One atom of an element X’ weighs `6.644 xx 10^(-23)` g. Calculate the number of gram atoms in 80 kg of it.

Explanation

To solve the problem, we need to find the number of gram atoms (or moles) in 80 kg of the element X, given that one atom of X weighs \(6.644 \times 10^{-23}\) g.

### Step 1: Convert the mass from kilograms to grams
First, we convert 80 kg to grams because the weight of one atom is given in grams.

\[ 80 \text{ kg} = 80 \times 1000 \text{ g} = 80000 \text{ g} \]

### Step 2: Calculate the mass of one mole of the element
To find the number of gram atoms, we need to know the mass of one mole of the element. The mass of one mole of atoms (also known as molar mass) can be calculated using Avogadro's number (\(6.022 \times 10^{23}\) atoms/mole).

The mass of one mole of the element can be calculated as:

\[ \text{Mass of one mole} = \text{mass of one atom} \times \text{Avogadro's number} \]

Substituting the values:

\[ \text{Mass of one mole} = 6.644 \times 10^{-23} \text{ g/atom} \times 6.022 \times 10^{23} \text{ atoms/mole} \]

### Step 3: Perform the calculation
Now we perform the multiplication:

\[ \text{Mass of one mole} = 6.644 \times 6.022 \text{ g} = 39.96 \text{ g} \quad (\text{approximately}) \]

### Step 4: Calculate the number of moles in 80000 g
Now that we have the mass of one mole, we can find out how many moles are in 80000 g.

Using the formula:

\[ \text{Number of moles} = \frac{\text{Total mass}}{\text{Mass of one mole}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{80000 \text{ g}}{39.96 \text{ g/mole}} \approx 2000.5 \text{ moles} \]

### Step 5: Conclusion
Thus, the number of gram atoms (or moles) in 80 kg of the element X is approximately 2000.5 moles.

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