One atom of an element `x` weight `6.643xx10^(-232)g`. Number of moles of atom in `20` kg is :

Options

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

Answer

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

### Step 1: Determine the mass of one mole of the element X.
We know that the weight 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.

**Calculation:**
\[ \text{Molar mass} = \text{mass of one atom} \times \text{Avogadro's number} \]
\[ \text{Molar mass} = 6.643 \times 10^{-23} \, \text{g} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]
\[ \text{Molar mass} = 40 \, \text{g/mole} \]

### Step 2: Convert the mass from kilograms to grams.
The problem states that we have 20 kg of the element. To work in grams, we convert kilograms to grams.

**Calculation:**
\[ 20 \, \text{kg} = 20 \times 10^{3} \, \text{g} = 20000 \, \text{g} \]

### Step 3: Calculate the number of moles of the element X.
Now that we have the molar mass and the total mass in grams, we can find the number of moles using the formula:

\[ \text{Number of moles} = \frac{\text{given mass}}{\text{molar mass}} \]

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

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

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