For a reaction `DeltaH=(+3kJ), DeltaS=(+10J//K)` beyond which temperature this reaction will be spontaneous

Options

A. 300 K
B. 200 K
C. 273 K
D. 373 K

Explanation

To determine the temperature beyond which the given reaction will be spontaneous, we can 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 zero:

\[ \Delta G < 0 \]

### Step 1: Convert \(\Delta H\) to Joules
Given:
\[ \Delta H = +3 \, \text{kJ} = 3 \times 1000 \, \text{J} = 3000 \, \text{J} \]

### Step 2: Identify \(\Delta S\)
Given:
\[ \Delta S = +10 \, \text{J/K} \]

### Step 3: Set up the inequality for spontaneity
Using the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
We need:
\[ \Delta H - T \Delta S < 0 \]
Substituting the values:
\[ 3000 - T \cdot 10 < 0 \]

### Step 4: Rearrange the inequality
Rearranging gives:
\[ 3000 < T \cdot 10 \]
Dividing both sides by 10:
\[ 300 < T \]

### Step 5: Conclusion
Thus, the reaction will be spontaneous at temperatures greater than 300 K.

### Final Answer
The reaction will be spontaneous beyond a temperature of **300 K**.

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