Question

How many grams do 3.6 x10^20 atoms of silicon weigh?

Answer 1

`3.6 * \(10^(20)\)` atoms of silicon weigh approximately 0.169 grams.

To calculate the weight of a given number of atoms, you can use the concept of molar mass and Avogadro's number.

1. Find the molar mass of silicon (Si). The molar mass is the mass of one mole of a substance. The atomic mass of silicon is approximately 28.09 g/mol.

2. Determine Avogadro's number, which is the number of atoms or molecules in one mole. Avogadro's number is
`\(6.022 * 10^(23)\)` entities/mol.

3. Calculate the weight (mass) using the formula:

`\[\text{Weight (g)} = \left(\frac{\text{Number of atoms}}{\text{Avogadro's number}}\right) * \text{Molar mass}\]`

For silicon:

`\[\text{Weight (g)} = \left((3.6 * 10^(20))/(6.022 * 10^(23))\right) * 28.09 \, \text{g/mol}\]`

Now, let's calculate:

`\[\text{Weight (g)} \approx \left((3.6 * 10^(20))/(6.022 * 10^(23))\right) * 28.09 \, \text{g/mol} \approx 0.169 \, \text{g}\]`

Therefore,
`3.6 * \(10^(20)\)` atoms of silicon weigh approximately 0.169 grams.

Answer 2

First, we divide the number of atoms of silicon given in the problem above by Avogadro's number 6.6022 x10^23. This will give us the number of moles of silicon. Then, we multiply the number of moles by the molar mass of silicon.
number of moles = (3.6 x 10^20 atoms/6.022x10^23 atoms) = 5.97x10^-4 moles
Then, multiplying by the molar mass
(5.97x10^-4 moles)(28.0855 g/mol) = 0.017 grams