For the reaction, `Ag_2O(s)to2Ag(s)+1/2O_2(g),/_\H,/_\S` and T are 40kJ, 100J and 380K respectively Hence `/_\G` in KJ is :

Explanation

To solve for the Gibbs free energy change (ΔG) for the reaction \( \text{Ag}_2\text{O}(s) \rightarrow 2\text{Ag}(s) + \frac{1}{2}\text{O}_2(g) \), we will use the formula:

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

### Step 1: Identify the values given in the problem
- ΔH = 40 kJ (which is equal to \( 40 \times 10^3 \) J for consistency in units)
- ΔS = 100 J
- T = 380 K

### Step 2: Convert ΔH to the same unit as ΔS
Since ΔS is given in joules, we convert ΔH from kilojoules to joules:
\[ \Delta H = 40 \, \text{kJ} = 40 \times 10^3 \, \text{J} = 40000 \, \text{J} \]

### Step 3: Calculate TΔS
Now we calculate \( T \Delta S \):
\[ T \Delta S = 380 \, \text{K} \times 100 \, \text{J} = 38000 \, \text{J} \]

### Step 4: Substitute values into the Gibbs free energy equation
Now we can substitute the values into the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
\[ \Delta G = 40000 \, \text{J} - 38000 \, \text{J} = 2000 \, \text{J} \]

### Step 5: Convert ΔG back to kilojoules
To express ΔG in kilojoules:
\[ \Delta G = \frac{2000 \, \text{J}}{1000} = 2 \, \text{kJ} \]

### Final Answer
Thus, the value of ΔG is:
\[ \Delta G = 2 \, \text{kJ} \]

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