The signs of `DeltaH,DeltaS and DeltaG` for a non-spontaneous reaction at all temperature would e

Options

A. `+,+,-`
B. `+,-,+`
C. `-,-,-`
D. `+,+,+`

Answer

To determine the signs of ΔH, ΔS, and ΔG for a non-spontaneous reaction at all temperatures, we can analyze the thermodynamic principles involved.

### Step-by-Step Solution:

1. **Understanding Non-Spontaneous Reactions**:
- A non-spontaneous reaction is one that does not occur on its own under standard conditions. This means that the reaction requires an input of energy to proceed.

2. **Sign of ΔH (Enthalpy Change)**:
- Non-spontaneous reactions are often endothermic, meaning they absorb heat from the surroundings. Therefore, the enthalpy change (ΔH) for a non-spontaneous reaction is **positive**.

3. **Sign of ΔS (Entropy Change)**:
- For a non-spontaneous reaction, the randomness or disorder of the system does not increase. In fact, it may decrease. Thus, the change in entropy (ΔS) is typically **negative**.

4. **Calculating ΔG (Gibbs Free Energy Change)**:
- The Gibbs free energy change (ΔG) is given by the equation:
\[ ΔG = ΔH - TΔS \]
- Since ΔH is positive and ΔS is negative, we can substitute these signs into the equation:
- ΔH > 0 (positive)
- ΔS < 0 (negative)
- Therefore, the term \( -TΔS \) becomes positive (since multiplying a negative ΔS by a positive temperature T gives a negative value, and subtracting a negative value results in a positive value).
- This means that ΔG will be positive:
\[ ΔG = \text{(positive)} - \text{(positive)} = \text{positive} \]

5. **Conclusion**:
- For a non-spontaneous reaction at all temperatures, the signs are:
- ΔH: **Positive**
- ΔS: **Negative**
- ΔG: **Positive**

### Summary of Signs:
- ΔH: **Positive**
- ΔS: **Negative**
- ΔG: **Positive**