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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 `700^(@)C` and `1.66` at `1000^(@)C`.
a. What is the average `DeltaH^(ɵ)` for the temperature range considered?
b. What is the value of K at `800^(@)C`?

Text Solution

Verified by Experts

`T_(1)=700+273=973 K`,
`T_(2)=1000+273=1273 K`
`K_(1)=0.63, K_(2)=1.66`
Using the van't Hoff equation
`"log"K_(2)/K_(1)=(DeltaH^(ɵ))/(2.303R)((T_(2)-T_(1))/(T_(1)T_(2)))`
`rArr "log" (1.66/0.63)=(DeltaH^(ɵ))/(2.303(1.99))((1273-973)/(1273xx973))`
`rArr DeltaH^(ɵ)=8.0xx10^(3) cal =8.0 kcal`
Note: The units of `R` and `DeltaH` must be same.
b. Let `K_(2)` be the equilibrium at `T_(2)=1073 K, T_(1)=973 K`, and then `K_(1)=0.63`
`rArr "log" (K_(2)/0.63)=(8.0xx10^(3))/(2.303(1.99))((1073-973)/(1073xx973))`
`rArr K_(2)=0.93`
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