To find the number of moles of propanoic acid (C3H6O2) from the given number of carbon atoms, we can follow these steps:
-
Determine how many carbon atoms are in one molecule of propanoic acid. Propanoic acid has 3 carbon atoms (C3) per molecule.
-
Use Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mole) to relate the number of molecules to moles.
-
Calculate the total number of molecules in the sample based on the number of carbon atoms.
Given:
- Total number of carbon atoms = \(2.80 \times 10^{23}\)
- Number of carbon atoms per molecule of propanoic acid = 3
We can calculate the number of molecules of propanoic acid in the sample:
\[ \text{Number of molecules of propanoic acid} = \frac{\text{Total carbon atoms}}{\text{Carbon atoms per molecule}} = \frac{2.80 \times 10^{23}}{3} \approx 9.33 \times 10^{22} \text{ molecules} \]
Next, we convert the number of molecules to moles:
\[ \text{Number of moles of propanoic acid} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} = \frac{9.33 \times 10^{22}}{6.022 \times 10^{23}} \approx 0.155 \text{ moles} \]
When we express this in scientific notation:
\[ 0.155 \text{ moles} = 1.55 \times 10^{-1} \text{ moles} \]
From the options provided, the closest answer is:
c) \(1.5 \times 10^{-1}\) moles.
1 answer