What is the enthalpy of reaction at #"373 K"# if the heat capacities are the same at #"273 K"# and we know #DeltaH_(rxn)# at #"273 K"#?
2 Answers
A) 20kJ
Explanation:
Enthalpy of a reaction is NOT affected by the temperature. The temperature may affect the reaction rate , but the inherent amount of heat energy produced or consumed by a reaction remains the same no matter what the conditions of the reaction environment are.
Ref:
https://cbcwb01x.chemistry.ohiostate.edu/~woodward/ch121/ch5_enthalpy.htm
Due to the assumption of the question that
Otherwise, there is a small difference. Remember, this is just Hess's Law...
#DeltaH_("rxn","373 K") = DeltaH_("rxn,273 K") + cancel(int_(273)^(373) DeltaC_(P,"rxn")(T)dT)^(~~ 0)#
if
See here for further discussion:
https://chemistry.stackexchange.com/questions/35756/calculatingenthalpychangesatdifferenttemperatures
And see here for further references to back up this answer.

https://www.et.byu.edu/~rowley/ChEn273/Topics/Energy_Balances/Reacting_Systems/Heat_of_Rxn_at_other_Temp.htm
(boxed equation) 
https://www.slideshare.net/mobile/mosamgpatel/temperatureeffectonheatofreaction
(Eq. 7)
We can write a thermodynamic cycle for that.
 State 1: Reactants at
#"273 K"#  State 2: Products at
#"273 K"#  State 3: Reactants at
#"373 K"#  State 4: Products at
#"373 K"#
#"State 1" stackrel(DeltaH_("rxn","273 K")" ")(>) "State 2"#
#"State 3" stackrel(DeltaH_("rxn","373 K")" ")(>) "State 4"#
#"State 1" stackrel(int_(273)^(373) C_(P("reactants"))(T)dT" ")(>) "State 3"#
#"State 2" stackrel(int_(273)^(373) C_(P("products"))(T)dT" ")(>) "State 4"#
We know the first one, and in principle can determine the last two, but do not know the second one. If we want to go from
#"Reactants at 373 K" > "Reactants at 273 K" > "Products at 273 K" > "Products at 373 K"#
This path is then going to result in calculating
#color(blue)(DeltaH_("rxn","373 K")) = int_(273)^(373) C_(P("reactants"))(T)dT + DeltaH_("rxn,273 K") + int_(273)^(373) C_(P("products"))(T)dT#
#= color(blue)(barul(stackrel(" ")(" "DeltaH_("rxn,273 K") + int_(273)^(373) DeltaC_(P,"rxn")(T)dT" ")))#
See here; this person quotes the same equation I just derived. The astute chemist would recognize that this is just Hess's Law.
In other words, we can calculate
NOTE: It is ultimately not entirely clear what the question means by "the heat capacities are the same".
Are we saying
#C_(P("Reactants"))(T) ~~ C_(P("Products"))(T)# ?#C_(P("Reactants/Products"))("273 K") ~~ C_(P("Reactants/Products"))("373 K")# ?
I interpret it is meaning that the products and reactants each have the same heat capacities at a particular temperature, and not that they are constant in the temperature range irrespective of what they are in relation to each other.
In that special case,
#int_(273)^(373) C_(P("products"))(T)dTint_(273)^(373) C_(P("reactants"))(T)dT#
#= int_(273)^(373) DeltaC_(P,"rxn")dT ~~ 0# since the integral of
#DeltaC_(P,"rxn") ~~ 0# is zero. Only then is#DeltaH_("rxn", "373 K") = DeltaH_("rxn", "273 K")# .
If the question means that
#C_(P("products"))int_(273)^(373) dT  C_(P("reactants"))int_(273)^(373) dT#
#= DeltaC_(P,"rxn") int_(273)^(373) dT#
#= color(red)(DeltaC_(P,"rxn") cdot DeltaT ne 0)# in general