A mole of any substance contains `6.023xx10^(23)` particles. The particles may be atom, molecule ions, electron, proton or neutron. One mole of atom is equal to 1 gm -atom which is equal to atomic weight of atom. 1 gm molecule of any gas is 1 mole of gas whose volume is 22.4 litre at N.T.P.
Mass of 1 atom of an element `X_(2)` is `6.64xx10^(-23)gm`. Molecular weight of `X_(2)` is

Options

A. 80
B. 60
C. 40
D. 20

Answer

To find the molecular weight of the diatomic molecule \( X_2 \), we can follow these steps:

### Step 1: Understand the mass of one atom of element \( X \)
The mass of one atom of element \( X \) is given as \( 6.64 \times 10^{-23} \) grams.

### Step 2: Calculate the mass of one molecule of \( X_2 \)
Since \( X_2 \) is a diatomic molecule, it contains two atoms of \( X \). Therefore, the mass of one molecule of \( X_2 \) can be calculated as:
\[ \text{Mass of one molecule of } X_2 = 2 \times \text{mass of one atom of } X \]
Substituting the value:
\[ \text{Mass of one molecule of } X_2 = 2 \times (6.64 \times 10^{-23}) = 1.328 \times 10^{-22} \text{ grams} \]

### Step 3: Calculate the molecular weight of \( X_2 \)
The molecular weight (or molar mass) is defined as the mass of one mole of the substance. According to Avogadro's number, one mole contains \( 6.022 \times 10^{23} \) molecules. Thus, the molecular weight of \( X_2 \) can be calculated as:
\[ \text{Molecular weight of } X_2 = \text{mass of one molecule of } X_2 \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Molecular weight of } X_2 = (1.328 \times 10^{-22} \text{ grams}) \times (6.022 \times 10^{23}) \]

### Step 4: Perform the calculation
Now, we will perform the multiplication:
\[ \text{Molecular weight of } X_2 = 1.328 \times 6.022 \approx 8.00 \text{ grams/mole} \]

### Conclusion
Thus, the molecular weight of \( X_2 \) is approximately \( 80 \) grams/mole.

---