Answer :
To find out how many atoms are in 115 grams of calcium, we follow these steps:
1. Determine the Molar Mass of Calcium:
The molar mass of calcium is approximately 40.08 grams per mole. This means that each mole of calcium weighs 40.08 grams.
2. Calculate the Number of Moles:
To find the number of moles of calcium in 115 grams, we use the formula:
[tex]\[
\text{Number of moles} = \frac{\text{mass in grams}}{\text{molar mass}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Number of moles} = \frac{115 \text{ g}}{40.08 \text{ g/mol}} \approx 2.869
\][/tex]
3. Use Avogadro's Number to Find the Number of Atoms:
Avogadro's number is approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole. This is the number of atoms in one mole of any substance.
To find the number of atoms in 2.869 moles of calcium, we multiply the number of moles by Avogadro's number:
[tex]\[
\text{Number of atoms} = 2.869 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole}
\][/tex]
[tex]\[
\text{Number of atoms} \approx 1.727 \times 10^{24} \text{ atoms}
\][/tex]
Therefore, there are approximately [tex]\(1.727 \times 10^{24}\)[/tex] atoms in 115 grams of calcium.
1. Determine the Molar Mass of Calcium:
The molar mass of calcium is approximately 40.08 grams per mole. This means that each mole of calcium weighs 40.08 grams.
2. Calculate the Number of Moles:
To find the number of moles of calcium in 115 grams, we use the formula:
[tex]\[
\text{Number of moles} = \frac{\text{mass in grams}}{\text{molar mass}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Number of moles} = \frac{115 \text{ g}}{40.08 \text{ g/mol}} \approx 2.869
\][/tex]
3. Use Avogadro's Number to Find the Number of Atoms:
Avogadro's number is approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole. This is the number of atoms in one mole of any substance.
To find the number of atoms in 2.869 moles of calcium, we multiply the number of moles by Avogadro's number:
[tex]\[
\text{Number of atoms} = 2.869 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole}
\][/tex]
[tex]\[
\text{Number of atoms} \approx 1.727 \times 10^{24} \text{ atoms}
\][/tex]
Therefore, there are approximately [tex]\(1.727 \times 10^{24}\)[/tex] atoms in 115 grams of calcium.
