Which of the following thermodynamic properties must be
associated with a reaction spontaneous at only high temperatures

Options

A. `DeltaHlt0,DeltaSlt0`
B. `DeltaHlt0,DeltaSgt0`
C. `DeltaHgt0,DeltaSgt0`
D. `DeltaHgt0,DeltaSlt0`

Explanation

To determine which thermodynamic properties must be associated with a reaction that is spontaneous only at high temperatures, we can analyze the Gibbs free energy equation:

### Step-by-Step Solution:

1. **Understanding Gibbs Free Energy**:
The spontaneity of a reaction is determined by the Gibbs free energy change (ΔG), which is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

**Hint**: Remember that a negative ΔG indicates a spontaneous reaction.

2. **Condition for Spontaneity**:
For a reaction to be spontaneous, ΔG must be less than 0:
\[ \Delta G < 0 \implies \Delta H - T \Delta S < 0 \]
Rearranging gives:
\[ \Delta H < T \Delta S \]

**Hint**: Think about how the signs of ΔH and ΔS affect the spontaneity.

3. **Analyzing High Temperature**:
We are interested in the case where the reaction is spontaneous only at high temperatures. This implies that as the temperature increases, the term \(T \Delta S\) must dominate over ΔH.

**Hint**: Consider what happens to the relationship as T increases.

4. **Determining Signs of ΔH and ΔS**:
For the condition \(T \Delta S > \Delta H\) to hold true at high temperatures:
- If ΔH is positive (endothermic reaction) and ΔS is also positive (increase in disorder), then at high temperatures, \(T \Delta S\) can become larger than ΔH, making ΔG negative.
- Conversely, if ΔH were negative, the reaction would be spontaneous at lower temperatures.

**Hint**: Recall the implications of positive and negative values for ΔH and ΔS.

5. **Conclusion**:
Therefore, for a reaction to be spontaneous only at high temperatures, we conclude that:
- ΔH must be positive (ΔH > 0)
- ΔS must be positive (ΔS > 0)

Thus, the correct answer is that both ΔH and ΔS must be positive.

**Final Answer**: The thermodynamic properties associated with a reaction that is spontaneous only at high temperatures are:
- ΔH > 0 (positive)
- ΔS > 0 (positive)