Solving Hess's Law Problem for ΔH of Formation of Hematite

[ice87]

So I'm taking Thermodynamics I in university. I'm just doing the homework now, and there is something that i don't really understand.

To get the Enthalpy of formation for hematite (Fe2O3) at 1200K, I first integrated the constant pressure heat capacity function over the temperature range from 298K to 1200K, then added the heats of transformation across this temperature range. but now, at the end, should the enthalpy of formation at 298K be added to the number that i found?

=> integrating over from 298K to 1200K, and adding the heat of transformation for hematite: I got this number: 129300J/mol

=> ΔH of formation at 298K is given as -821300J/mol, should i add these two numbers together?

 

[Bystander]

You integrated the heat capacities of what from 298 - 1200? Hess's Law.

 

[ice87]

roughly speaking I integrated the C_p function of Fe2O3 - hematite from 298 to 1200.
I really integrated it three times, because hematite has 3 states in this temperature range, and the C_p function for each state is different.

 

[Bystander]

Okay, that gives you the difference in enthalpy between hematite at 298 and 1200, right? Says nothing about absolute or standard enthalpy of formation of hematite at either temperature. Enthalpy of formation is defined as the enthalpy change when the compound is formed from the elements at their standard states at the same temperature. You are looking for the enthalpy of formation of hematite at 1200 K, the enthalpy change you would observe if you combined oxygen and iron to form hematite at 1200 K. What you have is the enthalpy change for heating hematite from 298 to 1200 and the enthalpy of formation of hematite at 298. Read the section on Hess's Law again.