Which of the following graphs most appropriately represents a zero order reaction ?

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 $$\Delta G > 0$$, the reaction is non-spontaneous.

Analysis of the Statements:

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

  Substituting the signs into the Gibbs equation: $$\Delta G = (+) - T(-)\ = (+) + (+)\ = (+)$$. Since $$\Delta G$$ is always positive regardless of temperature, the reaction is permanently non-spontaneous. (This statement is TRUE)

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

  When both are positive: $$\Delta G = (+) - T(+)$$. At low temperatures, the magnitude of $$T\Delta S$$ is small, so the positive $$\Delta H$$ dominates, making $$\Delta G > 0$$ (non-spontaneous). It only becomes spontaneous at high temperatures. (This statement is FALSE)

• 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 $$T\Delta S$$ is small, so the negative $$\Delta H$$ term dominates, making $$\Delta G < 0$$ (spontaneous). (This statement is FALSE)

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

  Substituting the signs into the equation: $$\Delta G = (-) - T(+)\ = (-) + (-)\ = (-)$$. Since $$\Delta G$$ is always negative regardless of temperature, the reaction is permanently spontaneous. (This statement is TRUE)

Conclusion:

Statements (A) and (D) correctly depict the thermodynamic criteria for reaction spontaneity.

Answer: Option C — (A) and (D) only