H_(2) gas is mixed with air at 25^(@)C under a pressure of 1 atmosphere and exploded in a closed vessel. The heat of the reaction, H_(2(g))+(1)/(2)O_(2(g))rarrH_(2)O_((v)) at constant volume, DeltaU_("298 K")=-"240.60 kJ mol"^(-1) and C_(V) values for GH_(2)O vapour and N_(2) in the temperature range "298 Kand 3200 K are 39.06 JK"^(-1)"mol"^(-1) and "26.40 JK"^(-1)"mol"^(-1) respectively. The explosion temperature under adiabatic conditions is (Given : n_(N_(2))=2)

H_(2) gas is mixed with air at 25^(@)C under a pressure of 1 atmospher

1.	H_(2) gas is mixed with air at 25^(@)C under a pressure of 1 atmosphere and exploded in a closed vessel. The heat of the reaction, H_(2(g))+(1)/(2)O_(2(g))rarrH_(2)O_((v)) at constant volume, DeltaU_("298 K")=-"240.60 kJ mol"^(-1) and C_(V) values for GH_(2)O vapour and N_(2) in the temperature range "298 Kand 3200 K are 39.06 JK"^(-1)"mol"^(-1) and "26.40 JK"^(-1)"mol"^(-1) respectively. The explosion temperature under adiabatic conditions is (Given : n_(N_(2))=2)
Answer» 2900 K `2900^(@)C` 2917 K `3000^(@)C` Solution :If the process is CARRIED out ADIABATICALLY and isochorically, `DeltaU=DeltaU_("heating")+DeltaU_("298 K")=0` or `DeltaY_("heating")=-DeltaU_(298K)` `=int_(298K)^(T_(F))n SigmaC_(v)dT=+240.60" kJ mol"^(-1)` `SigmanC_(v)=n.C_(v(H_(2)O_((v)))+nC_(v(V_(2(g))))` `=(39.06+2xx26.40)=91.86JK^(-1)mol^(-1)` by using the value of `SigmanC_(v)` in the above equation `(91.86)(T_(f)-298)=240600"J mol"^(-1)` `T_(f)-298=(240600)/(91.86)=2619K` `T_(f)=2619+298=2917K`