Consider the graph of Gibbs free energy G vs extent of reaction. The number of statement/s from the following which are true with respect to points (a), (b) and (c) is ______

A. Reaction is spontaneous at (a) and (b)
B. Reaction is at equilibrium at point (b) and non-spontaneous at point (c)
C. Reaction is spontaneous at (a) and non-spontaneous at (c)
D. Reaction is non-spontaneous at (a) and (b)

In a graph of Gibbs free energy $$G$$ versus extent of reaction, the spontaneity of the reaction depends on the slope of the curve.

• If the curve slopes downward, $$\Delta G<0$$ and the reaction is spontaneous.
• At the minimum point of the curve, $$\Delta G=0$$ and the system is at equilibrium.
• If the curve slopes upward, $$\Delta G>0$$ and the reaction is non-spontaneous in the forward direction.

From the graph:

• At point $$a$$, the curve has a negative slope.

  $$\Delta G<0$$

  Hence, the reaction is spontaneous at $$a$$.

• At point $$b$$, the curve is at its minimum.

  $$\Delta G=0$$

  Hence, the reaction is at equilibrium at $$b$$.

• At point $$c$$, the curve has a positive slope.

  $$\Delta G>0$$

  Hence, the reaction is non-spontaneous at $$c$$.

Evaluating the statements:

• Statement A: Reaction is spontaneous at $$a$$ and $$b$$

  False, because the reaction is at equilibrium at $$b$$.

• Statement B: Reaction is at equilibrium at $$b$$ and non-spontaneous at $$c$$

  True.

• Statement C: Reaction is spontaneous at $$a$$ and non-spontaneous at $$c$$

  True.

• Statement D: Reaction is non-spontaneous at $$a$$ and $$b$$

  False, because the reaction is spontaneous at $$a$$ and at equilibrium at $$b$$.

Therefore, only Statements B and C are true.

Hence, the number of true statements is

$$\boxed{2}$$