Step 1 :

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The hypothetical reaction :

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$\"\"$

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For the reaction $\"\"$ .

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Equilibrium constant for the reaction is $\"\"$ .

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From the given data : $\"\"$ .

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Step 2 :

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Find $\"\"$ for the reaction $\"\"$ .

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Equilibrium constant for the reaction is $\"\"$ .

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$\"\"$

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Thus, the value of $\"\"$ is $\"\"$ .