Question

determine the number of atoms in each of the following samples:

1. 62.1 g titanium, ti \boxed{} atoms
2. 9.24 g neon, ne \boxed{} atoms
3. 879 g lead, pb \boxed{} atoms

Explanation:

To determine the number of atoms in each sample, we use the following steps:

Step 1: Recall the formula for moles and Avogadro’s number

The number of moles (\(n\)) of a substance is given by \( n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).
The number of atoms is then \( \text{Number of atoms} = n \times N_A \), where \( N_A = 6.022 \times 10^{23} \, \text{atoms/mol} \) (Avogadro’s number).

1. 62.1 g titanium (Ti)

• Molar mass of Ti: \( 47.87 \, \text{g/mol} \) (from periodic table).

Step 1: Calculate moles of Ti

\( n_{\text{Ti}} = \frac{62.1 \, \text{g}}{47.87 \, \text{g/mol}} \approx 1.297 \, \text{mol} \)

Step 2: Calculate number of Ti atoms

\( \text{Atoms of Ti} = 1.297 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 7.81 \times 10^{23} \, \text{atoms} \)

2. 9.24 g neon (Ne)

• Molar mass of Ne: \( 20.18 \, \text{g/mol} \) (from periodic table).

Step 1: Calculate moles of Ne

\( n_{\text{Ne}} = \frac{9.24 \, \text{g}}{20.18 \, \text{g/mol}} \approx 0.4579 \, \text{mol} \)

Step 2: Calculate number of Ne atoms

\( \text{Atoms of Ne} = 0.4579 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 2.76 \times 10^{23} \, \text{atoms} \)

3. 879 g lead (Pb)

• Molar mass of Pb: \( 207.2 \, \text{g/mol} \) (from periodic table).

Step 1: Calculate moles of Pb

\( n_{\text{Pb}} = \frac{879 \, \text{g}}{207.2 \, \text{g/mol}} \approx 4.242 \, \text{mol} \)

Step 2: Calculate number of Pb atoms

\( \text{Atoms of Pb} = 4.242 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 2.55 \times 10^{24} \, \text{atoms} \)

Answer:

s:

1. \( \boldsymbol{7.81 \times 10^{23}} \) atoms of Ti
2. \( \boldsymbol{2.76 \times 10^{23}} \) atoms of Ne
3. \( \boldsymbol{2.55 \times 10^{24}} \) atoms of Pb