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# How can we define a non-spontaneous reaction?

Consider a reaction:$$\ce{aA + bB <=> cC + dD}$$

The value of reaction quotient at a certain time $$t$$, $${Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}}$$
where the concentrations $$[A], [B], [C]$$ and $$[D]$$ are at time $$t$$.

Let the reaction start initially at $$t = 0$$, with only reactants $$i.e.$$ $$[A]$$ and $$[B]$$ equal to say $$1$$ mol and $$[C]$$ and $$[D]$$ equal to $$0$$ mol. Hence, $$Q_c = 0$$

We know that the value of equilibrium constant $$K_c$$ must be such that, $$K_c > 0$$
Thus, $$Q_c < K_c$$
Which is the only condition for the advancement of reaction in forward direction. This condition does not consider the value of change in Gibbs energy $$\Delta G$$.

Now, considering the relation $$\Delta G = \Delta G^o + RT~\mathrm{ln}~Q_c$$
When $$Q_c = 0+$$ then $$\mathrm{ln}~Q_c \to -\infty$$, which means $$\Delta G << 0$$ and reaction is spontaneous in forward direction.

Hence, can it be concluded that every reaction is spontaneous in forward direction if it starts with only reactants?

If so, how can we define a non-spontaneous reaction?