Find the no. of moles of `O_2` present in 2.20x`10^21` molecules of oxygen gas?

Options

A. 3.65 x `10^(-3)`
B. 2.65 x `10^(-3)`
C. 1.65 x `10^(-3)`
D. 2.65 x `10^(-3)`

Explanation

To find the number of moles of \( O_2 \) present in \( 2.20 \times 10^{21} \) molecules of oxygen gas, we can follow these steps:

### Step 1: Understand the relationship between moles and molecules
We know that 1 mole of any substance contains \( 6.02 \times 10^{23} \) molecules. This number is known as Avogadro's number.

### Step 2: Set up the equation
To find the number of moles (\( n \)) from the number of molecules (\( N \)), we can use the formula:
\[ n = \frac{N}{N_A} \]
where \( N_A \) is Avogadro's number (\( 6.02 \times 10^{23} \) molecules/mole).

### Step 3: Substitute the values into the equation
In this case, \( N = 2.20 \times 10^{21} \) molecules. Thus, we can substitute the values into the equation:
\[ n = \frac{2.20 \times 10^{21}}{6.02 \times 10^{23}} \]

### Step 4: Perform the calculation
Now, we will carry out the division:
\[ n = \frac{2.20}{6.02} \times \frac{10^{21}}{10^{23}} = \frac{2.20}{6.02} \times 10^{-2} \]

Calculating \( \frac{2.20}{6.02} \):
\[ \frac{2.20}{6.02} \approx 0.365 \]
So,
\[ n \approx 0.365 \times 10^{-2} = 3.65 \times 10^{-3} \text{ moles} \]

### Step 5: Conclusion
Therefore, the number of moles of \( O_2 \) present in \( 2.20 \times 10^{21} \) molecules of oxygen gas is approximately \( 3.65 \times 10^{-3} \) moles.