A compound containing only C, H, and O was extracted from the bark of the sassafras tree. The combustion of 36.3mg produced 98.6 of CO2 and 20.2mg of H2O. The molar mass of the compound was 162 g/mol. Determine its empirical and molecular formulas
Convert 98.6 mg CO2 to mg C.
Convert 20.1 g H2O to mg H (not H2).
Then mg C + mg H + mg O = 36.3 mg an solve for mg O (not O2).
Now convert mg to moles of the three elements.
moles = g/molar mass
Find the ratio of the elements to each other with the smallest number being 1.00. The easy way to do that is to divide the smallest number by itself. That assures you of getting 1.00 for that element. Then divide all of the other numbers by the same small number.
Post your work if you get stuck.
To determine the empirical and molecular formulas of the compound, we need to first find the empirical formula. The empirical formula gives the simplest whole-number ratio of atoms in a compound.
1. Calculate the number of moles of CO2 produced:
- The molar mass of CO2 is 44.01 g/mol.
- To find the number of moles, divide the mass of CO2 produced (98.6 g) by its molar mass:
moles of CO2 = 98.6 g / 44.01 g/mol = 2.24 mol
2. Calculate the number of moles of H2O produced:
- The molar mass of H2O is 18.02 g/mol.
- To find the number of moles, divide the mass of H2O produced (20.2 g) by its molar mass:
moles of H2O = 20.2 g / 18.02 g/mol = 1.12 mol
3. Determine the ratio of carbon atoms to oxygen atoms in the compound:
- Since the CO2 produced contains 2.24 mol of CO2 and each CO2 molecule has one carbon atom, multiply the number of moles of CO2 by the carbon-to-CO2 ratio:
carbon atoms = 2.24 mol CO2 × 1 mol C/1 mol CO2 = 2.24 mol C
- Since each CO2 molecule contains two oxygen atoms, multiply the number of moles of CO2 by the oxygen-to-CO2 ratio:
oxygen atoms = 2.24 mol CO2 × 2 mol O/1 mol CO2 = 4.48 mol O
4. Determine the ratio of hydrogen atoms to oxygen atoms in the compound:
- Since the H2O produced contains 1.12 mol of H2O and each H2O molecule has two hydrogen atoms, multiply the number of moles of H2O by the hydrogen-to-H2O ratio:
hydrogen atoms = 1.12 mol H2O × 2 mol H/1 mol H2O = 2.24 mol H
- Since each H2O molecule contains one oxygen atom, multiply the number of moles of H2O by the oxygen-to-H2O ratio:
oxygen atoms = 1.12 mol H2O × 1 mol O/1 mol H2O = 1.12 mol O
5. Divide the number of atoms by the smallest number of atoms to obtain the simplest whole-number ratio:
- The smallest number of atoms is 1.12 mol O, so divide the number of atoms by 1.12 mol O:
carbon atoms / 1.12 mol O = 2.24 mol C / 1.12 mol O = 2
hydrogen atoms / 1.12 mol O = 2.24 mol H / 1.12 mol O = 2
oxygen atoms / 1.12 mol O = 1.12 mol O / 1.12 mol O = 1
The empirical formula of the compound is C2H2O.
To determine the molecular formula, we need to know the molar mass of the compound. In this case, the molar mass is 162 g/mol.
6. Calculate the empirical formula mass:
- The empirical formula contains 2 carbon atoms (12.01 g/mol each) + 2 hydrogen atoms (1.01 g/mol each) + 1 oxygen atom (16.00 g/mol) = 42.04 g/mol
7. Determine the multiple of the empirical formula that equals the molar mass:
- Divide the molar mass of the compound (162 g/mol) by the empirical formula mass (42.04 g/mol):
Multiple = 162 g/mol / 42.04 g/mol ≈ 3.85
8. Round the multiple to the nearest whole number to obtain the subscripts in the molecular formula:
- The empirical formula C2H2O multiplied by 3.85 becomes C7.7H7.7O3.85
- Round the subscripts to the nearest whole number:
C8H8O4
The molecular formula of the compound is C8H8O4.
To find the empirical formula, we need to determine the ratio of carbon, hydrogen, and oxygen in the compound based on the given information.
First, let's find the moles of CO2 produced:
Molar mass of CO2 = 12.01 g/mol (C) + 2 * 16.00 g/mol (O) = 44.01 g/mol
Moles of CO2 = 98.6 g / 44.01 g/mol = 2.240 mol
Next, let's find the moles of H2O produced:
Molar mass of H2O = 2 * 1.01 g/mol (H) + 16.00 g/mol (O) = 18.02 g/mol
Moles of H2O = 20.2 g / 18.02 g/mol = 1.122 mol
From the combustion, we can see that the mole ratio of CO2 to H2O is approximately 2:1.
Now, let's determine the moles of carbon (C), hydrogen (H), and oxygen (O) in the compound.
Moles of C = 2.240 mol
Moles of H = 2 * 1.122 mol = 2.244 mol
Moles of O = 2.240 mol - 1.122 mol = 1.118 mol
We need to convert the moles to whole numbers by dividing by the smallest number of moles, which is 1.118 mol.
Moles of C = 2.240 mol / 1.118 mol ≈ 2
Moles of H = 2.244 mol / 1.118 mol ≈ 2
Moles of O = 1.118 mol / 1.118 mol = 1
Therefore, the empirical formula of the compound is C2H2O.
To find the molecular formula, we need to determine the molar mass of the empirical formula and compare it to the given molar mass (162 g/mol).
Molar mass of C2H2O = (2 * 12.01 g/mol) + (2 * 1.01 g/mol) + 16.00 g/mol = 42.03 g/mol
To find the ratio of the molecular formula to the empirical formula, divide the given molar mass by the molar mass of the empirical formula.
Ratio = 162 g/mol / 42.03 g/mol ≈ 3.85
Round this ratio to the nearest whole number, which is 4.
Multiply the subscripts in the empirical formula by this whole number to get the molecular formula.
Molecular formula = C2H2O * 4 = C8H8O4
Therefore, the molecular formula of the compound is C8H8O4.