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H(2) gas is mixed with air at 25^(@)C un...

`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 K and 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)`

A

2900 K

B

`2900^(@)C`

C

2917 K

D

`3000^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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