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:
B. [tex]\(2.40 \times 10^{24}\)[/tex] atoms Si.
