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How many atoms are in 112 g of Si?
- Molar mass of Si = [tex]$28.09 \, \text{g/mol}$[/tex] - 1 mole = [tex]$6.02 \times 10^{23}$[/tex] atoms
A. [tex]$1.51 \times 10^{23}$[/tex] atoms Si B. [tex]$2.40 \times 10^{24}$[/tex] atoms Si C. [tex]$6.62 \times 10^{-24}$[/tex] atoms Si D. [tex]$1.89 \times 10^{27}$[/tex] atoms Si
To determine the number of atoms in 112 grams of silicon (Si), we need to follow a series of steps, making use of the given molar mass of silicon and Avogadro's number. Here's a detailed step-by-step solution:
1. Determine the molar mass of silicon (Si): - The molar mass of silicon is given as 28.09 grams per mole (g/mol).
2. Calculate the number of moles of silicon (Si): - Mass of silicon (Si) provided: 112 grams (g). - Number of moles ([tex]\( n \)[/tex]) can be calculated using the formula: [tex]\[
n = \frac{\text{mass}}{\text{molar mass}}
\][/tex] - Plugging in the values: [tex]\[
n = \frac{112 \text{ g}}{28.09 \text{ g/mol}}
\][/tex]
3. Evaluate the number of moles: - Performing the division: [tex]\[
n \approx 3.987 \text{ moles}
\][/tex]
4. Use Avogadro's number to find the number of atoms: - Avogadro's number, which represents the number of atoms in one mole of a substance, is given as [tex]\( 6.02 \times 10^{23} \)[/tex] atoms per mole. - The number of atoms ([tex]\( N \)[/tex]) can be calculated using the formula: [tex]\[
N = n \times \text{Avogadro's number}
\][/tex] - Plugging in the values: [tex]\[
N = 3.987 \text{ moles} \times 6.02 \times 10^{23} \text{ atoms/mole}
\][/tex]
5. Evaluate the number of atoms: - Multiplying these values: [tex]\[
N \approx 2.40 \times 10^{24} \text{ atoms}
\][/tex]
Given our calculations, the number of atoms in 112 grams of silicon is approximately [tex]\( 2.40 \times 10^{24} \)[/tex] atoms. Therefore, the correct answer is:
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