2 Sodium hydride, NaH, can be used to generate hydrogen for fuel cells. (a) In order to calculate the first electron affinity of hydrogen, a student was asked to draw

a Born-Haber cycle for sodium hydride. The cycle had two errors but the numerical data were correct. (i) Identify and correct the two errors in this Born-Haber cycle. (ii) Calculate the first electron affinity, in kJmol", of hydrogen, using the values given in the cycle. (b) The equation for the formation of sodium hydride is \mathrm{Na}(\mathrm{s})+1 / 2 \mathrm{H}_{2}(\mathrm{q}) \rightarrow \mathrm{NaH}(\mathrm{s}) \quad \Delta_{\mathrm{f}} H^{\theta}=-56 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { The standard entropy change of the system, } \Delta S_{\text {system }}^{\ominus}, \text { for this reaction is } -76.5 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} i) Deduce the feasibility of this reaction at 298 K by calculating the free energy change, AG.וא) \text { Calculate the temperature at which } \Delta G=0 (c) The sodium hydride is crushed in the presence of water to release the hydrogen gas for a fuel cell. The overall equation for the reaction occurring in the fuel cell is \mathrm{H}_{2}(\mathrm{~g})+1 / \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) In an alkaline fuel cell the oxidation half-equation is \mathrm{H}_{2}(\mathrm{~g})+2 \mathrm{OH}^{-}(\mathrm{aq}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+2 \mathrm{e}^{-} Deduce the reduction half-equation for the alkaline fuel cell.