Respuesta :
To determine the number of carbon atoms present in a sample of \( \text{C}_3\text{H}_8 \) with a mass of 5.01 grams, we need to use the molar mass of \( \text{C}_3\text{H}_8 \) to calculate the number of moles of the compound present, and then use Avogadro's number to convert moles to the number of atoms.
First, let's calculate the molar mass of \( \text{C}_3\text{H}_8 \):
\[
\text{Molar mass of } \text{C}_3\text{H}_8 = (3 \times \text{molar mass of C}) + (8 \times \text{molar mass of H})
\]
The molar mass of carbon (C) is approximately 12.01 g/mol, and the molar mass of hydrogen (H) is approximately 1.008 g/mol.
\[
\text{Molar mass of } \text{C}_3\text{H}_8 = (3 \times 12.01 \, \text{g/mol}) + (8 \times 1.008 \, \text{g/mol})
\]
\[
= (36.03 \, \text{g/mol}) + (8.064 \, \text{g/mol})
\]
\[
= 44.094 \, \text{g/mol}
\]
Now, we can calculate the number of moles of \( \text{C}_3\text{H}_8 \) in the sample:
\[
\text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{5.01 \, \text{g}}{44.094 \, \text{g/mol}}
\]
\[
\approx 0.1137 \, \text{moles}
\]
Finally, we'll use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles/mol, to convert moles to the number of carbon atoms:
\[
\text{Number of carbon atoms} = (\text{Number of moles}) \times (\text{Avogadro's number})
\]
\[
= 0.1137 \, \text{moles} \times (6.022 \times 10^{23} \, \text{atoms/mol})
\]
\[
\approx 6.84 \times 10^{22} \, \text{carbon atoms}
\]
So, there are approximately \(6.84 \times 10^{22}\) carbon atoms present in the sample of \( \text{C}_3\text{H}_8 \) with a mass of 5.01 grams.
First, let's calculate the molar mass of \( \text{C}_3\text{H}_8 \):
\[
\text{Molar mass of } \text{C}_3\text{H}_8 = (3 \times \text{molar mass of C}) + (8 \times \text{molar mass of H})
\]
The molar mass of carbon (C) is approximately 12.01 g/mol, and the molar mass of hydrogen (H) is approximately 1.008 g/mol.
\[
\text{Molar mass of } \text{C}_3\text{H}_8 = (3 \times 12.01 \, \text{g/mol}) + (8 \times 1.008 \, \text{g/mol})
\]
\[
= (36.03 \, \text{g/mol}) + (8.064 \, \text{g/mol})
\]
\[
= 44.094 \, \text{g/mol}
\]
Now, we can calculate the number of moles of \( \text{C}_3\text{H}_8 \) in the sample:
\[
\text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{5.01 \, \text{g}}{44.094 \, \text{g/mol}}
\]
\[
\approx 0.1137 \, \text{moles}
\]
Finally, we'll use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles/mol, to convert moles to the number of carbon atoms:
\[
\text{Number of carbon atoms} = (\text{Number of moles}) \times (\text{Avogadro's number})
\]
\[
= 0.1137 \, \text{moles} \times (6.022 \times 10^{23} \, \text{atoms/mol})
\]
\[
\approx 6.84 \times 10^{22} \, \text{carbon atoms}
\]
So, there are approximately \(6.84 \times 10^{22}\) carbon atoms present in the sample of \( \text{C}_3\text{H}_8 \) with a mass of 5.01 grams.
