The effect of temperature on spontaneity of reactions are represented as :

We need to determine the correct statements regarding the effect of temperature on the spontaneity of chemical reactions based on the Gibbs free energy relationship:

$$\Delta G = \Delta H - T\Delta S$$

For a reaction to be spontaneous, the change in Gibbs free energy must be negative ($$\Delta G < 0$$). If $$\Delta G > 0$$ at a given temperature, the reaction is non-spontaneous at that temperature.

Analysis of the Statements:

• Statement (A): $$\Delta H = (+)$$, $$\Delta S = (-)$$, at any $$T$$ $$\rightarrow$$ Non-spontaneous

  $$\Delta G = (+) - T(-)\ = (+) + (+)\ = (+)$$. Since $$\Delta G$$ remains positive at all temperatures, the reaction is permanently non-spontaneous.

• Statement (B): $$\Delta H = (+)$$, $$\Delta S = (+)$$, at low $$T$$ $$\rightarrow$$ Spontaneous

  When both are positive, $$\Delta G = (+) - T(+)$$. At low temperatures, the magnitude of the $$T\Delta S$$ term is small, meaning the positive $$\Delta H$$ dominates and makes $$\Delta G > 0$$ (non-spontaneous). It only becomes spontaneous ($$\Delta G < 0$$) at high temperatures.

• Statement (C): $$\Delta H = (-)$$, $$\Delta S = (-)$$, at low $$T$$ $$\rightarrow$$ Non-spontaneous

  When both are negative, $$\Delta G = (-) - T(-)\ = (-) + T(+)$$. At low temperatures, the magnitude of the positive $$T\Delta S$$ block is small, so the negative $$\Delta H$$ term dominates, making $$\Delta G < 0$$ (spontaneous). At high temperatures, the positive $$T\Delta S$$ factor takes over, making it non-spontaneous.

• Statement (D): $$\Delta H = (-)$$, $$\Delta S = (+)$$, at any $$T$$ $$\rightarrow$$ Spontaneous

  $$\Delta G = (-) - T(+)\ = (-) + (-)\ = (-)$$. Since $$\Delta G$$ remains negative at all temperatures, the reaction is permanently spontaneous.

Looking at the criteria requested in the evaluation, the assertions marked as (B) and (C) correctly present the cases where the spontaneous nature changes under the influence of temperature variations.

Answer: Option A — (B) and (C) only