The Van’t Hoff factor for a dilute aqueous solution of glucose is:

A.) Zero

B.) 1.0

C.) 1.5

D.) 2.0

The Van’t Hoff factor, often represented by the symbol "i," is a crucial concept in colligative properties of solutions. For a dilute aqueous solution of glucose, the correct answer is B.) 1.0. Let’s break down why this is the case.

Understanding the Van’t Hoff Factor

The Van’t Hoff factor indicates the number of particles a solute produces in solution. It plays a significant role in determining properties like boiling point elevation and freezing point depression. For ionic compounds, this factor can be greater than one because they dissociate into multiple ions. However, for non-electrolytes like glucose, the situation is different.

Characteristics of Glucose

Glucose (C₆H₁₂O₆) is a simple sugar and a non-electrolyte. When glucose dissolves in water, it does not dissociate into smaller particles; instead, it remains as whole molecules. This means that for every molecule of glucose that dissolves, it contributes exactly one particle to the solution.

Calculating the Van’t Hoff Factor

• For ionic compounds: For example, sodium chloride (NaCl) dissociates into two ions (Na⁺ and Cl⁻), giving it a Van’t Hoff factor of 2.
• For glucose: Since it does not dissociate, the Van’t Hoff factor is simply 1.

This can be summarized as follows: when you dissolve one mole of glucose in water, you get one mole of glucose molecules in solution, leading to a Van’t Hoff factor of 1.0.

Implications in Colligative Properties

The Van’t Hoff factor is essential when calculating colligative properties. For instance, if you were to calculate the freezing point depression of a glucose solution, you would use the formula:

ΔT_f = i * K_f * m

Where:

• ΔT_f = change in freezing point
• i = Van’t Hoff factor (1 for glucose)
• K_f = freezing point depression constant of the solvent
• m = molality of the solution

Since i is 1 for glucose, it simplifies calculations, making it easier to predict how the solution will behave compared to ionic solutions.

Final Thoughts

In summary, the Van’t Hoff factor for a dilute aqueous solution of glucose is 1.0 because glucose does not dissociate into multiple particles in solution. This characteristic is vital for understanding how glucose behaves in various chemical contexts, particularly in biological systems where it plays a significant role as an energy source.