Answer :
To find out how many atoms are in 195 grams of calcium, we can follow these steps:
1. Determine the Molar Mass of Calcium:
- The molar mass of calcium is 40.08 grams per mole. This means that one mole of calcium weighs 40.08 grams.
2. Calculate the Number of Moles of Calcium:
- We are given 195 grams of calcium. To find out how many moles of calcium this is, divide the mass of calcium by its molar mass:
[tex]\[
\text{Number of moles} = \frac{195 \, \text{g}}{40.08 \, \text{g/mole}} \approx 4.87 \, \text{moles}
\][/tex]
3. Use Avogadro's Number to Find the Number of Atoms:
- Avogadro's number tells us that there are approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms in one mole of any substance.
- To find the total number of atoms in 195 grams of calcium, multiply the number of moles by Avogadro's number:
[tex]\[
\text{Number of atoms} = 4.87 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \approx 2.93 \times 10^{24} \, \text{atoms}
\][/tex]
Thus, there are approximately [tex]\(2.93 \times 10^{24}\)[/tex] atoms in 195 grams of calcium.
1. Determine the Molar Mass of Calcium:
- The molar mass of calcium is 40.08 grams per mole. This means that one mole of calcium weighs 40.08 grams.
2. Calculate the Number of Moles of Calcium:
- We are given 195 grams of calcium. To find out how many moles of calcium this is, divide the mass of calcium by its molar mass:
[tex]\[
\text{Number of moles} = \frac{195 \, \text{g}}{40.08 \, \text{g/mole}} \approx 4.87 \, \text{moles}
\][/tex]
3. Use Avogadro's Number to Find the Number of Atoms:
- Avogadro's number tells us that there are approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms in one mole of any substance.
- To find the total number of atoms in 195 grams of calcium, multiply the number of moles by Avogadro's number:
[tex]\[
\text{Number of atoms} = 4.87 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \approx 2.93 \times 10^{24} \, \text{atoms}
\][/tex]
Thus, there are approximately [tex]\(2.93 \times 10^{24}\)[/tex] atoms in 195 grams of calcium.
