Suppose that a reaction has `DeltaH=-40kJ` and `DeltaS =- 50J//K`. At what temperature range will it change from spontaneous to non-spontaneous?

Options

A. 0.8 K to 1 K
B. 799 K to 800 K
C. 800 K to 801 K
D. 799 K to 801 K

Explanation

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

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

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

### Given Data:
- \(\Delta H = -40 \, \text{kJ} = -40,000 \, \text{J}\) (since we need to convert kJ to J)
- \(\Delta S = -50 \, \text{J/K}\)

### Step 1: Set up the equation for spontaneity
For a reaction to be spontaneous, \(\Delta G\) must be less than 0. Therefore, we set up the inequality:

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

Substituting the values of \(\Delta H\) and \(\Delta S\):

\[ -40,000 \, \text{J} - T(-50 \, \text{J/K}) < 0 \]

### Step 2: Simplify the inequality
This simplifies to:

\[ -40,000 + 50T < 0 \]

### Step 3: Solve for \(T\)
Rearranging the inequality gives:

\[ 50T < 40,000 \]

Dividing both sides by 50:

\[ T < \frac{40,000}{50} \]

Calculating the right side:

\[ T < 800 \, \text{K} \]

### Step 4: Determine the temperature at which \(\Delta G = 0\)
To find the temperature where the reaction changes from spontaneous to non-spontaneous, we set \(\Delta G = 0\):

\[ 0 = -40,000 + 50T \]

Solving for \(T\):

\[ 50T = 40,000 \]

\[ T = \frac{40,000}{50} = 800 \, \text{K} \]

### Step 5: Determine the temperature range
At \(T < 800 \, \text{K}\), the reaction is spontaneous (\(\Delta G < 0\)). At \(T = 800 \, \text{K}\), the reaction is at equilibrium (\(\Delta G = 0\)). At \(T > 800 \, \text{K}\), the reaction becomes non-spontaneous (\(\Delta G > 0\)).

Thus, the temperature range where the reaction changes from spontaneous to non-spontaneous is:

\[ T = 800 \, \text{K} \]

### Conclusion
The reaction changes from spontaneous to non-spontaneous at \(T = 800 \, \text{K}\).