## Answer :

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).