The plot of \( \log K_f \) versus \( \dfrac{1}{T} \) for a reversible reaction \( \mathrm{A(g)} \rightleftharpoons \mathrm{P(g)} \) is shown.
Pre-exponential factors for the forward and backward reactions are \( 10^{15} \, \mathrm{s^{-1}} \) and \( 10^{11} \, \mathrm{s^{-1}} \), respectively. If the value of \( \log K \) for the reaction at \( 500 \, \mathrm{K} \) is \( 6 \), the value of \( \left| \log k_b \right| \) at \( 250 \, \mathrm{K} \) is _______.
[\( K = \) equilibrium constant of the reaction, \( k_f = \) rate constant of forward reaction, \( k_b = \) rate constant of backward reaction]
