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Question

The equilibrium constants for the following reactions at 1400 K are given:


2H2O(g)2H2(g)+O2(g);K1=2.1×1013
2CO2(g)2CO(g)+O2(g);K2=1.4×1012

Then, the equilibrium constant K for the reaction, H2(g)+CO2(g)CO(g)+H2O(g), is:

A
2.04
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B
20.5
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C
2.6
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D
6.67
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Solution

The correct option is C 2.6
(I) 2H2O(g)2H2(g)+O2(g)
K1=(pH2)2.pO2(pH2O)2=2.1×1013(I)

(II) 2CO2(g)2CO(g)+O2(g)
K2=(pCO)2.pO2(pCO2)2=1.4×1012(II)

Now, H2(g)+CO2(g)CO(g)+H2O(g)

K=pCO.pH2OpH2.pCO2

=(K2)1/2×(1K1)1/2

K=(1.42.1×10121013)1/2=(20/3)1/2=2.6

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