How many grams of butyric acid contain 3.28 x 10^23 atoms of oxygen?
Express your answer to three significant figures and include the appropriate units.
To determine the number of grams of butyric acid that contain 3.28 x 10^23 atoms of oxygen, we need to find the molar mass of butyric acid and convert the given number of atoms to moles and then to grams.
The molecular formula of butyric acid is C4H8O2.
First, let's find the molar mass of butyric acid:
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.008 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of butyric acid = (4 * Molar mass of C) + (8 * Molar mass of H) + (2 * Molar mass of O)
Molar mass of butyric acid = (4 * 12.01 g/mol) + (8 * 1.008 g/mol) + (2 * 16.00 g/mol)
Molar mass of butyric acid = 88.11 g/mol
Next, convert the given number of oxygen atoms to moles:
Number of moles of oxygen = (3.28 x 10^23 atoms) / (6.022 x 10^23 atoms/mol)
Number of moles of oxygen = 0.544 moles
Finally, convert the number of moles of oxygen to grams using the molar mass of butyric acid:
Mass of butyric acid = (0.544 moles) * (88.11 g/mol)
Mass of butyric acid = 47.94 g
Therefore, 3.28 x 10^23 atoms of oxygen are contained in approximately 47.9 grams of butyric acid.
To find the grams of butyric acid that contain 3.28 x 10^23 atoms of oxygen, we need to use the molar ratio between oxygen atoms and butyric acid.
The molar ratio is based on Avogadro's number, which states that 1 mole of any substance contains 6.022 x 10^23 particles (atoms, molecules, ions, etc.).
First, we need to determine the molar mass of butyric acid (C4H8O2):
C = 4 x 12.01 g/mol = 48.04 g/mol
H = 8 x 1.01 g/mol = 8.08 g/mol
O = 2 x 16.00 g/mol = 32.00 g/mol
Total molar mass = 48.04 + 8.08 + 32.00 = 88.12 g/mol
Next, we calculate the number of moles of oxygen atoms:
Number of moles = 3.28 x 10^23 atoms / (6.022 x 10^23 atoms/mol)
Number of moles = 0.544 mol
Finally, we can determine the mass in grams of butyric acid:
Mass in grams = Number of moles × Molar mass
Mass in grams = 0.544 mol × 88.12 g/mol
Mass in grams = 47.98 g
Therefore, 3.28 x 10^23 atoms of oxygen correspond to 47.98 grams of butyric acid (to three significant figures)
To determine the number of grams of butyric acid that contain 3.28 x 10^23 atoms of oxygen, we can follow these steps:
1. Find the molar mass of butyric acid (C4H8O2).
- Carbon (C): Atomic mass = 12.01 g/mol
- Hydrogen (H): Atomic mass = 1.008 g/mol
- Oxygen (O): Atomic mass = 16.00 g/mol
- Molar mass of butyric acid = (4 * carbon) + (8 * hydrogen) + (2 * oxygen)
Molar mass of butyric acid = (4 * 12.01 g/mol) + (8 * 1.008 g/mol) + (2 * 16.00 g/mol)
Molar mass of butyric acid ≈ 88.11 g/mol
2. Determine the number of moles of oxygen atoms.
- Given: Number of atoms of oxygen = 3.28 x 10^23 atoms
- Avogadro's number: 1 mol = 6.022 x 10^23 atoms (approximately)
Number of moles of oxygen = (Number of atoms of oxygen) / Avogadro's number
Number of moles of oxygen ≈ (3.28 x 10^23 atoms) / (6.022 x 10^23 atoms/mol)
3. Calculate the mass of butyric acid.
- Using the molar mass of butyric acid from step 1 and the number of moles of oxygen from step 2:
Mass of butyric acid = (Number of moles of oxygen) * (Molar mass of butyric acid)
Now let's calculate the mass of butyric acid:
Mass of butyric acid ≈ (3.28 x 10^23 atoms) / (6.022 x 10^23 atoms/mol) * 88.11 g/mol
Mass of butyric acid ≈ 4.783 g (rounded to three significant figures)
Therefore, approximately 4.783 grams of butyric acid contains 3.28 x 10^23 atoms of oxygen.