Question

conversions with avogadros number($n_a$) and molar mass
how many atoms are in 2.50 moles of silicon (si)?

how many atoms are in 2.50 moles of iron (fe)?

how many atoms are in 14.8 moles of copper (cu)?

how many moles of silver (ag) are in $9.75 \times 10^{25}$ atoms of ag?

how many moles of magnesium (mg) contain $5.00 \times 10^{21}$ mg atoms?

what mass of manganese (mn) is in 0.750 moles of mn?

what mass of cobalt (co) is in 0.0804 moles of co?

Explanation:

Step1: Relate moles to atoms

Use Avogadro's number $N_A = 6.022 \times 10^{23}\ \text{atoms/mol}$.
Formula: $\text{Number of atoms} = n \times N_A$

For 2.50 mol Si:

$\text{Atoms of Si} = 2.50\ \text{mol} \times 6.022 \times 10^{23}\ \text{atoms/mol} = 1.5055 \times 10^{24}\ \text{atoms}$

For 2.50 mol Fe:

$\text{Atoms of Fe} = 2.50\ \text{mol} \times 6.022 \times 10^{23}\ \text{atoms/mol} = 1.5055 \times 10^{24}\ \text{atoms}$

For 14.8 mol Cu:

$\text{Atoms of Cu} = 14.8\ \text{mol} \times 6.022 \times 10^{23}\ \text{atoms/mol} = 8.91256 \times 10^{24}\ \text{atoms}$

Step2: Relate atoms to moles

Formula: $n = \frac{\text{Number of atoms}}{N_A}$

For $9.75 \times 10^{26}$ Ag atoms:

$n_{\text{Ag}} = \frac{9.75 \times 10^{26}\ \text{atoms}}{6.022 \times 10^{23}\ \text{atoms/mol}} \approx 1.62 \times 10^{3}\ \text{mol}$

For $5.00 \times 10^{21}$ Mg atoms:

$n_{\text{Mg}} = \frac{5.00 \times 10^{21}\ \text{atoms}}{6.022 \times 10^{23}\ \text{atoms/mol}} \approx 0.00830\ \text{mol}$

Step3: Relate moles to mass

Use molar mass $M$: $\text{Mass} = n \times M$

For 0.750 mol Mn ($M_{\text{Mn}} = 54.94\ \text{g/mol}$):

$\text{Mass of Mn} = 0.750\ \text{mol} \times 54.94\ \text{g/mol} = 41.205\ \text{g}$

For 0.0804 mol Co ($M_{\text{Co}} = 58.93\ \text{g/mol}$):

$\text{Mass of Co} = 0.0804\ \text{mol} \times 58.93\ \text{g/mol} \approx 4.74\ \text{g}$

Answer:

1. Atoms in 2.50 mol Si: $1.51 \times 10^{24}$ atoms
2. Atoms in 2.50 mol Fe: $1.51 \times 10^{24}$ atoms
3. Atoms in 14.8 mol Cu: $8.91 \times 10^{24}$ atoms
4. Moles of Ag: $1.62 \times 10^{3}$ mol
5. Moles of Mg: $0.00830$ mol
6. Mass of Mn: $41.2$ g
7. Mass of Co: $4.74$ g