Total number of moles of oxygen atoms in 3 litre `O_3 (g)` at `27^@C and 8.21` atm are :

Options

A. 3
B. 1
C. 1
D. None of these

Answer

To find the total number of moles of oxygen atoms in 3 liters of ozone (O₃) at 27°C and 8.21 atm, we can follow these steps:

### Step 1: Convert the temperature to Kelvin
The temperature given is 27°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
So,
\[ T = 27 + 273.15 = 300.15 \text{ K} \approx 300 \text{ K} \]

### Step 2: Use the Ideal Gas Law
The Ideal Gas Law is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure in atm (8.21 atm)
- \( V \) = volume in liters (3 L)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin (300 K)

### Step 3: Rearrange the Ideal Gas Law to solve for n
We can rearrange the equation to solve for \( n \):
\[ n = \frac{PV}{RT} \]

### Step 4: Substitute the values into the equation
Now we substitute the known values into the equation:
\[ n = \frac{(8.21 \, \text{atm}) \times (3 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (300 \, \text{K})} \]

### Step 5: Calculate the number of moles of O₃
Now, we perform the calculation:
\[ n = \frac{24.63}{24.63} = 1 \text{ mole of O₃} \]

### Step 6: Determine the number of moles of oxygen atoms
Since each molecule of O₃ contains 3 oxygen atoms, the total number of moles of oxygen atoms is:
\[ \text{Moles of O atoms} = 1 \, \text{mole of O₃} \times 3 \, \text{moles of O atoms/mole of O₃} = 3 \, \text{moles of O atoms} \]

### Final Answer:
The total number of moles of oxygen atoms in 3 liters of O₃ at 27°C and 8.21 atm is **3 moles**.

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