If ammonia is manufactured at 356 K, is the reaction spontaneous, given that the enthalpy and entropy change for the reaction are -93 kJ/mol and -198

J/mol K, respectively?

﻿﻿A. No, the AG is 92 kJ/mol.

﻿﻿B. Yes, the AG is -22.5 kJ/mol.

O C. No, the AGis 22.5 kJ/mol.

• D. Yes, the AG is -92 kJ/mol.

To determine whether the reaction is spontaneous at 356 K, we need to calculate the Gibbs free energy change (\( \Delta G \)) using the following equation:

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

where:
- \( \Delta G \) is the Gibbs free energy change,
- \( \Delta H \) is the enthalpy change,
- \( T \) is the temperature in Kelvin,
- \( \Delta S \) is the entropy change.

### Step 1: Convert the given values to consistent units
Given:
- \( \Delta H = -93 \, \text{kJ/mol} \) 
- \( \Delta S = -198 \, \text{J/mol K} \) 

Since \( \Delta H \) is in kJ/mol and \( \Delta S \) is in J/mol K, we need to convert \( \Delta H \) into J/mol to match the units:

\[
\Delta H = -93 \, \text{kJ/mol} \times 1000 \, \text{J/kJ} = -93000 \, \text{J/mol}
\]

### Step 2: Substitute the values into the Gibbs free energy equation
Now, substitute the values into the equation:

\[
\Delta G = -93000 \, \text{J/mol} - (356 \, \text{K} \times -198 \, \text{J/mol K})
\]

### Step 3: Perform the calculation
First, calculate the term \( T \Delta S \):

\[
T \Delta S = 356 \, \text{K} \times -198 \, \text{J/mol K} = -70488 \, \text{J/mol}
\]

Then, calculate \( \Delta G \):

\[
\Delta G = -93000 \, \text{J/mol} - (-70488 \, \text{J/mol}) = -93000 \, \text{J/mol} + 70488 \, \text{J/mol} = -22512 \, \text{J/mol}
\]

### Step 4: Convert the result back to kJ/mol
Convert \( \Delta G \) back to kJ/mol:

\[
\Delta G = -22.512 \, \text{kJ/mol}
\]

### Conclusion:
Since \( \Delta G \) is negative, the reaction is spontaneous. The closest answer is:

**B. Yes, the \( \Delta G \) is -22.5 kJ/mol.**

Would you like further details or have any questions?

Here are some related questions:
1. What does a negative \( \Delta G \) indicate about the spontaneity of a reaction?
2. How would the spontaneity of the reaction change if the temperature was increased?
3. What is the significance of the enthalpy change \( \Delta H \) being negative?
4. How does entropy \( \Delta S \) influence the Gibbs free energy?
5. What is the relationship between \( \Delta G \), \( \Delta H \), and \( \Delta S \) in determining spontaneity?

**Tip:** Always ensure that the units of \( \Delta H \) and \( \Delta S \) are consistent before performing calculations for \( \Delta G \).

Calculate whether the production of ammonia at 356 K is spontaneous using Gibbs free energy (ΔG) calculation. Given ΔH = -93 kJ/mol and ΔS = -198 J/mol K, determine if the reaction is spontaneous based on ΔG. Explore the thermodynamic principles involved.

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