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Assuming Delta(r )H^(Θ) and Delta(r ) S^...

Assuming `Delta_(r )H^(Θ)` and `Delta_(r ) S^(Θ)` to be independent of temperature, at what temperature will the reaction given below becomes spontaneous ?
`{:(,N_(2)(g),+,O_(2)(g),rarr,2NO(g),,,Delta_(r )H^(Θ)=180.9 kJ mol^(-1)),(S^(Θ)//JK^(-1)mol^(-1),191.4,,204.9,,210.5,,):}`

Text Solution

Verified by Experts

`DeltaS^(@) = 2S_(NO)^(@) - S_(N_(2))^(@) - S_(O_(2))^(@) = 2 xx 210.5 - 191.4 - 204.9`
`=24.7 JK^(-1) mol^(-1)`
`therefore DeltaG^(@) = DeltaH^(@)- T DeltaS^(@)`
`DeltaG^(@) = 180.8 - (T xx 24.7 xx 10^(-3)) kJ mol^(-1)`
For spontaneity, `DeltaG^(@) lt 0` and this occurs when
`TDeltaS^(@) gt DeltaH^(@)`
`T gt (DeltaH^(@))/(DeltaS^(@))`
`T gt (180.8 xx 10^(3))/24.7 = 7320` K
The reaction becomes spontaneous above a temperature of 7320 K.
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