Question
How many grams of butyric acid contain 3.28 x 10^23 atoms of oxygen?
Answers
GPT-4o mini
To determine how many grams of butyric acid contain \(3.28 \times 10^{23}\) atoms of oxygen, we first need to analyze the molecular formula of butyric acid, which is \(C_4H_8O_2\).
1. **Identify the number of oxygen atoms in butyric acid**:
The formula tells us that each molecule of butyric acid contains 2 oxygen atoms.
2. **Calculate the number of moles of butyric acid that contain \(3.28 \times 10^{23}\) oxygen atoms**:
Since there are 2 oxygen atoms per molecule of butyric acid, the number of molecules of butyric acid that contains \(3.28 \times 10^{23}\) oxygen atoms can be calculated as follows:
\[
\text{Number of molecules of} \ C_4H_8O_2 = \frac{3.28 \times 10^{23} \ \text{atoms of O}}{2 \ \text{atoms of O per molecule}} = 1.64 \times 10^{23} \ \text{molecules of} \ C_4H_8O_2
\]
3. **Calculate the number of moles of butyric acid**:
To find the number of moles of butyric acid, we use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules/mol:
\[
\text{Number of moles of} \ C_4H_8O_2 = \frac{1.64 \times 10^{23}}{6.022 \times 10^{23}} \approx 0.273 \ \text{moles}
\]
4. **Calculate the molar mass of butyric acid**:
The molar mass of butyric acid (\(C_4H_8O_2\)) can be calculated by adding the atomic masses of its constituent elements:
- Carbon (C): \(4 \times 12.01 \, \text{g/mol} = 48.04 \, \text{g/mol}\)
- Hydrogen (H): \(8 \times 1.01 \, \text{g/mol} = 8.08 \, \text{g/mol}\)
- Oxygen (O): \(2 \times 16.00 \, \text{g/mol} = 32.00 \, \text{g/mol}\)
Adding these together:
\[
\text{Molar mass of} \ C_4H_8O_2 = 48.04 + 8.08 + 32.00 = 88.12 \ \text{g/mol}
\]
5. **Calculate the mass of butyric acid**:
Finally, to find the mass of \(0.273\) moles of butyric acid, we multiply the number of moles by the molar mass:
\[
\text{Mass of butyric acid} = 0.273 \ \text{moles} \times 88.12 \ \text{g/mol} \approx 24.06 \ \text{g}
\]
Therefore, the mass of butyric acid that contains \(3.28 \times 10^{23}\) atoms of oxygen is approximately **24.06 grams**.
1. **Identify the number of oxygen atoms in butyric acid**:
The formula tells us that each molecule of butyric acid contains 2 oxygen atoms.
2. **Calculate the number of moles of butyric acid that contain \(3.28 \times 10^{23}\) oxygen atoms**:
Since there are 2 oxygen atoms per molecule of butyric acid, the number of molecules of butyric acid that contains \(3.28 \times 10^{23}\) oxygen atoms can be calculated as follows:
\[
\text{Number of molecules of} \ C_4H_8O_2 = \frac{3.28 \times 10^{23} \ \text{atoms of O}}{2 \ \text{atoms of O per molecule}} = 1.64 \times 10^{23} \ \text{molecules of} \ C_4H_8O_2
\]
3. **Calculate the number of moles of butyric acid**:
To find the number of moles of butyric acid, we use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules/mol:
\[
\text{Number of moles of} \ C_4H_8O_2 = \frac{1.64 \times 10^{23}}{6.022 \times 10^{23}} \approx 0.273 \ \text{moles}
\]
4. **Calculate the molar mass of butyric acid**:
The molar mass of butyric acid (\(C_4H_8O_2\)) can be calculated by adding the atomic masses of its constituent elements:
- Carbon (C): \(4 \times 12.01 \, \text{g/mol} = 48.04 \, \text{g/mol}\)
- Hydrogen (H): \(8 \times 1.01 \, \text{g/mol} = 8.08 \, \text{g/mol}\)
- Oxygen (O): \(2 \times 16.00 \, \text{g/mol} = 32.00 \, \text{g/mol}\)
Adding these together:
\[
\text{Molar mass of} \ C_4H_8O_2 = 48.04 + 8.08 + 32.00 = 88.12 \ \text{g/mol}
\]
5. **Calculate the mass of butyric acid**:
Finally, to find the mass of \(0.273\) moles of butyric acid, we multiply the number of moles by the molar mass:
\[
\text{Mass of butyric acid} = 0.273 \ \text{moles} \times 88.12 \ \text{g/mol} \approx 24.06 \ \text{g}
\]
Therefore, the mass of butyric acid that contains \(3.28 \times 10^{23}\) atoms of oxygen is approximately **24.06 grams**.