For the reaction at `298 K`
`2A+B rarr C`
`DeltaH=400 kJ mol^(-1)` and `DeltaS=0.2 kJ K^(-1) mol^(-1)`
At what temperature will the reaction becomes spontaneous considering `DeltaH` and `DeltaS` to be contant over the temperature range.

Explanation

To determine the temperature at which the reaction becomes spontaneous, we need to analyze the relationship between the Gibbs free energy change (ΔG), enthalpy change (ΔH), and entropy change (ΔS) for the reaction.

### Step-by-Step Solution:

1. **Understand the Condition for Spontaneity**:
For a reaction to be spontaneous, the Gibbs free energy change (ΔG) must be negative:
\[ \Delta G < 0 \]

2. **Use the Gibbs Free Energy Equation**:
The Gibbs free energy change is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
To find the temperature at which the reaction becomes spontaneous, we set ΔG to 0:
\[ 0 = \Delta H - T \Delta S \]

3. **Rearranging the Equation**:
Rearranging the equation gives:
\[ T \Delta S = \Delta H \]
Therefore, we can express the temperature (T) as:
\[ T = \frac{\Delta H}{\Delta S} \]

4. **Substituting the Given Values**:
We know from the problem:
- ΔH = 400 kJ/mol
- ΔS = 0.2 kJ/K·mol

Substituting these values into the equation:
\[ T = \frac{400 \text{ kJ/mol}}{0.2 \text{ kJ/K·mol}} \]

5. **Calculating the Temperature**:
Performing the division:
\[ T = \frac{400}{0.2} = 2000 \text{ K} \]

6. **Conclusion**:
The reaction becomes spontaneous at temperatures greater than 2000 K.

### Final Answer:
The temperature at which the reaction becomes spontaneous is greater than **2000 K**.

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