A mole is a collection of `6.022 xx 10^23` particles and the number `6.022 xx 10^23` is called Avogadro number. The mass of this number of atoms in an element is equal to its gram atomic mass and mass of this number of molecules in a compound is equal to its gram molecular mass. The volume occupied by this number of molecules of a gas at N.T.P is 22.4 L. When `6.022 xx 10^23` molecules of a substance are dissolved in 1L of solution, the solution is known as 1 molar volume.
Suppose the chemists would have choosen `10^20` as the number of particles in a mole, the mass of 1 mole of oxygen gas would be:

Options

A. `5.32 xx 10^(3)` g
B. `5.32 xx 10^(-3)` g
C. `5.32 xx 10^(-23)` g
D. `5.32 xx 10^(3)` g

Explanation

To find the mass of 1 mole of oxygen gas (O₂) if a chemist had chosen \(10^{20}\) as the number of particles in a mole, we can follow these steps:

### Step 1: Determine the mass of 1 mole of oxygen gas using Avogadro's number.
The molar mass of oxygen gas (O₂) is 32 grams per mole. This means that \(6.022 \times 10^{23}\) molecules of O₂ weigh 32 grams.

### Step 2: Calculate the mass of a single molecule of O₂.
To find the mass of one molecule of O₂, we divide the molar mass by Avogadro's number:
\[ \text{Mass of one molecule of O₂} = \frac{32 \text{ g}}{6.022 \times 10^{23}} \approx 5.314 \times 10^{-23} \text{ g} \]

### Step 3: Calculate the mass of \(10^{20}\) molecules of O₂.
Now, we need to find the mass of \(10^{20}\) molecules of O₂. We can do this by multiplying the mass of one molecule by \(10^{20}\):
\[ \text{Mass of } 10^{20} \text{ molecules of O₂} = 10^{20} \times 5.314 \times 10^{-23} \text{ g} \]

### Step 4: Perform the multiplication.
Calculating the above expression:
\[ \text{Mass} = 10^{20} \times 5.314 \times 10^{-23} = 5.314 \times 10^{-3} \text{ g} \]

### Conclusion:
Thus, if a chemist had chosen \(10^{20}\) as the number of particles in a mole, the mass of 1 mole of oxygen gas would be approximately \(5.314 \times 10^{-3}\) grams or \(0.005314\) grams.

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