One atom of an element `x` weight `6.643xx10^(-23)g`. Number of moles of atom in `20` kg is :

Options

A. 4
B. 40
C. 100
D. 500

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the weight of one atom of element X
The weight of one atom of element X is given as \( 6.643 \times 10^{-23} \) g.

### Step 2: Calculate the weight of one mole of atoms
We know that one mole of any substance contains \( 6.022 \times 10^{23} \) atoms (Avogadro's number). Therefore, the weight of one mole of element X can be calculated using the formula:

\[ \text{Weight of 1 mole} = \text{Weight of 1 atom} \times \text{Number of atoms in 1 mole} \]

Substituting the values:

\[ \text{Weight of 1 mole} = 6.643 \times 10^{-23} \, \text{g/atom} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]

### Step 3: Perform the multiplication
Calculating the above expression:

\[ \text{Weight of 1 mole} = 6.643 \times 6.022 \approx 40 \, \text{g} \]

### Step 4: Convert the mass from kg to g
The mass of the substance is given as \( 20 \) kg. We need to convert this to grams:

\[ 20 \, \text{kg} = 20 \times 1000 \, \text{g} = 20000 \, \text{g} \]

### Step 5: Calculate the number of moles
The number of moles can be calculated using the formula:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{20000 \, \text{g}}{40 \, \text{g/mole}} = 500 \, \text{moles} \]

### Final Answer
The number of moles of element X in 20 kg is **500 moles**.

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