For the reaction, `Ag_(2)O(s)rarr2Ag(s)+(1)/(2)O_(2)(g),DeltaH,DeltaS and T` are 40kJ, 100J and 380K respectively. Hence `DeltaG` in kJ is :

Explanation

To find the value of ΔG for the given reaction, we will use the Gibbs free energy equation:

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

### Step 1: Identify the given values
- ΔH = 40 kJ
- ΔS = 100 J
- T = 380 K

### Step 2: Convert ΔS from J to kJ
Since ΔH is given in kJ, we need to convert ΔS from J to kJ for consistency in units.

\[ \Delta S = 100 \, \text{J} = \frac{100}{1000} \, \text{kJ} = 0.1 \, \text{kJ} \]

### Step 3: Substitute the values into the Gibbs free energy equation
Now, we can substitute the values into the equation:

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

Substituting the values we have:

\[ \Delta G = 40 \, \text{kJ} - (380 \, \text{K} \times 0.1 \, \text{kJ}) \]

### Step 4: Calculate TΔS
Now calculate \(T \Delta S\):

\[ T \Delta S = 380 \times 0.1 = 38 \, \text{kJ} \]

### Step 5: Calculate ΔG
Now substitute this back into the equation for ΔG:

\[ \Delta G = 40 \, \text{kJ} - 38 \, \text{kJ} = 2 \, \text{kJ} \]

### Final Answer
Thus, the value of ΔG is:

\[ \Delta G = 2 \, \text{kJ} \]

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