First, let's consider the reaction :
2Al(s)+Fe2O3(s)→Al2O3(s)+2Fe(s)
The heat change for this reaction
can be calculated from the heats of formation of the reactants and the products :
ΔH0=[ΔHf0(Al2O3)+2ΔHf0(Fe)]−[2ΔHf0(Al)+ΔHf0(Fe2O3)]
Assuming the elements in their standard states have zero enthalpy of formation, i.e.,
ΔHf0(Al)=ΔHf0(Fe)=0 , we can simplify this to :
ΔH0=ΔHf0(Al2O3)−ΔHf0(Fe2O3)
Substitute the given heats of formation into the equation :
ΔH0=(−1700 kJ/mol)−(−840 kJ/mol)=−860 kJ/mol
This is the heat of reaction for the above reaction. However, we are asked to find the heat evolved per gram of the mixture.
To find this, we need to determine the molar mass of the reactants in the reaction. The molar mass of
Fe2O3 is
2×56+3×16=160 g/mol and the molar mass of 2 moles of
is
2×27=54 g/mol . The total molar mass of the mixture is
160+54=214 g/mol .
So, the heat evolved per gram of the mixture is
214 g/mol−860 kJ/mol=−4.0187 kJ/g
Rounded to the nearest integer, this value is approximately -4 kJ/g. The negative sign indicates that the heat is evolved (exothermic reaction).
