Sure, let's walk through the detailed solution step by step.
1. Determine the number of moles of acetone:
- Given the mass of acetone [tex]\( (\text{CH}_3 \text{COCH}_3) \)[/tex] is [tex]\( 22.1 \, \text{g} \)[/tex].
- The molar mass of acetone is [tex]\( 58.08 \, \text{g/mol} \)[/tex].
Using the formula for moles:
[tex]\[
\text{moles} = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
Substitute in the given values:
[tex]\[
\text{moles of acetone} = \frac{22.1 \, \text{g}}{58.08 \, \text{g/mol}} \approx 0.3805 \, \text{mol}
\][/tex]
2. Calculate the energy released:
- The enthalpy change ([tex]\(\Delta H\)[/tex]) for the combustion of one mole of acetone is given as [tex]\( -1.79 \times 10^3 \, \text{kJ} \)[/tex].
To find the total energy released when [tex]\( 0.3805 \, \text{mol} \)[/tex] of acetone is burned, multiply the moles of acetone by the enthalpy change per mole:
[tex]\[
\text{energy released} = \text{moles of acetone} \times \Delta H
\][/tex]
Substitute the known values:
[tex]\[
\text{energy released} = 0.3805 \, \text{mol} \times \left( -1.79 \times 10^3 \, \text{kJ/mol} \right)
\][/tex]
[tex]\[
\text{energy released} \approx -681.112 \, \text{kJ}
\][/tex]
Thus, when a 22.1-g sample of acetone is burned, approximately [tex]\( -681.112 \, \text{kJ} \)[/tex] of energy is released as heat. The negative sign indicates that the energy is released (exothermic reaction).
