Answer :
To calculate the molality of a solution, we need to understand the concept of molality first. Molality (m) is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per kilogram of solvent.
Given:
- Mass of glycerol (C₃H₈O₃) = 9.23 g
- Mass of ethanol (C₂H₅OH) = 97.8 g
Steps to calculate molality:
Convert the mass of glycerol to moles:
The molar mass of glycerol (C₃H₈O₃) is calculated as follows:
[tex]\text{Molar mass of C₃H₈O₃} = (3 \times 12.01) \text{ g/mol (carbon)} + (8 \times 1.01) \text{ g/mol (hydrogen)} + (3 \times 16.00) \text{ g/mol (oxygen)}
= 36.03 + 8.08 + 48.00 = 92.11 \text{ g/mol}[/tex]Now, calculate the moles of glycerol:
[tex]\text{Moles of glycerol} = \frac{9.23 \text{ g}}{92.11 \text{ g/mol}} = 0.1003 \text{ mol}[/tex]
Convert the mass of ethanol to kilograms:
Since molality is moles per kilogram of solvent, we need to convert grams of ethanol to kilograms:
[tex]97.8 \text{ g} = 0.0978 \text{ kg}[/tex]
Calculate molality:
Now use the formula for molality:
[tex]m = \frac{\text{moles of glycerol}}{\text{kg of ethanol}}[/tex]
Substitute the values:
[tex]m = \frac{0.1003 \text{ mol}}{0.0978 \text{ kg}} = 1.026 \text{ mol/kg}[/tex]
Given the significant figures in the problem (three significant figures in the mass of glycerol and ethanol),
the final answer for molality is:
[tex]m = 1.03 \text{ mol/kg}[/tex]
So, the molality of the solution is 1.03 mol/kg.