To calculate delta rH° and delta rU° at 298K for the hydrogenation of ethyne to ethene, we need to first write the balanced chemical equation for the reaction:
C₂H₂ + H₂ -> C₂H₄
The enthalpy change for this reaction can be calculated using Hess's Law as follows:
ΔrH° = ΣΔfH°(products) - ΣΔfH°(reactants)
ΔfH°(C₂H₄) = 52.26 kJ/mol
ΔfH°(C₂H₂) = 226.73 kJ/mol
ΔfH°(H₂) = 0
ΔrH° = 52.26 - (226.73 + 0) = -174.47 kJ/mol
Next, we need to calculate the internal energy change for the reaction at 298K using the formula:
ΔrU° = ΔrH° - TΔrS°
Since we are given that the heat capacities are constant over the temperature range, we can assume that ΔrS° is also constant and calculate it at 298K:
ΔrS° = ΔrH° - ΔrU° / T
ΔrS° = -174.47 kJ/mol - (298K)(ΔrU/298)
Now, we can calculate delta rH° at 348K using the formula:
ΔrH(348K) = ΔrH(298K) + ∫(Cp)dT
ΔrH(348K) = -174.47 kJ/mol + ∫(Cp)dT
At this point, we would need the specific heat capacity data to continue with the calculation.
Hope this helps.