Question

how many moles of nickel (ni) atoms are in 48.5 g of ni?

how many moles of potassium (k) atoms are in 321 g of k?

how many moles of tin (sn) atoms are in 150.0 g of sn?

how many atoms are present in 15.00 g of sodium (na)?

how many atoms are present in 0.557 g of lead (pb)?

how many moles of lithium (li) atoms are in 8500 mg of li?

how many moles of boron (b) atoms are in 3400 kg of b?

Explanation:

Step1: Recall mole formula

The number of moles $n$ is calculated by $n = \frac{m}{M}$, where $m$ is mass, $M$ is molar mass. For atom count, use $N = n \times N_A$, $N_A = 6.022 \times 10^{23} \text{ atoms/mol}$.
---

Subquestion 1 (Ni):

Step1: Identify values

$m=48.5\ \text{g}$, $M_{\text{Ni}}=58.69\ \text{g/mol}$

Step2: Calculate moles

$n = \frac{48.5}{58.69}$
$n \approx 0.826\ \text{mol}$
---

Subquestion 2 (K):

Step1: Identify values

$m=321\ \text{g}$, $M_{\text{K}}=39.10\ \text{g/mol}$

Step2: Calculate moles

$n = \frac{321}{39.10}$
$n \approx 8.21\ \text{mol}$
---

Subquestion 3 (Sn):

Step1: Identify values

$m=150.0\ \text{g}$, $M_{\text{Sn}}=118.71\ \text{g/mol}$

Step2: Calculate moles

$n = \frac{150.0}{118.71}$
$n \approx 1.263\ \text{mol}$
---

Subquestion 4 (Na atoms):

Step1: Identify values

$m=15.00\ \text{g}$, $M_{\text{Na}}=22.99\ \text{g/mol}$

Step2: Calculate moles first

$n = \frac{15.00}{22.99} \approx 0.6525\ \text{mol}$

Step3: Calculate atom count

$N = 0.6525 \times 6.022 \times 10^{23}$
$N \approx 3.93 \times 10^{23}\ \text{atoms}$
---

Subquestion 5 (Pb atoms):

Step1: Identify values

$m=0.557\ \text{g}$, $M_{\text{Pb}}=207.2\ \text{g/mol}$

Step2: Calculate moles first

$n = \frac{0.557}{207.2} \approx 0.002688\ \text{mol}$

Step3: Calculate atom count

$N = 0.002688 \times 6.022 \times 10^{23}$
$N \approx 1.62 \times 10^{21}\ \text{atoms}$
---

Subquestion 6 (Li):

Step1: Convert mass to grams

$m=8500\ \text{mg} = 8.5\ \text{g}$, $M_{\text{Li}}=6.94\ \text{g/mol}$

Step2: Calculate moles

$n = \frac{8.5}{6.94}$
$n \approx 1.22\ \text{mol}$
---

Subquestion 7 (B):

Step1: Convert mass to grams

$m=3400\ \text{kg} = 3.4 \times 10^6\ \text{g}$, $M_{\text{B}}=10.81\ \text{g/mol}$

Step2: Calculate moles

$n = \frac{3.4 \times 10^6}{10.81}$
$n \approx 3.15 \times 10^5\ \text{mol}$

Answer:

1. $0.826\ \text{mol}$
2. $8.21\ \text{mol}$
3. $1.263\ \text{mol}$
4. $3.93 \times 10^{23}\ \text{atoms}$
5. $1.62 \times 10^{21}\ \text{atoms}$
6. $1.22\ \text{mol}$
7. $3.15 \times 10^5\ \text{mol}$