Areaction has a forward rate constant of 2.3 × 106 s-1 and an equilibrium constant of 4.0 × 108. what is the rate constant for the reverse reaction?

Answer is: 5,75·10⁻¹.
Kf = 2,3·10⁶ 1/s.
K = 4,0·10⁸ 1/s.
Kr = ?
Kf - forward rate constant.
K - equilibrium constant.
Kr - reverse rate constant.
Since both Kf and Kr are constants at a given temperature, their ratio is also a constant that is equal to the equilibrium constant K.
K = Kf/Kr.
Kr = Kf/K = 2,3·10⁶ 1/s ÷ 4,0·10⁸ 1/s = 5,75·10⁻¹.