Which one of the following statements: is (are) true?

Options

A. For a given transfer of energy, the increase in entropy is directly proportinal to the temperature.
B. `Br_(g)(g)` has a lower entropy than `Br_(2)`?
C. The standard free energy of formation of Hg(l) is zero .
D. Endothermic reaction wit a neegative entropy change are always non-spontaneous

Explanation

To determine which statements are true, we will analyze each option step by step:

### Step 1: Analyze Option 1
**Statement:** For a given transfer of energy, the increase in entropy is directly proportional to the temperature.

**Analysis:**
The relationship between entropy (ΔS), heat transfer (q), and temperature (T) is given by the formula:
\[ \Delta S = \frac{q}{T} \]
From this equation, we can see that entropy is inversely proportional to temperature. Therefore, this statement is **false**.

### Step 2: Analyze Option 2
**Statement:** Br2 gas has a lower entropy than Br2 solid.

**Analysis:**
Entropy is a measure of randomness or disorder in a system. Gases have higher entropy than liquids, and liquids have higher entropy than solids due to their molecular arrangement and freedom of movement. Therefore, Br2 gas would have a higher entropy than Br2 solid. This statement is **false**.

### Step 3: Analyze Option 3
**Statement:** The standard free energy of formation of mercury liquid is zero.

**Analysis:**
The standard free energy of formation of a substance in its standard state is defined as zero. Since mercury (Hg) is found in liquid form at standard conditions, its standard free energy of formation is indeed zero. Therefore, this statement is **true**.

### Step 4: Analyze Option 4
**Statement:** Endothermic reactions with a negative entropy change are always non-spontaneous.

**Analysis:**
For a reaction to be spontaneous, the Gibbs free energy change (ΔG) must be less than zero:
\[ \Delta G = \Delta H - T \Delta S \]
In an endothermic reaction, ΔH is positive. If the entropy change (ΔS) is negative, then:
\[ \Delta G = \Delta H - T(-S) = \Delta H + T|S| \]
Both ΔH and T|S| are positive, which means ΔG will be positive, indicating that the reaction is non-spontaneous. Therefore, this statement is **true**.

### Conclusion
The true statements are:
- Option 3: The standard free energy of formation of mercury liquid is zero.
- Option 4: Endothermic reactions with a negative entropy change are always non-spontaneous.

### Final Answer
**True Statements:** Option 3 and Option 4.

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