How many grams of butyric acid contain 3.28 x 1023 atoms of oxygen?
Express your answer to three significant figures and include the appropriate units.
To determine the amount of butyric acid that contains 3.28 x 10^23 atoms of oxygen, we need to use the conversion factor between the two.
1 mole of butyric acid (C4H8O2) contains 2 moles of oxygen atoms (O).
The molar mass of butyric acid is:
(4*12.01 g/mol) + (8*1.01 g/mol) + (2*16.00 g/mol) = 88.11 g/mol
The molar mass of oxygen is 16.00 g/mol.
Therefore, 1 mole of butyric acid contains (2*16.00) = 32.00 grams of oxygen.
Using this information, we can set up the following conversion factor:
(32.00 g of O / 1 mol of butyric acid) x (1 mol of butyric acid / 6.022 x 10^23 atoms of O) = 5.31 x 10^-24 g of O per atom
To find the amount of butyric acid that contains 3.28 x 10^23 atoms of oxygen, we can use the inverse of this conversion factor:
(3.28 x 10^23 atoms of O) x (5.31 x 10^-24 g of O per atom) = 1.74 g of butyric acid
Therefore, 3.28 x 10^23 atoms of oxygen are contained in 1.74 grams (rounded to three significant figures) of butyric acid.
To determine the number of grams of butyric acid that contain a given number of atoms of oxygen, we need to use the molar mass of butyric acid and convert the number of oxygen atoms into moles.
1. Find the molar mass of butyric acid (C4H8O2):
- Carbon (C) has a molar mass of 12.01 g/mol.
- Hydrogen (H) has a molar mass of 1.01 g/mol.
- Oxygen (O) has a molar mass of 16.00 g/mol.
The molar mass of butyric acid is:
(4 * 12.01 g/mol) + (8 * 1.01 g/mol) + (2 * 16.00 g/mol) = 88.11 g/mol.
2. Convert the number of oxygen atoms to moles:
Given that there are 3.28 x 10^23 atoms of oxygen, we can use Avogadro's number to convert this to moles:
3.28 x 10^23 atoms * (1 mol/6.022 x 10^23 atoms) = 0.544 mol.
3. Convert moles of butyric acid to grams:
Multiply the number of moles by the molar mass of butyric acid:
0.544 mol * 88.11 g/mol = 47.6 g.
Therefore, 3.28 x 10^23 atoms of oxygen is equivalent to 47.6 grams of butyric acid.
To calculate the number of grams of butyric acid that contain a given number of oxygen atoms, we need to use the molar mass of butyric acid and Avogadro's number.
1. Start by finding the molar mass of butyric acid. Butyric acid has the chemical formula C4H8O2, so we need to calculate the sum of the atomic masses of carbon, hydrogen, and oxygen.
- The atomic mass of carbon (C) is approximately 12.01 grams/mol.
- The atomic mass of hydrogen (H) is approximately 1.01 grams/mol.
- The atomic mass of oxygen (O) is approximately 16.00 grams/mol.
We have four carbons, eight hydrogens, and two oxygens in butyric acid. Therefore, the molar mass of butyric acid is:
Molar mass of butyric acid = (4 * 12.01) + (8 * 1.01) + (2 * 16.00) = 88.11 grams/mol.
2. Next, we need to find the number of moles of oxygen atoms present in 3.28 x 10^23 oxygen atoms. To do this, divide the given number of atoms by Avogadro's number.
Number of moles of oxygen atoms = (3.28 x 10^23) / (6.022 x 10^23) = 0.544 moles.
3. Finally, use the molar mass of butyric acid and the number of moles of oxygen atoms to calculate the mass of butyric acid.
Mass of butyric acid = (Molar mass of butyric acid) * (Number of moles of oxygen atoms)
Mass of butyric acid = 88.11 grams/mol * 0.544 moles = 47.98 grams.
Therefore, 3.28 x 10^23 atoms of oxygen correspond to 47.98 grams of butyric acid (to three significant figures).
Answer: 47.98 grams