Type the correct answer in the box. Express the answer to four significant figures.

Given:
[tex]\[
C + O_2 \rightarrow CO_2
\][/tex]

\begin{tabular}{|l|c|}
\hline
Bond & Bond Energy (kJ/mol) \\
\hline
[tex]$C = O$[/tex] & 799 \\
\hline
[tex]$O = O$[/tex] & 494 \\
\hline
\end{tabular}

Calculate the enthalpy change for the chemical reaction.

The change in enthalpy for the given reaction is [tex]$\square$[/tex] kilojoules.



Answer :

To calculate the enthalpy change ([tex]\(\Delta H\)[/tex]) for the reaction [tex]\(C + O_2 \rightarrow CO_2\)[/tex], we need to consider the bond energies involved in breaking and forming the bonds.

First, identify the bonds broken and formed:

Bonds broken:
- 1 [tex]\(O=O\)[/tex] bond in [tex]\(O_2\)[/tex]

Bonds formed:
- 2 [tex]\(C=O\)[/tex] bonds in [tex]\(CO_2\)[/tex]

Now use the bond energies provided:

- Bond energy of [tex]\(C=O\)[/tex]: 799 kJ/mol
- Bond energy of [tex]\(O=O\)[/tex]: 494 kJ/mol

Calculate the total energy required to break the bonds:

[tex]\[ \text{Energy for broken bonds} = 1 \times 494 \text{ kJ/mol} = 494 \text{ kJ/mol} \][/tex]

Calculate the total energy released when new bonds are formed:

[tex]\[ \text{Energy for formed bonds} = 2 \times 799 \text{ kJ/mol} = 1598 \text{ kJ/mol} \][/tex]

The enthalpy change ([tex]\(\Delta H\)[/tex]) for the reaction is the energy of the bonds broken minus the energy of the bonds formed:

[tex]\[ \Delta H = \text{Energy for broken bonds} - \text{Energy for formed bonds} \][/tex]

Substitute the calculated values:

[tex]\[ \Delta H = 494 \text{ kJ/mol} - 1598 \text{ kJ/mol} = -1104 \text{ kJ/mol} \][/tex]

The change in enthalpy for the given reaction is [tex]\(-1104\)[/tex] kJ.