Tell whether reactions with the following values of DH and DS are spontaneous or nonspontaneous, and
whether they are exothermic or endothermic at the given temperature. Circle your choices for all of them;
show a sample calculation for at least one of them.
(a) DH = – 128 kJ ; DS = + 35 J/K ; @ 500 K spontaneous / nonspontaneous endothermic / exothermic
(b) DH = + 67 kJ ; DS = – 140 J/K ; @ 250 K spontaneous / nonspontaneous endothermic / exothermic
(c) DH = + 75 kJ ; DS = + 95 J/K ; @ 800 K spontaneous / nonspontaneous endothermic / exothermi

To determine if the reactions are **spontaneous** or **nonspontaneous** and whether they are **exothermic** or **endothermic**, we can use the **Gibbs Free Energy equation**:

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

- **ΔG (Gibbs free energy)**: If ΔG < 0, the reaction is **spontaneous**; if ΔG > 0, the reaction is **nonspontaneous**.
- **ΔH (Enthalpy)**: If ΔH < 0, the reaction is **exothermic**; if ΔH > 0, the reaction is **endothermic**.
- **T (Temperature)**: Given in Kelvin.
- **ΔS (Entropy)**: Convert to kJ/K by dividing J/K by 1000.

Let's do a sample calculation for case (a):

### (a) \( \Delta H = -128 \, \text{kJ} \), \( \Delta S = +35 \, \text{J/K} \), \( T = 500 \, \text{K} \)
1. Convert ΔS to kJ/K:
   \[
   \Delta S = \frac{35 \, \text{J/K}}{1000} = 0.035 \, \text{kJ/K}
   \]
   
2. Apply the Gibbs free energy equation:
   \[
   \Delta G = \Delta H - T\Delta S
   \]
   \[
   \Delta G = -128 \, \text{kJ} - (500 \, \text{K}) \times (0.035 \, \text{kJ/K})
   \]
   \[
   \Delta G = -128 \, \text{kJ} - 17.5 \, \text{kJ}
   \]
   \[
   \Delta G = -145.5 \, \text{kJ}
   \]

Since \( \Delta G = -145.5 \, \text{kJ} \), the reaction is **spontaneous** because ΔG < 0. Additionally, since ΔH is negative, it is an **exothermic** reaction.

### (b) \( \Delta H = +67 \, \text{kJ} \), \( \Delta S = -140 \, \text{J/K} \), \( T = 250 \, \text{K} \)

1. Convert ΔS to kJ/K:
   \[
   \Delta S = \frac{-140 \, \text{J/K}}{1000} = -0.14 \, \text{kJ/K}
   \]
   
2. Apply the Gibbs free energy equation:
   \[
   \Delta G = 67 \, \text{kJ} - (250 \, \text{K}) \times (-0.14 \, \text{kJ/K})
   \]
   \[
   \Delta G = 67 \, \text{kJ} + 35 \, \text{kJ}
   \]
   \[
   \Delta G = 102 \, \text{kJ}
   \]

Since \( \Delta G = 102 \, \text{kJ} \), the reaction is **nonspontaneous** because ΔG > 0. Additionally, since ΔH is positive, it is an **endothermic** reaction.

### (c) \( \Delta H = +75 \, \text{kJ} \), \( \Delta S = +95 \, \text{J/K} \), \( T = 800 \, \text{K} \)

1. Convert ΔS to kJ/K:
   \[
   \Delta S = \frac{95 \, \text{J/K}}{1000} = 0.095 \, \text{kJ/K}
   \]
   
2. Apply the Gibbs free energy equation:
   \[
   \Delta G = 75 \, \text{kJ} - (800 \, \text{K}) \times (0.095 \, \text{kJ/K})
   \]
   \[
   \Delta G = 75 \, \text{kJ} - 76 \, \text{kJ}
   \]
   \[
   \Delta G = -1 \, \text{kJ}
   \]

Since \( \Delta G = -1 \, \text{kJ} \), the reaction is **spontaneous** because ΔG < 0. Additionally, since ΔH is positive, it is an **endothermic** reaction.

### Summary:

- **(a)** Spontaneous / Exothermic
- **(b)** Nonspontaneous / Endothermic
- **(c)** Spontaneous / Endothermic

Let me know if you would like more details or have any questions!

Here are some related questions:
1. How does temperature affect spontaneity in reactions?
2. Can a reaction be nonspontaneous at one temperature and spontaneous at another?
3. What is the physical meaning of ΔH and ΔS in a reaction?
4. How do exothermic reactions relate to heat transfer in systems?
5. What are real-world examples of spontaneous endothermic reactions?

**Tip:** Always remember to check the units when applying the Gibbs Free Energy equation!

Tell whether reactions with the following values of DH and DS are spontaneous or nonspontaneous, and whether they are exothermic or endothermic at the given temperature. Circle your choices for all of them; show a sample calculation for at least one of them.
(a) DH = – 128 kJ ; DS = + 35 J/K ; @ 500 K spontaneous / nonspontaneous endothermic / exothermic
(b) DH = + 67 kJ ; DS = – 140 J/K ; @ 250 K spontaneous / nonspontaneous endothermic / exothermic
(c) DH = + 75 kJ ; DS = + 95 J/K ; @ 800 K spontaneous / nonspontaneous endothermic / exothermic

Analyze whether chemical reactions are spontaneous or nonspontaneous, exothermic or endothermic, using Gibbs Free Energy. This problem involves enthalpy and entropy changes at different temperatures, applying the ΔG = ΔH - TΔS formula. Suitable for Grades 11-12.

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