Answer :
The number of silicon atoms that are in this sample is: B. [tex]2.11 \times 10^{23} \;atoms[/tex]
Given the following data:
- Mass of silicon = 98.3 grams
Scientific data:
- Avogadro's number = [tex]6.02 \times 10^{23}[/tex]
- Molar mass of silicon = 28.09 g/mol.
To determine the number of silicon atoms that are in this sample:
First of all, we would determine the number of moles contained in 98.3 grams of silicon.
[tex]Number\;of\;moles = \frac{mass}{molar\;mass}\\\\Number\;of\;moles = \frac{98.3}{28.09}[/tex]
Number of moles = 3.4995 moles
By stoichiometry:
1 mole of silicon = [tex]6.02 \times 10^{23}[/tex] atoms
3.4995 moles of silicon = X atoms
Cross-multiplying, we have:
[tex]X = 6.02 \times 10^{23} \times 3.4995\\\\X= 2.11 \times 10^{23} \;atoms[/tex]
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Final answer:
The 98.3 g sample of silicon contains approximately 2.11 × 10²´ atoms, which is option B.
Explanation:
To calculate the number of silicon atoms in a 98.3 g sample, we need to first determine the molar mass of silicon and how many moles are in the sample. From the periodic table, the molar mass of silicon (Si) is approximately 28.1 g/mol. This means each mole of silicon comprises 6.022 × 10²³ atoms (Avogadro's number). The calculation to convert grams to moles is as follows:
- Number of moles = mass of sample (g) / molar mass (g/mol)
- Number of moles of silicon = 98.3 g / 28.1 g/mol ≈ 3.498 moles of Si
With the number of moles of silicon established, we can now find the number of atoms:
- Number of atoms = number of moles × Avogadro's number
- Number of Si atoms = 3.498 moles × 6.022 × 10²³ atoms/mol ≈ 2.11 × 10²´ atoms
Therefore, the correct answer is (B) 2.11 × 10²´ atoms of silicon in the 98.3 g sample.
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