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Show that the equilibrium constant of the reverse chemical reaction (Kc) is the reciprocal of the equilibrium constant (Kc).

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Consider a reversible chemical reaction: aA + bB ⇌ cC + dD

The equilibrium constant, Kc\(\frac{[C]^c [D]^d}{ [A]^a [B]^b} \)

Consider the reverse reaction:

cC + dD ⇌ aA + bB.

The equilibrium constant, Kc is:

Kc = \(\frac{[A]^a [B]^b}{ [C]^c [D]^d} \) = \(\frac{1}{K_c}\)

Thus, equilibrium constant of the reverse chemical reaction (Kc) is the reciprocal of the equilibrium constant Kc

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