Question

1. how many atoms are in 3.00 moles of helium (he)?a. $6.02 \times 10^{23}$b. $1.81 \times 10^{24}$c. $3.00 \times 10^{23}$d. $9.03 \times 10^{23}$8. how many moles are in $1.20 \times 10^{24}$ molecules of $nh_3$?a. 0.20 molb. 2.00 molc. 12.0 mold. 0.50 mol9. how many moles are present in $6.02 \times 10^{22}$ atoms of sodium (na)?a. 0.01 molb. 0.10 molc. 1.00 mold. 10.0 mol10. what is the molar mass of calcium carbonate ($caco_3$)?a. 60 g/molb. 100 g/molc. 40 g/mold. 120 g/mol11. how many moles are in 50.0 g of $caco_3$?a. 0.25 molb. 0.50 molc. 1.00 mold. 2.00 mol

Explanation:

Step1: Use Avogadro's number for He

Number of atoms = Moles × Avogadro's number
$\text{Atoms} = 3.00\ \text{mol} \times 6.02 \times 10^{23}\ \text{atoms/mol}$

Step2: Calculate He atom count

$3.00 \times 6.02 \times 10^{23} = 1.806 \times 10^{24} \approx 1.81 \times 10^{24}$

Step3: Moles from $NH_3$ molecules

Moles = $\frac{\text{Number of molecules}}{\text{Avogadro's number}}$
$\text{Moles} = \frac{1.20 \times 10^{24}}{6.02 \times 10^{23}\ \text{molecules/mol}}$

Step4: Calculate $NH_3$ moles

$\frac{1.20 \times 10^{24}}{6.02 \times 10^{23}} \approx 2.00\ \text{mol}$

Step5: Moles from Na atoms

Moles = $\frac{\text{Number of atoms}}{\text{Avogadro's number}}$
$\text{Moles} = \frac{6.02 \times 10^{22}}{6.02 \times 10^{23}\ \text{atoms/mol}}$

Step6: Calculate Na moles

$\frac{6.02 \times 10^{22}}{6.02 \times 10^{23}} = 0.10\ \text{mol}$

Step7: Sum atomic masses for $CaCO_3$

Molar mass = $M_{Ca} + M_{C} + 3 \times M_{O}$
$\text{Molar mass} = 40\ \text{g/mol} + 12\ \text{g/mol} + 3 \times 16\ \text{g/mol}$

Step8: Calculate $CaCO_3$ molar mass

$40 + 12 + 48 = 100\ \text{g/mol}$

Step9: Moles from $CaCO_3$ mass

Moles = $\frac{\text{Mass}}{\text{Molar mass}}$
$\text{Moles} = \frac{50.0\ \text{g}}{100\ \text{g/mol}}$

Step10: Calculate $CaCO_3$ moles

$\frac{50.0}{100} = 0.50\ \text{mol}$

Answer:

1. B. $1.81 \times 10^{24}$
2. B. 2.00 mol
3. B. 0.10 mol
4. B. 100 g/mol
5. B. 0.50 mol