The definition of enthalpy and the perfect gas equation of state can be used to estimate the standard enthalpy of ionization or electron gain and the corresponding change in internal energy. (a) Starting from Kirchhoff's law, and remembering that the molar constant-pressure heat capacity of aperfect gas is (5)/(2)R, derive an expression for the difference betweenthe change in enthalpy and change in internal energy for a gas-phase process if all species behave as if perfect gases. (b) Hence show that for ionization, ΔionHΘ - ΔionUΘ = (5)/(2)RT. (c) Use this expression to estimate the difference between the standard enthalpy of ionization of Ca(g) to Ca2+(g) and the accompanying change in internal energy at 25 °c. (d) In thesame way, show that for electron gain, ΔegHΘ - ΔegUΘ = -(5)/(2)RT.(e) Hence estimate the difference between the standard electron-gain enthalpy of Br(g) and the corresponding change in internal energy at 25 °c.

The definition of enthalpy and the perfect gas equation of state can be used to estimate the standard enthalpy of ionization or electron gain and the corresponding change in internal energy. (a) Starting from Kirchhoff's law, and remembering that the molar constant-pressure heat capacity of a
perfect gas is (5)/(2)R, derive an expression for the difference between
the change in enthalpy and change in internal energy for a gas-phase process if all species behave as if perfect gases. (b) Hence show that for ionization, Δ_ionH^Θ - Δ_ionU^Θ = (5)/(2)RT. (c) Use this expression to estimate the difference between the standard enthalpy of ionization of Ca(g) to Ca²⁺(g) and the accompanying change in internal energy at 25 °c. (d) In the
same way, show that for electron gain, Δ_egH^Θ - Δ_egU^Θ = -(5)/(2)RT.
(e) Hence estimate the difference between the standard electron-gain enthalpy of Br(g) and the corresponding change in internal energy at 25 °c.