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Solutions
The combustion of diborane includes following reaction:
\({B}_{2} {H}_{6({~g})}+3 {O}_{2({~g})} \longrightarrow {B}_{2} {O}_{3({~s})}+3 {H}_{2} {O}_{({g})}\)
According to Hess Law of heat summation :
\(\Delta {H}_{\text {combustion }}=\left[\Delta {H}_{{formB}_{2} {O}_{3}}({~s})+3 \Delta {H}_{{formH}_{2} {O}}({g})\right]-\Delta {H}_{{formB}_{2} {H}_{6}}\)
\(\Delta {H}_{\text {combustion }}=\text { Heat of combustion of diborane }=-1941 {~kJ}\)
\(\Delta {H}_{{formB}_{2} {O}_{3}({~g})}=\text { Heat of formation of borane oxide }=-2368 {~kJ}\)
\(\Delta {H}_{{formH}_{2} {O}({g})}=\text { Heat of formation of water }=-241.8 {~kJ}\)
\(\Delta \mathrm{H}_{\text {formB }_{2}} {H}_{6}({~g})=\) Heat of formation fo diborane Putting the values in the equation above,
We get :
\(-1941=[-2368+3(-241.8)]-\Delta {H}_{{formB}_{2} {H}_{6}} \)
\(\Delta {H}_{{formB}_{2} {H}_{6}}=[-2368-725.4]+1941 \)
\(=-3093.4+1941 \)
\(=-1152.4 {~kJ} / {mol} .\)
The heat of the formation of diborane is \(=-1152.4 {~kJ} / {mol} .\)