To find the total number of atoms in 3.00 g of CaCl[tex]\(_2\)[/tex], we need to follow these steps:
1. Determine the molar mass of CaCl[tex]\(_2\)[/tex]:
- The molar mass of calcium (Ca) is [tex]\(40.08 \text{ g/mol}\)[/tex].
- The molar mass of chlorine (Cl) is [tex]\(35.453 \text{ g/mol}\)[/tex].
- Since there are two chlorine atoms in CaCl[tex]\(_2\)[/tex], the total molar mass for chlorine is [tex]\(35.453 \times 2 = 70.906 \text{ g/mol}\)[/tex].
- Adding these together, the molar mass of CaCl[tex]\(_2\)[/tex] is:
[tex]\[
40.08 \text{ g/mol} + 70.906 \text{ g/mol} = 110.986 \text{ g/mol}
\][/tex]
2. Calculate the moles of CaCl[tex]\(_2\)[/tex]:
- Using the given mass of CaCl[tex]\(_2\)[/tex] which is 3.00 g:
- Moles of CaCl[tex]\(_2\)[/tex] is calculated by dividing the mass by the molar mass:
[tex]\[
\text{Moles of CaCl\(_2\)} = \frac{3.00 \text{ g}}{110.986 \text{ g/mol}} = 0.027030436271241416 \text{ mol}
\][/tex]
3. Determine the number of moles of atoms in one mole of CaCl[tex]\(_2\)[/tex]:
- Each molecule of CaCl[tex]\(_2\)[/tex] contains 1 atom of calcium and 2 atoms of chlorine, for a total of 3 atoms:
[tex]\[
1 \text{ (Ca atom)} + 2 \text{ (Cl atoms)} = 3 \text{ atoms}
\][/tex]
4. Use Avogadro's number to convert moles to atoms:
- Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole.
- The total number of atoms can be calculated by multiplying the moles of CaCl[tex]\(_2\)[/tex] by the number of atoms per molecule and then by Avogadro's number:
[tex]\[
\text{Total number of atoms} = 0.027030436271241416 \text{ mol} \times 3 \text{ atoms/molecule} \times 6.022 \times 10^{23} \text{ atoms/mol}
= 4.8833186167624745 \times 10^{22} \text{ atoms}
\][/tex]
So, in 3.00 g of CaCl[tex]\(_2\)[/tex], there are approximately [tex]\(4.88 \times 10^{22}\)[/tex] atoms.
