$$A\rightarrow D$$ is an endothermic reaction occurring in three steps ( elementary).
(i) $$A\rightarrow B \triangle H_{i}=+ve$$
(ii) $$B\rightarrow C \triangle H_{ii}=-ve$$
(iii) $$C\rightarrow D \triangle H_{iii}=-ve$$
Which of the following graphs between potential energy (y-axis) vs reaction coordinate (x-axis) correctly represents the reaction profile of A-> D?

The energy profile must respect both the sign of the enthalpy change for every elementary step and the sign of the overall enthalpy change.

Let the potential energies of the species be $$E(A),\,E(B),\,E(C),\,E(D).$$ Take $$E(A)$$ as the zero reference.

Step (i): $$A \rightarrow B$$ is endothermic, $$\Delta H_i \gt 0.$$
 Therefore $$E(B) \gt E(A)=0.$$ So the curve must rise from the level of $$A$$ to the level of $$B$$ (after passing through the first transition state).

Step (ii): $$B \rightarrow C$$ is exothermic, $$\Delta H_{ii} \lt 0.$$
 Hence $$E(C) \lt E(B).$$ The curve must drop from the level of $$B$$ to the level of $$C$$ (again crossing a new transition state that lies above $$E(B)$$).

Step (iii): $$C \rightarrow D$$ is exothermic, $$\Delta H_{iii} \lt 0,$$ so $$E(D) \lt E(C).$$ The curve therefore falls once more after its third transition state.

Overall reaction: $$A \rightarrow D$$ is given to be endothermic, $$\Delta H_{\text{overall}} \gt 0.$$
 Thus $$E(D)$$ must still be higher than $$E(A).$$ Combining this with the inequalities from Steps (ii) and (iii) we obtain the ordering

$$E(B) \gt E(C) \gt E(D) \gt E(A).$$

The correct energy diagram must therefore display

• three maxima (one for each transition state),
• two intermediates $$B$$ and $$C$$ between those maxima,
• a step-wise fall in the intermediate levels $$B \rightarrow C \rightarrow D,$$
• the final level $$D$$ above the initial level $$A.$$

Inspecting the given sketches, only Option D shows all these features. The other options fail in at least one respect—either the number of maxima/minima is wrong, or the final level $$D$$ is not higher than the initial level $$A.$$

Therefore, the correct reaction-coordinate diagram is provided in Option D.

Answer: Option D which is: the diagram with three peaks, intermediates descending $$B \gt C \gt D$$, and $$E(D)\gt E(A).$$