For the reaction
`CO_(2)(g)+H_(2)(g) hArr CO(g)+H_(2)O(g)`
K is `0.63` at `727^(@)C` and `1.26` at `927^(@)C`.
a. What is the average `DeltaH` for the temperature range considered? [Use log 2=0.3]
b. What is the value of K at `1227^(@)C`?

Explanation

`T_(1)=1000K, T_(2)=1200K,`
`K_(1)=0.63, K_(2)=1.26`
Using the Vant' Hoff equation:
`"log"_(10)(K_(2))/(K_(1))=(DeltaH^(@))/(2.303R)((T_(2)-T_(1))/(T_(1)T_(2))) rArr log_(10)((1.26)/(0.63))=(DeltaH)/(2.303(2))((1200-1000)/(1200xx1000)) rArr DeltaH=8.32`kcal/mol
(b) Let `K_(2)` be the equilibrium constant at `T_(2)=1500K`
`T_(1)=100K` and then `K_(1)=0.63`
`rArr log_(10)((K_(2))/(0.63))=(8.32xx10^(3))/(2.303(2))((1500-1000)/(1500xx1000))rArr "log"_(10)(K_(2))/(0.63)~~0.6=log_(10)4`
`rArr K_(2)=0.63xx4=2.52`