The equilibrium-constant expression for a reaction written in one direction is the __________ of the one for the reaction written for the reverse direction.

The equilibrium constant for an equilibrium reaction is the ratio of the equilibrium constant for the forward reaction, Kf, to the equilibrium constant for the reverse reaction, Kr:

For A ⇄ B

The forward reaction is: A → B, with rate constant is Kf = K₁ and
The reverse reaction is: B → A, with rate constant Kr = K₂

[tex]K_{eq}=\dfrac{K_f}{K_r}=\dfrac{K_1}{K_2}[/tex]

When you write the reaction in the other reaction, the forward and the reverse reaction are exchanged:

For B ⇄ A

The forward reaction is B → A, with rate constant Kf = K₂
The reverse reaction is A → B, with rate constant Kr = K₁

[tex]K'_{eq}=\dfrac{K_f}{K_r}=\dfrac{K_2}{K_1}[/tex]

As you see:

[tex]K'_{eq}=\dfrac{1}{K_{eq}}[/tex]

Thus, the equilibrium-constant expression for a reaction written in one direction is the reciprocal___ of the one for the reaction written for the reverse direction.