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How much heat is required to vaporize 38.5 g of acetone (C₃H₆O) at 25 °C?

The heat of vaporization for acetone at this temperature is 31.0 kJ/mol.

Answer :

To determine the amount of heat required to vaporize 38.5 g of acetone at 25 °C, we use the concept of the heat of vaporization. The heat of vaporization is the amount of heat needed to convert a given amount of liquid into vapor without changing its temperature.

Here's a step-by-step calculation:

  1. Find the molar mass of acetone (C₃H₆O):

    • Carbon (C): 12.01 g/mol × 3 = 36.03 g/mol
    • Hydrogen (H): 1.01 g/mol × 6 = 6.06 g/mol
    • Oxygen (O): 16.00 g/mol × 1 = 16.00 g/mol

    So, the molar mass of acetone is:
    [tex]36.03 \text{ g/mol} + 6.06 \text{ g/mol} + 16.00 \text{ g/mol} = 58.09 \text{ g/mol}[/tex]

  2. Calculate the number of moles of acetone in 38.5 g:

    Use the formula:
    [tex]\text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}}[/tex]

    [tex]\text{Number of moles} = \frac{38.5 \text{ g}}{58.09 \text{ g/mol}} \approx 0.663 \text{ mol}[/tex]

  3. Calculate the heat required for the vaporization:

    The heat of vaporization of acetone is given as 31.0 kJ/mol. To find the total heat required, multiply the number of moles by the heat of vaporization:

    [tex]\text{Heat required} = \text{Number of moles} \times \text{Heat of vaporization}[/tex]

    [tex]\text{Heat required} = 0.663 \text{ mol} \times 31.0 \text{ kJ/mol} \approx 20.55 \text{ kJ}[/tex]

Therefore, approximately 20.55 kJ of heat is required to vaporize 38.5 g of acetone at 25 °C.

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