Answer:
-99.8 kJ
Explanation:
We are given the methodology to answer this question, which is basically Kirchhoff law . We just need to find the heats of formation for the reactants and products and perform the calculations.
The standard heat of reaction is
ΔrHº = ∑ ν x ΔfHº products - ∑ ν x ΔfHº reactants
where ν are the stoichiometric coefficients in the balanced equation, and ΔfHº are the heats of formation at their standard states.
Compound ΔfHº (kJmol⁻¹)
SO₂ -296.8
O₂ 0
SO₃ -395.8
The balanced chemical equation is
SO₂(g) + ½O₂(g) → SO₃(g)
Thus
Δr, 298K Hº( kJmol⁻¹ ) = 1 x (-395.8) - 1 x (-296.8) = -99.0 kJmol⁻¹
Now the heat capacity of reaction will be be given in a similar fashion:
Cp rxn = ∑ ν x Cp of products - ∑ ν x Cp of reactants
where ν is as above the stoichiometric coefficient in the balanced chemical equation.
Cprxn ( JK⁻¹mol⁻¹) = 50.7 - ( 39.9 + 1/2 x 29.4 ) = - 3.90
= -3.90 JK⁻¹mol⁻¹
Finally Δr,500 K Hº = Δr, 298K Hº + CprxnΔT
Δr,500 K Hº = - 99 x 10³ J + (-3.90) JK⁻¹ ( 500 - 298 ) K = -99,787.8
= -99,787.8 J x 1 kJ/1000 J = -99.8 kJ
Notice thie difference is relatively small that is why in some problems it is o.k to assume the change in enthalpy is constant over a temperature range, especially if it is a small range of temperatures.
