Respuesta :
Answer: [tex]\Delta H = -272.25kJ[/tex] for 1 mole of NO.
Explanation: Hess' Law of Constant Summation or Hess' Law states that the total enthalpy change of a reaction with multiple stages is the sum of the enthalpies of all the changes.
For this question:
1) [tex]N_{2}_{(g)} + 3H_{2}_{(g)}[/tex] => [tex]2NH_{3}_{(g)}[/tex] [tex]\Delta H=-92kJ[/tex]
2) [tex]4NH_{3}_{(g)}+5O_{2}_{(g)}[/tex] => [tex]4NO_{(g)}+6H_{2}O_{(g)}[/tex] [tex]\Delta H=-905kJ[/tex]
Amonia ([tex]NH_{3}_{(g)}[/tex]) appeares as product in the first equation and as reagent in the 2 reaction, so when adding both, there is no need to inverse reactions. However, in the 2nd, there are 4 moles of that molecule, so to cancel it, you have to multiply by 2 the first chemical equation and enthalpy:
[tex]2N_{2}_{(g)} + 6H_{2}_{(g)}[/tex] => [tex]4NH_{3}_{(g)}[/tex] [tex]\Delta H=-184kJ[/tex]
Now, adding them:
[tex]2N_{2}_{(g)} + 6H_{2}_{(g)}[/tex] => [tex]4NH_{3}_{(g)}[/tex] [tex]\Delta H=-184kJ[/tex]
[tex]4NH_{3}_{(g)}+5O_{2}_{(g)}[/tex] => [tex]4NO_{(g)}+6H_{2}O_{(g)}[/tex] [tex]\Delta H=-905kJ[/tex]
[tex]2N_{2}_{(g)}+6H_{2}_{(g)}+5O_{2}_{(g)}=>4NO_{(g)}+6H_{2}O_{(g)}[/tex] [tex]\Delta H = -185-905[/tex]
[tex]2N_{2}_{(g)}+6H_{2}_{(g)}+5O_{2}_{(g)}=>4NO_{(g)}+6H_{2}O_{(g)}[/tex] [tex]\Delta H = -1089kJ[/tex]
Note net enthalpy is for the formation of 4 moles of nitric oxide.
For 1 mole:
[tex]\Delta H = \frac{-1089}{4}[/tex]
[tex]\Delta H=-272.25kJ[/tex]
To form 1 mol of nitric oxide from nitrogen, oxygen and hydrogen, net change in enthalpy is [tex]\Delta H=-272.25kJ[/tex].
