A solution of glucose in water is labelled as 10% w/w, what would be the molality and mole fraction of each component in the solution? If the density of solution is 1.2 g mL–1, then what shall be the molarity of the solution?

To determine the molality, mole fraction, and molarity of a 10% w/w glucose solution, we need to break down the problem step by step. Let's start by understanding what each term means and how we can calculate them using the information provided.

Understanding the Composition of the Solution

A 10% w/w glucose solution means that there are 10 grams of glucose in every 100 grams of solution. The remaining mass (90 grams) is primarily water. We can use this information to find the molality, mole fraction, and molarity.

Calculating Molality

Molality (m) is defined as the number of moles of solute per kilogram of solvent. To find the molality, we first need to calculate the number of moles of glucose.

• Molar mass of glucose (C₆H₁₂O₆): 180 g/mol
• Number of moles of glucose:

  Number of moles = mass (g) / molar mass (g/mol) = 10 g / 180 g/mol = 0.0556 moles

• Mass of solvent (water): 90 g = 0.090 kg

Now we can calculate the molality:

Molality (m) = moles of solute / mass of solvent (kg) = 0.0556 moles / 0.090 kg = 0.617 m

Finding Mole Fraction

Mole fraction (X) is the ratio of the number of moles of a component to the total number of moles in the solution. We need to calculate the total moles in the solution, which includes both glucose and water.

• Number of moles of water:

  Molar mass of water (H₂O) = 18 g/mol

  Number of moles of water = mass (g) / molar mass (g/mol) = 90 g / 18 g/mol = 5 moles

• Total moles in the solution:

  Total moles = moles of glucose + moles of water = 0.0556 + 5 = 5.0556 moles

Now we can calculate the mole fractions:

• Mole fraction of glucose (X_glucose):

  X_glucose = moles of glucose / total moles = 0.0556 / 5.0556 = 0.0110

• Mole fraction of water (X_water):

  X_water = moles of water / total moles = 5 / 5.0556 = 0.9890

Calculating Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. To find molarity, we need the volume of the solution. Given the density of the solution is 1.2 g/mL, we can find the volume of 100 grams of solution.

• Volume of solution:

  Volume = mass / density = 100 g / (1.2 g/mL) = 83.33 mL = 0.08333 L

• Molarity (M):

  M = moles of solute / volume of solution (L) = 0.0556 moles / 0.08333 L = 0.667 M

Summary of Results

To summarize our findings:

• Molality: 0.617 m
• Mole fraction of glucose: 0.0110
• Mole fraction of water: 0.9890
• Molarity: 0.667 M

This breakdown should give you a clear understanding of how to approach similar problems involving solutions. Each calculation builds on the previous one, allowing you to derive the necessary values systematically.