For a reaction to occur spontaneously

Options

A. `Delta H` must be negative
B. `Delta S` must be negative
C. `( DeltaH - TDeltaS)` must be negative
D. `(Delta H + T Delta S)` must be negative

Answer

To determine the conditions under which a reaction occurs spontaneously, we can analyze the Gibbs free energy equation:

### Step-by-Step Solution:

1. **Understanding Gibbs Free Energy (G)**:
The Gibbs free energy (G) is defined by the equation:
\[ G = \Delta H - T \Delta S \]
where:
- \( \Delta H \) = change in enthalpy
- \( T \) = absolute temperature (in Kelvin)
- \( \Delta S \) = change in entropy

2. **Condition for Spontaneity**:
For a reaction to be spontaneous, the change in Gibbs free energy (\( \Delta G \)) must be negative:
\[ \Delta G < 0 \]

3. **Analyzing the Equation**:
From the Gibbs free energy equation, we can rearrange it to understand when \( \Delta G \) will be negative:
\[ \Delta G = \Delta H - T \Delta S < 0 \]
This implies:
\[ \Delta H < T \Delta S \]

4. **Determining the Sign of \( \Delta H \) and \( \Delta S \)**:
- If \( \Delta H \) is negative (exothermic reaction), it favors spontaneity.
- If \( \Delta S \) is positive (increase in disorder), it also favors spontaneity.
- If \( \Delta H \) is positive (endothermic reaction), \( \Delta S \) must be significantly positive to ensure that \( T \Delta S \) is greater than \( \Delta H \) at high temperatures.

5. **Conclusion**:
Therefore, for a reaction to occur spontaneously, the conditions can be summarized as:
- \( \Delta H \) should be negative or \( \Delta S \) should be sufficiently positive to outweigh a positive \( \Delta H \).
- \( \Delta S \) should be positive to contribute to a negative \( \Delta G \) when multiplied by the positive temperature \( T \).

### Final Answer:
The correct condition for a reaction to occur spontaneously is:
\[ \Delta G = \Delta H - T \Delta S < 0 \]
This means that \( \Delta H \) should ideally be negative and \( \Delta S \) should be positive.

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