A sample of an alcohol is tested and found to contain 52% carbon, 35% oxygen, and 13% hydrogen by mass. Tests indicate that the molecular weight of the molecule is between 30 and 80. What is the molecular formula of the alcohol?

After I did everything, I got the empirical formula to be C2 H5.8 O?

To determine the molecular formula of the alcohol, we need to find the empirical formula first. The empirical formula gives the simplest whole number ratio of atoms in a compound.

First, assume we have 100 grams of the alcohol. Then we can calculate the masses of carbon, oxygen, and hydrogen in the sample:

Carbon: 52% of 100g = 52g
Oxygen: 35% of 100g = 35g
Hydrogen: 13% of 100g = 13g

Next, we need to convert the masses to moles using the atomic masses:

Carbon: 52g / (12 g/mol) = 4.33 mol
Oxygen: 35g / (16 g/mol) = 2.19 mol
Hydrogen: 13g / (1 g/mol) = 13 mol

Now, we need to find the lowest whole number ratio of these atoms. Dividing the number of moles by the smallest number of moles (2.19) gives us:

Carbon: 4.33 mol / 2.19 mol = 1.98 ≈ 2
Oxygen: 2.19 mol / 2.19 mol = 1
Hydrogen: 13 mol / 2.19 mol = 5.94 ≈ 6

The empirical formula is C2H6O.

Since the given range for the molecular weight is between 30 and 80, we can calculate the molecular weight of the empirical formula:

(2 x atomic mass of carbon) + (6 x atomic mass of hydrogen) + atomic mass of oxygen
(2 x 12 g/mol) + (6 x 1 g/mol) + 16 g/mol = 46 g/mol

The molecular weight of the empirical formula is 46 g/mol, which falls within the given range.

Therefore, the molecular formula of the alcohol is C2H6O.

To determine the molecular formula of the alcohol, we need to find the empirical formula and the molecular weight.

Let's assume we have 100 grams of the sample. From the given percentages, we can find the masses of carbon, oxygen, and hydrogen in the sample:

- Mass of carbon = 52% of 100 grams = 52 grams
- Mass of oxygen = 35% of 100 grams = 35 grams
- Mass of hydrogen = 13% of 100 grams = 13 grams

Next, we need to find the number of moles of each element. To do this, we divide the mass of each element by its molar mass:

- Moles of carbon = Mass of carbon / molar mass of carbon
- Moles of oxygen = Mass of oxygen / molar mass of oxygen
- Moles of hydrogen = Mass of hydrogen / molar mass of hydrogen

From the periodic table, we find the molar masses:

- Molar mass of carbon = 12 g/mol
- Molar mass of oxygen = 16 g/mol
- Molar mass of hydrogen = 1 g/mol

Substituting the given values:

- Moles of carbon = 52 grams / 12 g/mol = 4.33 moles
- Moles of oxygen = 35 grams / 16 g/mol = 2.19 moles
- Moles of hydrogen = 13 grams / 1 g/mol = 13 moles

To find the empirical formula, we need to determine the ratio of the moles of each element. We divide all the moles by the smallest number of moles (in this case, oxygen):

- Moles of carbon (C) = 4.33 / 2.19 = 1.98 (approximately 2)
- Moles of oxygen (O) = 2.19 / 2.19 = 1
- Moles of hydrogen (H) = 13 / 2.19 = 5.94 (approximately 6)

Now we have the mole ratios: C2O1H6

To find the molecular formula, we need to know the molecular weight. The given information states that the molecular weight is between 30 and 80.

Using the empirical formula, we can calculate the molecular weight by summing up the atomic weights:

- Molecular weight = (2 * atomic weight of carbon) + atomic weight of oxygen + (6 * atomic weight of hydrogen)
- Molecular weight = (2 * 12 g/mol) + 16 g/mol + (6 * 1 g/mol)
- Molecular weight = 24 g/mol + 16 g/mol + 6 g/mol
- Molecular weight = 46 g/mol

Since the molecular weight falls within the given range of 30 and 80, the empirical formula C2O1H6 is already the molecular formula for the alcohol.

You should have obtained C2H6O (my numbers were 1.98 for C which rounds to 2, 5.94 for H which rounds to 6, and O.

empirical formula mass is 46
46 is between 30 and 80. Twice that (C2H6O)2 would have a molar mass of 46*2 = 92 and that's out of the range. So the empirical and molecular formulae are the same.