For the reaction between `CO_2` and graphite `CO_2(g)+C(s) hArr2CO(g)`
`DeltaH=+170.0kJ and DeltaS = 170 JK^(-1)`. The reaction is spontaneous at

Options

A. 298 K
B. 500 K
C. 900 K
D. 1200 K

Answer

To determine when the reaction between \( CO_2 \) and graphite becomes spontaneous, we can use the Gibbs free energy equation:

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

### Step 1: Identify the given values
We are given:
- \( \Delta H = +170.0 \, \text{kJ} \)
- \( \Delta S = 170 \, \text{J/K} \)

### Step 2: Convert \( \Delta H \) to Joules
Since \( \Delta S \) is in Joules, we need to convert \( \Delta H \) from kJ to J:
\[ \Delta H = 170.0 \, \text{kJ} \times 1000 \, \text{J/kJ} = 170000 \, \text{J} \]

### Step 3: Set up the equation for spontaneity
For the reaction to be spontaneous, \( \Delta G \) must be less than 0:
\[ \Delta G < 0 \implies \Delta H - T \Delta S < 0 \]

### Step 4: Rearrange the equation
Rearranging gives us:
\[ \Delta H < T \Delta S \]
or
\[ T > \frac{\Delta H}{\Delta S} \]

### Step 5: Substitute the values
Substituting the values we have:
\[ T > \frac{170000 \, \text{J}}{170 \, \text{J/K}} = 1000 \, \text{K} \]

### Step 6: Conclusion
The reaction is spontaneous at temperatures greater than \( 1000 \, \text{K} \).

### Final Answer
The reaction is spontaneous at temperatures greater than \( 1000 \, \text{K} \).

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