To determine how many grams are in [tex]\(4.60 \times 10^{22}\)[/tex] formula units of potassium cyanide (KCN), follow these steps:
1. Find Avogadro’s Number:
- Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] formula units per mole. This is a known constant used to convert between the number of formula units and the number of moles.
2. Calculate the Molar Mass of KCN:
- Potassium (K) has an atomic mass of approximately 39.1 g/mol.
- Carbon (C) has an atomic mass of approximately 12.0 g/mol.
- Nitrogen (N) has an atomic mass of approximately 14.0 g/mol.
- Therefore, the molar mass of KCN is:
[tex]\[
39.1 \, \text{g/mol} + 12.0 \, \text{g/mol} + 14.0 \, \text{g/mol} = 65.1 \, \text{g/mol}
\][/tex]
3. Convert Formula Units to Moles:
- The given number of formula units is [tex]\(4.60 \times 10^{22}\)[/tex].
- To convert formula units to moles, use Avogadro's number:
[tex]\[
\text{Moles of KCN} = \frac{4.60 \times 10^{22} \, \text{formula units}}{6.022 \times 10^{23} \, \text{formula units/mol}}
\][/tex]
- Perform the division:
[tex]\[
\text{Moles of KCN} \approx 0.07643 \, \text{moles}
\][/tex]
4. Convert Moles to Grams:
- To find the mass in grams, multiply the moles of KCN by its molar mass:
[tex]\[
\text{Mass of KCN} = 0.07643 \, \text{moles} \times 65.1 \, \text{g/mol}
\][/tex]
- Perform the multiplication:
[tex]\[
\text{Mass of KCN} \approx 4.97 \, \text{grams}
\][/tex]
Therefore, there are approximately 4.97 grams in [tex]\(4.60 \times 10^{22}\)[/tex] formula units of potassium cyanide (KCN).
