Question
The molar entropies of $$HI\left( g \right)$$ and $$I\left( g \right)$$ at $$298\,K$$ are $$206.5,114.6,$$ and $$180.7\,J\,mo{l^{ - 1}}{K^{ - 1}}$$ respectively. Using the $$\Delta {G^ \circ }$$ given Below, calculate the bond energy of $$HI.$$
$$HI\left( g \right) \to H\left( g \right) + I\left( g \right);\Delta {G^ \circ } = 271.8\,kJ$$
A.
$$282.4\,kJ\,mo{l^{ - 1}}$$
B.
$$298.3\,kJ\,mo{l^{ - 1}}$$
C.
$$290.1\,kJ\,mo{l^{ - 1}}$$
D.
$$315.4\,kJ\,mo{l^{ - 1}}$$
Answer :
$$298.3\,kJ\,mo{l^{ - 1}}$$
Solution :
$$\eqalign{
& \Delta {S^ \circ } = - 206.5 + 114.6 + 180.7 = 88.8 \cr
& \Delta {G^ \circ } = \Delta {H^ \circ } - T\Delta {S^ \circ } \cr
& \Delta {H^ \circ } = 271.8 + 298 \times 88.8 \times {10^{ - 3}} \cr
& \Delta {H^ \circ } = 298.3\,kJ\,mo{l^{ - 1}} \cr} $$