For a reaction to occur spontaneously

Options

A. `(triangleH - TtriangleS)` must be negative
B. `(triangleH + TtriangleS`) must be negative
C. `triangleH` must be negative
D. `triangleS` must be negative

Answer

To determine the conditions for a reaction to occur spontaneously, we can analyze the Gibbs free energy equation. Here’s a step-by-step solution:

### Step 1: Understanding Gibbs Free Energy
Gibbs free energy (G) is a thermodynamic potential that helps predict whether a process will occur spontaneously at constant temperature and pressure. The change in Gibbs free energy (ΔG) is calculated using the formula:

\[ \Delta G = \Delta H - T \Delta S \]

Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy (total heat content)
- T = absolute temperature (in Kelvin)
- ΔS = change in entropy (measure of disorder)

### Step 2: Conditions for Spontaneity
For a reaction to be spontaneous, the change in Gibbs free energy (ΔG) must be negative:

\[ \Delta G < 0 \]

This implies that the equation can be rearranged to:

\[ \Delta H - T \Delta S < 0 \]

### Step 3: Analyzing the Terms
From the rearranged equation, we can derive the conditions under which ΔG will be negative:

1. If ΔH is negative (exothermic reaction) and ΔS is positive (increase in disorder), then ΔG will definitely be negative, indicating spontaneity.
2. If ΔH is positive (endothermic reaction) but ΔS is significantly positive, then at high temperatures, the term \(T \Delta S\) can outweigh ΔH, making ΔG negative.
3. If ΔH is positive and ΔS is negative, the reaction will not be spontaneous as ΔG will be positive.

### Conclusion
Thus, the conditions for spontaneity can be summarized as:
- A reaction is spontaneous if ΔG < 0, which can occur when ΔH is negative and/or ΔS is positive, depending on the temperature.

### Final Answer
The correct option for the conditions for a reaction to occur spontaneously is that ΔH - TΔS must be negative.

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