Respuesta :
Answer : The enthalpy change for the reaction is, 201.9 kJ
Explanation :
According to Hess’s law of constant heat summation, the heat absorbed or evolved in a given chemical equation is the same whether the process occurs in one step or several steps.
According to this law, the chemical equation can be treated as ordinary algebraic expression and can be added or subtracted to yield the required equation. That means the enthalpy change of the overall reaction is the sum of the enthalpy changes of the intermediate reactions.
The balanced reaction of [tex]CH_4[/tex] will be,
[tex]2CH_4(g)\rightarrow C_2H_4(g)+2H_2(g)[/tex] [tex]\Delta H^o=?[/tex]
The intermediate balanced chemical reaction will be,
(1) [tex]CH_4(g)+2O_2(g)\rightarrow CO_2(g)+2H_2O(l)[/tex] [tex]\Delta H_1=-890.3kJ[/tex]
(2) [tex]C_2H_4(g)+H_2(g)\rightarrow C_2H_6(g)[/tex] [tex]\Delta H_2=-136.3kJ[/tex]
(3) [tex]2H_2(g)+O_2(g)\rightarrow 2H_2O(l)[/tex] [tex]\Delta H_3=-571.6kJ[/tex]
(4) [tex]2C_2H_6(g)+7O_2(g)\rightarrow 4CO_2(g)+6H_2O(l)[/tex] [tex]\Delta H_4=-3120.8kJ[/tex]
Now we will multiply the reaction 1 by 2, revere the reaction 2, reverse and half the reaction 3 and 4 then adding all the equations, we get :
(1) [tex]2CH_4(g)+4O_2(g)\rightarrow 2CO_2(g)+4H_2O(l)[/tex] [tex]\Delta H_1=2\times (-890.3kJ)=-1780.6kJ[/tex]
(2) [tex]C_2H_6(g)\rightarrow C_2H_4(g)+H_2(g)[/tex] [tex]\Delta H_2=-(-136.3kJ)=136.3kJ[/tex]
(3) [tex]H_2O(l)\rightarrow H_2(g)+\frac{1}{2}O_2(g)[/tex] [tex]\Delta H_3=-\frac{1}{2}\times (-571.6kJ)=285.8kJ[/tex]
(4) [tex]2CO_2(g)+3H_2O(l)\rightarrow C_2H_6(g)+\frac{7}{2}O_2(g)[/tex] [tex]\Delta H_4=-\frac{1}{2}\times (-3120.8kJ)=1560.4kJ[/tex]
The expression for enthalpy of the reaction will be,
[tex]\Delta H^o=\Delta H_1+\Delta H_2+\Delta H_3+\Delta H_4[/tex]
[tex]\Delta H=(-1780.6kJ)+(136.3kJ)+(285.8kJ)+(1560.4kJ)[/tex]
[tex]\Delta H=201.9kJ[/tex]
Therefore, the enthalpy change for the reaction is, 201.9 kJ
