For a certain reaction `Delta H^(@) =- 224 kJ ` and `Delta S^(@) =- 153 JK`
At what temperature will it change from spontaneous to non- spontaneous ?

Explanation

To determine the temperature at which a reaction changes from spontaneous to non-spontaneous, we can use the Gibbs free energy equation:

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

### Step 1: Understand the conditions for spontaneity
For a reaction to be spontaneous, \(\Delta G\) must be less than zero (\(\Delta G < 0\)). At the temperature where the reaction changes from spontaneous to non-spontaneous, \(\Delta G\) will be equal to zero (\(\Delta G = 0\)).

### Step 2: Set up the equation
We set \(\Delta G\) to zero:

\[ 0 = \Delta H - T \Delta S \]

Rearranging gives us:

\[ T = \frac{\Delta H}{\Delta S} \]

### Step 3: Convert units
We need to ensure that \(\Delta H\) and \(\Delta S\) are in compatible units. Given:

- \(\Delta H = -224 \, \text{kJ} = -224 \times 1000 \, \text{J} = -224000 \, \text{J}\)
- \(\Delta S = -153 \, \text{J/K}\)

### Step 4: Substitute the values into the equation
Now we can substitute the values into the equation:

\[ T = \frac{-224000 \, \text{J}}{-153 \, \text{J/K}} \]

### Step 5: Calculate the temperature
Calculating \(T\):

\[ T = \frac{224000}{153} \approx 1465.4 \, \text{K} \]

### Conclusion
The temperature at which the reaction changes from spontaneous to non-spontaneous is approximately **1465.4 K**.

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