Question

calculate the mass, in grams, of 229.0 atoms of cadmium, cd. one mol of cd has a mass of 112.41 g.

Explanation:

Step1: Recall Avogadro's number

Avogadro's number is \( 6.022 \times 10^{23} \) atoms/mol. We need to find the number of moles of Cd from the number of atoms. The formula for moles (\( n \)) from atoms (\( N \)) is \( n=\frac{N}{N_A} \), where \( N_A \) is Avogadro's number.
So, \( n = \frac{229.0\ \text{atoms}}{6.022\times 10^{23}\ \text{atoms/mol}} \)

Step2: Calculate mass from moles

The mass (\( m \)) is given by \( m = n\times M \), where \( M \) is the molar mass (112.41 g/mol for Cd). Substitute \( n \) from Step 1 into this formula:
\( m=\frac{229.0\ \text{atoms}}{6.022\times 10^{23}\ \text{atoms/mol}}\times112.41\ \text{g/mol} \)
First, calculate \( \frac{229.0}{6.022\times 10^{23}} \approx 3.803\times 10^{-22}\ \text{mol} \)
Then, multiply by 112.41: \( 3.803\times 10^{-22}\ \text{mol}\times112.41\ \text{g/mol} \approx 4.275\times 10^{-20}\ \text{g} \)

Answer:

\( 4.275\times 10^{-20} \)