Question

Question 12 (3 points)
A sample of propanoic acid, CH3 - CH2 -COOH, 2.80 x 1023 carbon atoms. How many moles of propanoic acid are in the sample?

Question 12 options:

a) 4.65 x 1022 moles


b) 9.3x 1022 moles


c) 1.5x 10-1 moles


d) 9.3x 1023 moles

Answer 1

To find the number of moles of propanoic acid (C3H6O2) from the given number of carbon atoms, we can follow these steps:

1. Determine how many carbon atoms are in one molecule of propanoic acid. Propanoic acid has 3 carbon atoms (C3) per molecule.

2. Use Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mole) to relate the number of molecules to moles.

3. 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**.