From the following `DeltaH^(@)` and `DeltaS^(@)` values, predict which of reactions I, II and III would be spontaneous at `25^(@)C`.
`{:(,DeltaH^(@)(kJ),,DeltaS^(@)(J//K),),(I.,+10.5,,+30,),(II.,+1.8,,-113,),(III.,-126,,+84,):}`

Options

A. III
B. I
C. II and III
D. I and II

Explanation

To determine which of the reactions I, II, and III are spontaneous at 25°C, we need to calculate the Gibbs free energy change (ΔG) for each reaction using the following formula:

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

Where:
- ΔG = Gibbs free energy change
- ΔH = Change in enthalpy (in joules)
- T = Temperature in Kelvin
- ΔS = Change in entropy (in joules per Kelvin)

### Step-by-Step Solution:

**Step 1: Convert the temperature to Kelvin.**
- Given temperature = 25°C
- Convert to Kelvin:
\[ T = 25 + 273 = 298 \text{ K} \]

**Step 2: Calculate ΔG for Reaction I.**
- Given:
- ΔH = +10.5 kJ = +10.5 × 1000 J = +10500 J
- ΔS = +30 J/K
- Substitute into the Gibbs free energy equation:
\[ \Delta G_I = 10500 \text{ J} - (298 \text{ K} \times 30 \text{ J/K}) \]
\[ = 10500 \text{ J} - 8940 \text{ J} = 1560 \text{ J} \]
- Since ΔG_I is positive, Reaction I is **non-spontaneous**.

**Step 3: Calculate ΔG for Reaction II.**
- Given:
- ΔH = +1.8 kJ = +1.8 × 1000 J = +1800 J
- ΔS = -113 J/K
- Substitute into the Gibbs free energy equation:
\[ \Delta G_{II} = 1800 \text{ J} - (298 \text{ K} \times -113 \text{ J/K}) \]
\[ = 1800 \text{ J} + 33764 \text{ J} = 35564 \text{ J} \]
- Since ΔG_{II} is positive, Reaction II is **non-spontaneous**.

**Step 4: Calculate ΔG for Reaction III.**
- Given:
- ΔH = -126 kJ = -126 × 1000 J = -126000 J
- ΔS = +84 J/K
- Substitute into the Gibbs free energy equation:
\[ \Delta G_{III} = -126000 \text{ J} - (298 \text{ K} \times 84 \text{ J/K}) \]
\[ = -126000 \text{ J} - 25032 \text{ J} = -151032 \text{ J} \]
- Since ΔG_{III} is negative, Reaction III is **spontaneous**.

### Conclusion:
- **Reaction I:** Non-spontaneous (ΔG > 0)
- **Reaction II:** Non-spontaneous (ΔG > 0)
- **Reaction III:** Spontaneous (ΔG < 0)

Thus, the only spontaneous reaction at 25°C is **Reaction III**.