Question:
$\text{An enthalpy diagram for a particular reaction is given below:}$
$\text{[Enthalpy diagram showing reactants at energy level H}_r\text{, products at energy level H}_p\text{, with }\Delta_f\text{H indicated as net heat absorbed from surroundings. The diagram shows H}_p > \text{H}_r\text{]}$
$\text{The correct statement among the following is-}$
$\text{1. Reaction is spontaneous}$
$\text{2. Reaction is non-spontaneous}$
$\text{3. Cannot predict spontaneity of the reaction from the graph given above}$
$\text{4. None of the above}$
Solution:
$\text{Hint:}$ $\Delta\text{G} = \Delta\text{H} - \text{T}\Delta\text{S}$
$\text{To determine whether a reaction is spontaneous or not, we need to analyze the Gibbs free energy change (}\Delta\text{G) for the reaction:}$
$\Delta\text{G} = \Delta\text{H} - \text{T}\Delta\text{S}$
$\text{For a reaction to be spontaneous, }\Delta\text{G must be negative.}$
$\text{From the enthalpy diagram provided:}$
$\text{1. We can observe that the enthalpy of products (H}_p\text{) is higher than the enthalpy of reactants (H}_r\text{).}$
$\text{2. This means that }\Delta\text{H = H}_p - \text{H}_r > 0\text{, indicating an endothermic reaction (heat is absorbed from the surroundings).}$
$\text{3. The diagram also shows }\Delta_f\text{H as the "net heat absorbed from surroundings," confirming that }\Delta\text{H is positive.}$
$\text{However, to determine spontaneity, we need to know both }\Delta\text{H and }\Delta\text{S values, along with the temperature:}$
$\text{- If }\Delta\text{H} > 0\text{ and }\Delta\text{S} > 0\text{, the reaction is spontaneous only at high temperatures (when T}\Delta\text{S} > \Delta\text{H).}$
$\text{- If }\Delta\text{H} > 0\text{ and }\Delta\text{S} < 0\text{, the reaction is never spontaneous.}$
$\text{- If }\Delta\text{H} < 0\text{ and }\Delta\text{S} > 0\text{, the reaction is always spontaneous.}$
$\text{- If }\Delta\text{H} < 0\text{ and }\Delta\text{S} < 0\text{, the reaction is spontaneous only at low temperatures (when |T}\Delta\text{S}| < |\Delta\text{H}|).}$
$\text{While the enthalpy diagram tells us that }\Delta\text{H} > 0\text{, it provides no information about the entropy change (}\Delta\text{S) for the reaction. Without knowing }\Delta\text{S, we cannot determine whether the reaction is spontaneous or non-spontaneous.}$
$\text{If }\Delta\text{S is positive and large enough, the reaction could be spontaneous at high temperatures despite having a positive }\Delta\text{H. If }\Delta\text{S is negative or not sufficiently positive, the reaction would be non-spontaneous.}$
$\text{Therefore, we cannot predict the spontaneity of the reaction solely from the enthalpy diagram provided.}$
$\text{The correct answer is option 3: Cannot predict spontaneity of the reaction from the graph given above.}$