these concentration units for a solution prepared by mixing ethyl alcohol (C2H5OH) with water. Specifically, we will explore the scenario where 50 mL of ethyl alcohol (density = 0.789 g/mL) is added to 50 mL of water, resulting in a 95 mL solution. We will calculate the molarity, molality, and mole fraction of ethanol (C2H5OH) in the solution. Mastering these calculations is fundamental to grasping solution chemistry and its practical implications.

Before diving into the calculations, it's important to define the concentration units we'll be working with:

  • Molarity (M): Molarity is defined as the number of moles of solute per liter of solution. It's a commonly used unit in chemistry because it directly relates the amount of solute to the volume of the solution. The formula for molarity is: Molarity (M) = Moles of solute / Liters of solution.
  • Molality (m): Molality, on the other hand, is defined as the number of moles of solute per kilogram of solvent. Unlike molarity, molality is independent of temperature because it's based on mass rather than volume. The formula for molality is: Molality (m) = Moles of solute / Kilograms of solvent.
  • Mole Fraction (χ): The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all components in the solution. It's a dimensionless quantity, often expressed as a decimal. The formula for mole fraction is: Mole fraction (χ) = Moles of component / Total moles in solution.

Understanding the distinction between these concentration units is essential for accurate calculations and interpreting experimental results. For example, molarity is convenient for volumetric measurements, while molality is preferred when temperature variations are significant. Mole fraction provides insight into the relative amounts of each component in the solution.

Now, let's proceed with the calculations for the given scenario. We'll break down the process into clear, manageable steps.

a) Molarity of C2H5OH

To calculate the molarity of C2H5OH, we need to determine the moles of C2H5OH and the volume of the solution in liters. Here's how we do it:

  1. Calculate the mass of C2H5OH:

    • We are given the volume of C2H5OH (50 mL) and its density (0.789 g/mL). We can use the formula: Mass = Volume × Density.
    • Mass of C2H5OH = 50 mL × 0.789 g/mL = 39.45 g

  2. Calculate the moles of C2H5OH:

    • To convert grams to moles, we need the molar mass of C2H5OH. The molar mass of C2H5OH (C2H5OH) is (2 × 12.01) + (6 × 1.01) + (1 × 16.00) = 46.08 g/mol.
    • Moles of C2H5OH = Mass of C2H5OH / Molar mass of C2H5OH = 39.45 g / 46.08 g/mol = 0.856 mol

  3. Convert the volume of the solution to liters:

    • We are given the volume of the solution as 95 mL. To convert this to liters, we divide by 1000: Volume of solution = 95 mL / 1000 mL/L = 0.095 L

  4. Calculate the molarity of C2H5OH:

    • Now we can use the formula for molarity: Molarity (M) = Moles of solute / Liters of solution.
    • Molarity of C2H5OH = 0.856 mol / 0.095 L = 9.01 M

Therefore, the molarity of C2H5OH in the solution is 9.01 M. This means there are 9.01 moles of ethanol per liter of solution. Understanding molarity is crucial for accurately measuring and dispensing solutions in laboratory settings and industrial applications.

b) Molality of C2H5OH

To calculate the molality of C2H5OH, we need the moles of C2H5OH (which we already calculated) and the mass of the solvent (water) in kilograms. Here's the process:

  1. Calculate the mass of water:

    • We are given the volume of water (50 mL). We need to use the density of water, which is approximately 1 g/mL. Mass of water = Volume of water × Density of water.
    • Mass of water = 50 mL × 1 g/mL = 50 g

  2. Convert the mass of water to kilograms:

    • To convert grams to kilograms, we divide by 1000: Mass of water = 50 g / 1000 g/kg = 0.05 kg

  3. Calculate the molality of C2H5OH:

    • Now we can use the formula for molality: Molality (m) = Moles of solute / Kilograms of solvent.
    • Molality of C2H5OH = 0.856 mol / 0.05 kg = 17.12 m

Thus, the molality of C2H5OH in the solution is 17.12 m. This indicates that there are 17.12 moles of ethanol per kilogram of water. Molality is particularly useful when dealing with colligative properties of solutions, such as boiling point elevation and freezing point depression, which depend on the number of solute particles relative to the amount of solvent.

c) Mole Fraction of C2H5OH

To determine the mole fraction of C2H5OH, we need the moles of C2H5OH (which we've already calculated) and the moles of water. Then, we can find the total moles in the solution and calculate the mole fraction.

  1. Calculate the moles of water:

    • We have the mass of water (50 g). The molar mass of water (H2O) is (2 × 1.01) + 16.00 = 18.02 g/mol.
    • Moles of water = Mass of water / Molar mass of water = 50 g / 18.02 g/mol = 2.77 mol

  2. Calculate the total moles in the solution:

    • Total moles = Moles of C2H5OH + Moles of water = 0.856 mol + 2.77 mol = 3.626 mol

  3. Calculate the mole fraction of C2H5OH:

    • Now we use the formula for mole fraction: Mole fraction (χ) = Moles of component / Total moles in solution.
    • Mole fraction of C2H5OH = 0.856 mol / 3.626 mol = 0.236

The mole fraction of C2H5OH in the solution is 0.236. This signifies that ethanol constitutes 23.6% of the total number of moles in the solution. Mole fraction is a dimensionless unit that provides a clear representation of the relative amounts of each component in a mixture. It's often used in thermodynamic calculations and phase diagrams.

Let's summarize our findings:

  • (a) Molarity of C2H5OH: 9.01 M
  • (b) Molality of C2H5OH: 17.12 m
  • (c) Mole Fraction of C2H5OH: 0.236

These values provide a comprehensive understanding of the concentration of ethanol in the water solution using different units. Molarity is convenient for volumetric measurements, molality is useful when temperature changes are a concern, and mole fraction provides a relative measure of the components in the mixture.

Understanding and calculating solution concentrations like molarity, molality, and mole fraction are fundamental in various fields:

  • Chemistry: These calculations are essential for preparing solutions of specific concentrations in laboratory experiments, titrations, and chemical reactions. Accurate concentration measurements are crucial for obtaining reliable results.
  • Biology: In biological research and medicine, solutions of specific concentrations are used for cell culture, drug preparation, and biochemical assays. For example, saline solutions used in intravenous drips need to have precise concentrations to match the osmotic pressure of blood.
  • Pharmacy: Pharmacists use concentration calculations to prepare medications, ensuring the correct dosage is administered. The concentration of active ingredients in drugs must be carefully controlled to ensure efficacy and safety.
  • Industry: In industrial processes, concentration control is vital for manufacturing chemicals, polymers, and other materials. For instance, in the food and beverage industry, the concentration of ingredients like sugar and acids must be carefully monitored to ensure product quality.
  • Environmental Science: Concentration measurements are used to assess water and air quality, monitor pollution levels, and determine the effectiveness of remediation efforts. Understanding the concentration of pollutants is critical for protecting ecosystems and human health.

The ability to accurately calculate and interpret solution concentrations is a cornerstone of scientific practice and has broad applications across various disciplines. The principles discussed in this article provide a solid foundation for understanding and working with solutions in diverse contexts.

In this article, we have demonstrated how to calculate the molarity, molality, and mole fraction of a solution prepared by mixing ethyl alcohol and water. We started with the basic definitions of these concentration units and then walked through a step-by-step calculation process for each. By understanding these calculations, you can accurately determine the concentration of solutions in various contexts, from laboratory experiments to real-world applications. Mastering these concepts is essential for anyone working in chemistry, biology, pharmacy, or related fields.

The ability to work with solution concentrations is a critical skill for scientists and professionals across many disciplines. Whether you are a student learning the fundamentals or a researcher conducting cutting-edge experiments, a solid grasp of these concepts will serve you well in your endeavors. Continue practicing these calculations and exploring their applications to deepen your understanding and enhance your problem-solving abilities in the fascinating world of chemistry.