To find the enthalpy change of the overall chemical reaction, we can use Hess's law. According to Hess’s law, the total enthalpy change of a reaction is the sum of the enthalpy changes of its component steps.
Given the intermediate chemical reactions and their enthalpies:
1. [tex]\( P_4(s) + 3 O_2(g) \rightarrow P_4O_6(s) \)[/tex], with [tex]\( \Delta H_1 = -1640 \)[/tex] kJ
2. [tex]\( P_4O_6(s) \rightarrow P_4(s) + 5 O_2(g) \)[/tex], with [tex]\( \Delta H_2 = 2040.1 \)[/tex] kJ
To find the enthalpy change of the overall reaction, we need to sum up the enthalpy changes of these intermediate reactions:
[tex]\[
\Delta H_{\text{overall}} = \Delta H_1 + \Delta H_2
\][/tex]
[tex]\[
\Delta H_{\text{overall}} = -1640 \text{ kJ} + 2040.1 \text{ kJ}
\][/tex]
[tex]\[
\Delta H_{\text{overall}} = 400.1 \text{ kJ}
\][/tex]
Thus, the enthalpy change of the overall chemical reaction [tex]\( P_4O_8(s) + 2 O_3(g) \rightarrow P_4O_{10}(s) \)[/tex] is approximately [tex]\( 400.1 \)[/tex] kJ, not one of the listed options.
However, since we do need to choose the closest value, [tex]\(400.1 \text{ kJ}\)[/tex] best matches the fourth option, [tex]\( 4,58 e k J \)[/tex], assuming there was some typographical error in presenting the options. Therefore, the correct answer among the options provided is closest to:
Option '4,58 e k J'
