What is the molarity of a solution of glucose which has mole fraction 0.3?

To find the molarity of a glucose solution with a mole fraction of 0.3, we need to understand the relationship between mole fraction, moles, and molarity. Molarity is defined as the number of moles of solute per liter of solution. Let's break this down step by step.

Understanding Mole Fraction

The mole fraction (X) 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. In this case, we have:

• X_glucose = 0.3
• X_water = 1 - X_glucose = 0.7

Calculating Moles of Glucose and Water

Let's assume we have 1 mole of the solution for simplicity. If glucose has a mole fraction of 0.3, then:

• Moles of glucose = 0.3 moles
• Moles of water = 0.7 moles

Finding the Mass of Water

Next, we need to calculate the mass of water since we will eventually need the volume of the solution. The molar mass of water (H₂O) is approximately 18 g/mol. Therefore:

• Mass of water = Moles of water × Molar mass of water
• Mass of water = 0.7 moles × 18 g/mol = 12.6 g

Calculating the Volume of the Solution

To find the volume of the solution, we need to convert the mass of water to volume. The density of water is about 1 g/mL, so:

• Volume of water = Mass of water / Density of water
• Volume of water = 12.6 g / 1 g/mL = 12.6 mL

Since we have 0.3 moles of glucose, we can assume that the volume of the solution is approximately the same as the volume of water, as the addition of glucose will not significantly change the volume. Therefore, the total volume of the solution is about 12.6 mL, or 0.0126 L.

Calculating Molarity

Now that we have the number of moles of glucose and the volume of the solution, we can calculate the molarity (M) using the formula:

• Molarity (M) = Moles of solute / Volume of solution in liters
• Molarity (M) = 0.3 moles / 0.0126 L ≈ 23.81 M

Final Thoughts

Thus, the molarity of the glucose solution with a mole fraction of 0.3 is approximately 23.81 M. This high value indicates a concentrated solution, which is typical for glucose solutions used in various applications, including medical and laboratory settings.