Predict the standard reaction enthalpy of `2NO_(2)(g)rarrN_(2)O_(4)(g)` at `100^(@)C`. `Delta H^(@)` at `25^(@)C` is `-57.2 kj.mol^(-1)C_(p)(NO_(2))=37.2j.mol^(-1)K^(-1)C_(p)(N_(2)O_(4))=77.28 J. mol^(-1)k^(-1)`

Answer

`-56.98 kJ mol^(-1)`

Explanation

When the heat capacities of all substances participating in a chemical reaction are assumed to be constant over the range of temperature involved kirchoff's law intergrates to
`DeltaH^(@)(T_(2))=DeltaH^(@)(T_(1))+DeltaC_(p)(T_(2)-T_(1))`
`DeltaC_(p)=underset("Product")(sum)upsilon C_(p,m)^(0)-underset("Reactants")(sum)upsilonC_(p,m)^(0)`
`Delta C_(p)=C_(p)(N_(2)O_(4),g)-2C_(p)(NO_(2),g)`
`=(77.28)-(2)xx(37.20j K^(-1) mol^(-1))`
`= +2.88JK^(-1)mol^(-1)`
`Delta H^(@)(373K)=Delta H^(@)(298 K)+DeltaC_(p)Delta T`
`=(-57.20kJmol^(-1))+(2.88JK^(-1)xx75K)/(1000)`
`={(-57.20)+(0.22)}kJ mol^(-1)`
`= -56.98 kJ mol^(-1)`