The standard Gibbs free energy change $\Delta G^\circ$ is related to the standard cell potential $E^\circ_{\text{cell}}$ by the equation: $\Delta G^\circ = -nFE^\circ_{\text{cell}}$ If $E^\circ_{\text{cell}}$ is negative, then $\Delta G^\circ$ must be positive ($\Delta G^\circ > 0$). Furthermore, $\Delta G^\circ$ is related to the equilibrium constant $K_{\text{eq}}$ by the equation: $\Delta G^\circ = -2.303 RT \log K_{\text{eq}}$ Since $\Delta G^\circ$ is positive, $\log K_{\text{eq}}$ must be negative. This means $K_{\text{eq}} < 1$. Therefore, the correct relationship is $\Delta G^\circ > 0$ and $K_{\text{eq}} < 1$.