Question

Find the ΔH° for the reaction? a) Fe2O3(s)+3CO2(g)→2Fe(s)+3CO2(g)

Answer 1

For

`"Fe"_2"O"_3(s) + 3"CO"(g) -> 2"Fe"(s) + 3"CO"_2(g)`

you should get `-"23.47 kJ/mol"`, if you use my numbers. Go look up numbers from your own book and try again... see what you get, and verify mine is correct.

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Well, when you manage to search your appendix for the substances in...

`"Fe"_2"O"_3(s) + 3"CO"(g) -> 2"Fe"(s) + 3"CO"_2(g)`

...and you manage to fix your reaction, you should find them. I'm using NIST, which is quite a reliable database, especially for thermochemistry and spectroscopic data.

`DeltaH_(f,Fe_2O_3(s))^@ = -"825.50 kJ/mol"`
http://webbook.nist.gov/cgi/cbook.cgi?ID=C1317608&Mask=2

`DeltaH_(f,CO(g))^@ = -"110.53 kJ/mol"`
http://webbook.nist.gov/cgi/cbook.cgi?ID=C630080&Units=SI&Mask=1

`DeltaH_(f,CO_2(g))^@ = -"393.52 kJ/mol"`
http://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Units=SI&Mask=1

(Why don't I need to look up `DeltaH_f^@` for `"Fe"(s)`?)

The standard enthalpy of reaction is then given by:

`DeltaH_(rxn)^@ = sum_P nu_P DeltaH_(f,P)^@ - sum_R nu_R DeltaH_(f,R)^@`

where:

• `nu` is the stoichiometric coefficient for product `P` or reactant `R`.
• `DeltaH_f^@` is the standard enthalpy of formation for a given substance in a given phase.

Thus, we get:

`color(blue)(DeltaH_(rxn)^@) = [2DeltaH_(f,Fe(s))^@ + 3DeltaH_(f,CO_2(g))^@] - [1DeltaH_(f,Fe_2O_3(s))^@ + 3DeltaH_(f,CO(g))^@]`

`= overbrace([underbrace(2(0))_"2Fe(s)" + underbrace(3(-393.52))_("3CO"_2(g))])^"Products" - overbrace([underbrace(1(-825.50))_("Fe"_2"O"_3(s)) + underbrace(3(-110.53))_(3"CO"(g))])^"Reactants"` `"kJ/mol"`

`= (0 - 1180.56 + 825.50 + 331.59)` `"kJ/mol"`

`= ulcolor(blue)(-"23.47 kJ/mol")`