Necessary conditions for spontanity of a reaction ________

Options

A. `(G)_("products") lt (G)_("reactants")`
B. `(S)_("products") lt (S)_("reactants")`
C. `[(DeltaS)_("reaction") + (DeltaS)_("surr")] gt 0`
D. `[-((DeltaH)_("sys"))/(T) + (DeltaS)_("sys")] gt 0`

Answer

To determine the necessary conditions for the spontaneity of a reaction, we can analyze the relationship between Gibbs free energy (ΔG), entropy (ΔS), and enthalpy (ΔH). Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding Gibbs Free Energy
The spontaneity of a reaction is determined by the change in Gibbs free energy (ΔG). For a reaction to be spontaneous, ΔG must be negative:
\[ \Delta G < 0 \]

### Step 2: Relationship Between ΔG, ΔH, and ΔS
The Gibbs free energy change is related to the enthalpy change (ΔH) and the entropy change (ΔS) by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where \( T \) is the temperature in Kelvin.

### Step 3: Conditions for Spontaneity
1. **Condition 1**: For ΔG to be negative, we can rearrange the equation:
\[ \Delta H - T \Delta S < 0 \]
This implies:
\[ \Delta H < T \Delta S \]
Therefore, if ΔS is positive (increasing disorder), it can help make ΔG negative even if ΔH is positive (endothermic reaction).

2. **Condition 2**: If ΔS is negative (decreasing disorder), then ΔG will likely be positive unless ΔH is significantly negative (exothermic reaction).

3. **Condition 3**: The total entropy change of the universe (ΔS_universe) must be positive for a spontaneous process:
\[ \Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} > 0 \]

### Step 4: Conclusion on Options
From the analysis:
- **Option 1**: ΔG must be less than zero (correct).
- **Option 2**: ΔS of products less than ΔS of reactants implies ΔS is negative, which does not guarantee spontaneity (incorrect).
- **Option 3**: ΔS_universe must be greater than zero (correct).
- **Option 4**: The rearranged condition \( \Delta S_{system} - \frac{\Delta H_{system}}{T} > 0 \) is also correct.

### Final Answer
The necessary conditions for the spontaneity of a reaction are:
- Option 1: Correct
- Option 3: Correct
- Option 4: Correct