Question

Use the table of molar masses to answer the question.

Element Molar Mass (g/mol)
carbon 12.01
oxygen 16.00
How many molecules of carbon dioxide (CO2
) are there in a 17-gram sample?

(1 point)
Responses

4.505×1023
4 point 5 0 5 times 10 to the 23th power

2.326×1023
2 point 3 2 6 times 10 to the 23th power

6.022×1023
6 point 0 2 2 times 10 to the 23th power

1.024×1023

Answer 1

To calculate the number of molecules of carbon dioxide (CO₂) in a 17-gram sample, we first need to determine the molar mass of CO₂.

The molar mass of CO₂ can be calculated as follows:

- Molar mass of carbon (C) = 12.01 g/mol
- Molar mass of oxygen (O) = 16.00 g/mol

Since CO₂ consists of one carbon atom and two oxygen atoms, its molar mass is:

\[
\text{Molar mass of CO₂} = 1 \times 12.01 \, \text{g/mol} + 2 \times 16.00 \, \text{g/mol}
\]
\[
= 12.01 \, \text{g/mol} + 32.00 \, \text{g/mol}
\]
\[
= 44.01 \, \text{g/mol}
\]

Next, we need to calculate the number of moles of CO₂ in a 17-gram sample:

\[
\text{Number of moles of CO₂} = \frac{\text{mass of CO₂}}{\text{molar mass of CO₂}} = \frac{17 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.3865 \, \text{mol}
\]

Now, using Avogadro's number (approximately \( 6.022 \times 10^{23} \) molecules/mol), we can calculate the number of molecules:

\[
\text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number}
\]
\[
= 0.3865 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 2.33 \times 10^{23} \, \text{molecules}
\]

Thus, the number of molecules of carbon dioxide in a 17-gram sample is approximately:

\[
\boxed{2.326 \times 10^{23}}
\]