An important reaction in production of smog is
`NO_(2)(g)+hv rarr NO(g)+O(g)`
If light of wavelength `4.4xx10^(-7) m` is used to cause above reaction. Calculate `N-N` bond enthalpy.
`{:("Given :",DeltaH_(f) [NO(g)]=91" kJ mol"^(-1)" ",,h=6.6xx10^(-34) Js),(,DeltaH_(f) [N_(2)O_(4)(g)]=9" kJ mol"^(-1)" ",,c=3xx10^(8) ms^(-1)),(,DeltaH_(O=O)=498" kJ mol"^(-1)" ",,N_(A)=6xx10^(23)):}`

Explanation

`NO_(2)(g)+hv rarr NO(g)+O(g)`
`DeltaH` for the reaction
`DeltaH=N_(A) xx (hc)/lambda`
`=6xx10^(23) xx(6.6xx10^(-34)xx3xx10^(8))/(4.4xx10^(-7))`
`=+270" kJ mol"^(-1)`
for the reaction,
`NO_(2)(g) rarr NO(g) +O(g)`
`Delta_(r)H= sum DeltaH_("f Product")-sum DeltaH_("f Reactant")`
`+270" kJ mol"^(-1)=91+498/2-DeltaH_(f" "NO_(2)(g))`
`DeltaH_(f(NO_(2)) (g))=+70" kJ mol"^(-1)`
Now for the reaction,
`2NO_(2)(g) rarr N_(2)O_(4)(g)`
`Delta_(r)H=sum DeltaH_("f Product")-sum DeltaH_("f Reactant")`
`=+9-(2xx70)=-131" kJ mol"^(-1)`
Thus bond energy for `N-N` bond `=+131" kJ mol"^(-1)`