Given: The equilibrium constant for reaction 1/2A2+1/2B2⇌AB is k.
To find: We have to find the equilibrium constant for [tex]A_2+B_2⇌2AB[/tex].
Solution:
The given reaction is [tex]1/2A_2+1/2B_2⇌AB[/tex].
The equilibrium constant for this reaction is k.
k is given as-
[tex]k=\dfrac {[AB]}{[A_2]^{1/2}[B_2]^{1/2}}[/tex].
The other reaction is [tex]A_2+B_2⇌2AB[/tex].
Let the equilibrium constant for this reaction be K.
So, the equilibrium constant is given as-
[tex]K=\dfrac {[AB]^2}{[A_2][B_2]}[/tex]
Taking square root in both sides we get-
[tex]√K=\dfrac {[AB]}{[A_2]^{1/2}[B_2]^{1/2}}[/tex]
[tex]√K=k[/tex]
[tex]K=k^2[/tex]
The value of the equilibrium constant is [tex]k^2[/tex].