`A+BtoC+D`
`DeltaH=-10,000 J mol^(-1)`
`DeltaS-33.3 J mol^(-1)K^(-1)`
At what temperature the reaction will occur spontaneous
from left to right ?

Options

A. `=300.3K`
B. `gt300.3K`
C. `lt300.3K`
D. None of these

Explanation

To determine the temperature at which the reaction \( A + B \rightarrow C + D \) will occur spontaneously from left to right, we will use the Gibbs free energy equation:

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

For a reaction to be spontaneous, \(\Delta G\) must be less than 0:

\[ \Delta G < 0 \]

### Step 1: Set up the inequality
We start by substituting the Gibbs free energy equation into the inequality:

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

### Step 2: Rearrange the inequality
Rearranging gives us:

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

### Step 3: Solve for temperature \( T \)
Now, we can express \( T \) in terms of \(\Delta H\) and \(\Delta S\):

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

### Step 4: Substitute the given values
We are given:
- \(\Delta H = -10,000 \, \text{J/mol}\)
- \(\Delta S = 33.3 \, \text{J/(mol K)}\)

Substituting these values into the equation:

\[ T > \frac{-10,000 \, \text{J/mol}}{33.3 \, \text{J/(mol K)}} \]

### Step 5: Calculate the temperature
Calculating the right-hand side:

\[ T > \frac{-10,000}{33.3} \approx -300.3 \, \text{K} \]

### Step 6: Interpret the result
Since temperature cannot be negative, we need to consider the conditions under which the reaction is spontaneous. Given that both \(\Delta H\) and \(\Delta S\) are negative, the reaction will be spontaneous at temperatures less than approximately 300.3 K.

### Final Conclusion
Thus, the reaction will occur spontaneously from left to right at temperatures less than approximately 300.3 K.

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