Math Problem Statement
A 12.0 g sample of a nonelectrolyte is dissolved in 80 g of water. The solution freezes at -1.94 degrees Celsius. Assuming ideal solution behavior, calculate the substance's molar mass
Solution
To calculate the molar mass of the nonelectrolyte, we can use the depression in the freezing point equation, which is based on the concept of freezing point depression:
Where:
- is the freezing point depression (the difference between the freezing point of pure solvent and the freezing point of the solution),
- is the van’t Hoff factor (for nonelectrolytes, since they do not dissociate),
- is the freezing point depression constant of the solvent (for water, K_f = 1.86 \, ^\circ \text{C} \cdot \text{kg/mol}),
- is the molality of the solution, defined as the number of moles of solute per kilogram of solvent.
Step-by-Step Calculation
-
Find the freezing point depression :
-
Use the freezing point depression equation to find molality:
Rearrange the equation for molality :
-
Calculate the number of moles of solute:
Molality is defined as the number of moles of solute per kilogram of solvent. Given the mass of water (solvent) is 80 g, or 0.080 kg, the number of moles of solute can be calculated as:
-
Calculate the molar mass of the solute:
Molar mass is the mass of the solute divided by the number of moles of solute:
Final Answer:
The molar mass of the nonelectrolyte is approximately 143.8 g/mol.
Do you want more details or have any questions?
Here are 5 related questions you might find interesting:
- What would happen if the substance were an electrolyte?
- How does the molar mass of a substance affect its properties in a solution?
- Can you calculate the boiling point elevation for the same solution?
- How does the choice of solvent impact freezing point depression?
- What assumptions are made in ideal solution behavior?
Tip: Always check the units when working with colligative properties to avoid errors!
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Math Problem Analysis
Mathematical Concepts
Freezing Point Depression
Colligative Properties
Molality
Formulas
ΔTf = i * Kf * m
m = ΔTf / (i * Kf)
Molar mass = mass of solute / moles of solute
Theorems
Freezing Point Depression Equation
Suitable Grade Level
Grades 11-12 (Advanced High School Chemistry)
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