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Calculate the molality of a solution containing 9.23 g of glycerol ([tex]C_3H_8O_3[/tex]) in 97.8 g of ethanol ([tex]C_2H_5OH[/tex]). Be sure your answer has the correct number of significant figures.

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:

  1. 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]

  2. 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]

  3. 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.

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