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For the reaction CO(2)(g)+H(2)(g) hArr...

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`?

Text Solution

Verified by Experts

`T_(1)=1000 K, T_(2)=1200 K`,
`K_(1)=0.63, K_(2)=1.26`
Using the van't Hoff equation:
`log_(10)K_(2)/K_(1)=(DeltaH^(ɵ))/(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"^(-1)`
b. Let `K_(2)` be the equilibrium constant at `T_(2)=1500 K`
`T_(1)=1000 K` 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`
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