One atom of an element `x` weighs `6.643 xx 10^(-23)g`. Number of moles of atoms in its `20kg` is :

Options

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

Answer

To solve the problem step by step, we will follow the outlined procedure:

### Step 1: Determine the Molar Mass of Element X
We know that the mass of one atom of element X is given as \( 6.643 \times 10^{-23} \) grams. To find the molar mass (mass of one mole of atoms), we use Avogadro's number, which is \( 6.022 \times 10^{23} \) atoms/mole.

The molar mass can be calculated using the formula:
\[ \text{Molar Mass} = \text{mass of one atom} \times \text{Avogadro's number} \]

Substituting the values:
\[ \text{Molar Mass} = 6.643 \times 10^{-23} \, \text{g/atom} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]

Calculating this gives:
\[ \text{Molar Mass} = 6.643 \times 6.022 \approx 40 \, \text{g/mole} \]

### Step 2: Convert the Given Mass from Kilograms to Grams
The problem states that we have \( 20 \, \text{kg} \). We need to convert this mass into grams:
\[ 20 \, \text{kg} = 20 \times 10^3 \, \text{g} = 20000 \, \text{g} \]

### Step 3: Calculate the Number of Moles
Now that we have the molar mass and the mass in grams, we can calculate the number of moles using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

Substituting the values:
\[ \text{Number of moles} = \frac{20000 \, \text{g}}{40 \, \text{g/mole}} \]

Calculating this gives:
\[ \text{Number of moles} = 500 \, \text{moles} \]

### Final Answer
The number of moles of atoms in \( 20 \, \text{kg} \) of element X is \( 500 \, \text{moles} \).

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