Which reaction, with the following values of `Delta H`, `Delta S`, at 400 K is spontaneous and endothermic?

Options

A. `Delta H = -48 kJ, Delta S = + 135 J/K`
B. `Delta H = -48 kJ, Delta S = - 135 J/K`
C. `Delta H = + 48 kJ, Delta S = + 135 J/K`
D. `Delta H = +48 kJ, Delta S = -135 J/K`

Answer

To determine which reaction is spontaneous and endothermic at 400 K, we need to analyze the given values of ΔH (enthalpy change) and ΔS (entropy change) for each reaction.

### Step-by-Step Solution:

1. **Identify Endothermic Reactions:**
- An endothermic reaction is characterized by a positive ΔH value. Therefore, we need to look for reactions with ΔH > 0.

2. **Check Given ΔH Values:**
- From the options provided, we discard any reactions with a negative ΔH value.

3. **Calculate ΔG:**
- The Gibbs free energy change (ΔG) can be calculated using the formula:
\[ ΔG = ΔH - TΔS \]
- We need to calculate ΔG for each reaction at T = 400 K.

4. **Analyze Each Option:**
- **Option 1:** ΔH = - (not endothermic, discard)
- **Option 2:** ΔH = - (not endothermic, discard)
- **Option 3:** ΔH = +48 kJ and ΔS = +135 J/K
- Convert ΔH to Joules: 48 kJ = 48,000 J
- Calculate ΔG:
\[ ΔG = 48,000 J - (400 K \times 135 J/K) = 48,000 J - 54,000 J = -6,000 J \]
- Since ΔG is negative, this reaction is spontaneous.
- **Option 4:** ΔH = +48 kJ and ΔS = -135 J/K
- Convert ΔH to Joules: 48 kJ = 48,000 J
- Calculate ΔG:
\[ ΔG = 48,000 J - (400 K \times -135 J/K) = 48,000 J + 54,000 J = 102,000 J \]
- Since ΔG is positive, this reaction is not spontaneous.

5. **Conclusion:**
- The only reaction that is both spontaneous and endothermic at 400 K is **Option 3**.

### Final Answer:
**Option 3** is the correct choice as it is spontaneous and endothermic.