Greenhouse gas `CO_(2)` can be converted to `CO(g)` by the following reaction
`CO_(2)(g)+H_(2)(g) rarr CO+H_(2)O(g)` , termed as water gas reaction.
Calculate `DeltaG` for the reaction at 1000K `(DeltaH_(1000K)=35040 J "mol"^(-1) DeltaS_(1000K) =32.11 J "mol"^(-1)K^(1))`.

Answer

To calculate the change in Gibbs free energy (ΔG) for the reaction at 1000 K, we will use the following formula:

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

Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = temperature in Kelvin
- ΔS = change in entropy

### Step 1: Identify the given values
From the problem statement, we have:
- ΔH (at 1000 K) = 35040 J/mol
- ΔS (at 1000 K) = 32.11 J/mol·K
- T = 1000 K

### Step 2: Substitute the values into the formula
Now, we substitute the values into the Gibbs free energy equation:

\[ \Delta G = 35040 \, \text{J/mol} - (1000 \, \text{K} \times 32.11 \, \text{J/mol·K}) \]

### Step 3: Calculate TΔS
First, we calculate \(T \Delta S\):

\[ T \Delta S = 1000 \, \text{K} \times 32.11 \, \text{J/mol·K} = 32110 \, \text{J/mol} \]

### Step 4: Complete the calculation for ΔG
Now, we can substitute this value back into the equation for ΔG:

\[ \Delta G = 35040 \, \text{J/mol} - 32110 \, \text{J/mol} \]

\[ \Delta G = 2930 \, \text{J/mol} \]

### Final Answer
Thus, the change in Gibbs free energy (ΔG) at 1000 K for the reaction is:

\[ \Delta G = 2930 \, \text{J/mol} \]

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