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At a certain temperature , the following...

At a certain temperature , the following reactions have the equilibrium constants as shown below:
`S(s)+O_(2)(g)hArrSO_(2)(g),K_(c)=5xx10^(52)`
`2S(s)+3O_(2)(g)hArr2SO_(3)(g),K_(c)=10^(29)`
what is the equilibrium constant `K_(c)`for the reaction at tahea same temperature?
`2SO_(2)(g)+O_(2)(g)hArr2SO_(3)(g)`

A

`K_(1)=K_(2)`

B

`K_(2)^(2)=K_(1)`

C

`K_(1)^(2)=K_(2)`

D

`K_(2)=sqrt(K_(1))`

Text Solution

Verified by Experts

The correct Answer is:
C
`SO_(2)+1/2 O_(2) overset(K_(1))(hArr)SO_(3)`, `:. K_(1)=([SO_(3)])/([SO_(2)][O_(2)]^(1//2))`
`2SO_(2)+O_(2) overset(K_(1))(hArr)2SO_(3)`, `:. K_(2)=([SO_(3)]^(2))/([SO_(2)]^(2)[O_(2)])`
`:. K_(2)=K_(1)^(2)`
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