Respuesta :
Answer: The enthalpy of the reaction for the production of [tex]CH_4[/tex] is coming out to be -74.9 kJ
Explanation:
Enthalpy change is defined as the difference in enthalpies of all the product and the reactants each multiplied with their respective number of moles. It is represented as [tex]\Delta H^o[/tex]
The equation used to calculate enthalpy change is of a reaction is:
[tex]\Delta H^o_{rxn}=\sum [n\times \Delta H^o_f_{(product)}]-\sum [n\times \Delta H^o_f_{(reactant)}][/tex]
For the given chemical reaction:
[tex]C(s)+2H_2(g)\rightarrow CH_4(g)[/tex]
The equation for the enthalpy change of the above reaction is:
[tex]\Delta H^o_{rxn}=[(1\times \Delta H^o_f_{(CH_4(g))})]-[(1\times \Delta H^o_f_{(C(s))})+(2\times \Delta H^o_f_{(H_2(g))})][/tex]
We are given:
[tex]\Delta H^o_f_{(C(s))}=0kJ/mol\\\Delta H^o_f_{(H_2)}=0kJ/mol\\\Delta H^o_f_{CH_4}=-74.9kJ/mol[/tex]
Putting values in above equation, we get:
[tex]\Delta H^o_{rxn}=[(1\times (-74.9))]-[1\times 0)+(2\times 0)]\\\\\Delta H^o_{rxn}=-74.9kJ[/tex]
Hence, the enthalpy of the reaction for the production of [tex]CH_4[/tex] is coming out to be -74.9 kJ
The heat of reaction [tex]\Delta H ^{0} _{rxn}[/tex], for the overall production of methane, CH₄ is -74.7 kJ
The heat of reaction for the formation of methane cannot be determined directly.
From Hess's law, which states that the change of enthalpy in a chemical reaction is the same regardless of whether the reaction takes place in one step or several steps.
Then, we will consider the heat of reaction values for the following reactions
(1) C + O₂(g) → CO₂(g) [tex]\Delta H ^{0} _{rxn} = -393.5 \ kJ[/tex]
(2) 2H₂(g) + O₂(g) → 2H₂O(l) [tex]\Delta H ^{0} _{rxn} = -571.6 \ kJ[/tex]
(3) CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) [tex]\Delta H ^{0} _{rxn} = -890.4 \ kJ[/tex]
Now, since we are interested in the production of methane, CH₄, we will reverse (3) to get
(4) CO₂(g) + 2H₂O(l) → CH₄(g) + 2O₂(g) [tex]\Delta H ^{0} _{rxn} = 890.4 \ kJ[/tex]
Now, add equations (1), (2), and (4), to get equation (5)
(1) C + O₂(g) → CO₂(g) [tex]\Delta H ^{0} _{rxn} = -393.5 \ kJ[/tex]
(2) 2H₂(g) + O₂(g) → 2H₂O(l) [tex]\Delta H ^{0} _{rxn} = -571.6 \ kJ[/tex]
(4) CO₂(g) + 2H₂O(l) → CH₄(g) + 2O₂(g) [tex]\Delta H ^{0} _{rxn} = 890.4 \ kJ[/tex]
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(5) C + 2H₂(g) → CH₄(g) [tex]\Delta H ^{0} _{rxn} = -74.7 \ kJ[/tex]
Hence, the heat of reaction [tex]\Delta H ^{0} _{rxn}[/tex], for the overall production of methane, CH₄ is -74.7 kJ
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