Standard Gibbs Free Energy Change at Chemical Equilibrium

To evaluate the truth value of each statement:

1. Analysis of STATEMENT-1:
   The relationship between the Gibbs free energy change ($\Delta G$) and the standard Gibbs free energy change ($\Delta G^\circ$) of a reaction at temperature $T$ is given by:
   $\Delta G = \Delta G^\circ + RT \ln Q$
   where $Q$ is the reaction quotient and $R$ is the universal gas constant.

   At chemical equilibrium, the condition for dynamic equilibrium is:
   $\Delta G = 0 \quad \text{and} \quad Q = K_{\text{eq}}$
   Substituting these values into the thermodynamic relation gives:
   $\Delta G^\circ = -RT \ln K_{\text{eq}}$
   The standard Gibbs energy of reaction, $\Delta G^\circ$, is zero if and only if the equilibrium constant $K_{\text{eq}} = 1$. For an arbitrary reaction at equilibrium, $K_{\text{eq}}$ can have any positive value, meaning $\Delta G^\circ$ is generally non-zero.
   Therefore, STATEMENT-1 is False.

2. Analysis of STATEMENT-2:
   According to the Second Law of Thermodynamics, the criterion for spontaneity of a process occurring at constant temperature ($T$) and pressure ($P$) is given by:
   $(\Delta G)_{T, P} < 0$
   A spontaneous chemical change proceeds in the direction where the total Gibbs energy of the system decreases until it reaches a minimum at equilibrium (where $(\Delta G)_{T, P} = 0$).
   Therefore, STATEMENT-2 is True.

Conclusion:
STATEMENT-1 is False, and STATEMENT-2 is True.

Thus, the correct option is D.