A compound has the % composition by mass that is 87.8% C and 12.2 % H. What is the molecular formula if it has a molecular mass of 82 g/mol?
Take a 100 g sample for convience to give you 87.8 g C and 12.2 g H.
mols C = grams/atomic mass = ? 87.8/12 = about 7.3
mols H = grams/atomic mass = ? = 12.2/1 = 12.2
You want to find the ratio. The easy way to do that is to divide the smaller number by itself and the other number by the smaller number. This will give you a fraction but you want whole numbers. Multiply each of those fractions by whole number (i.e., 2,3,4, etc) until you get two whole numbers (or two numbers that can be rounded to whole numbers. Remember not to round anything larger than 0.1 or so). I get C3H5 but you should confirm that. That gives you the empirical formula. To find the molecular formula, do this,
empirical formula mass x factor(n) = 82 or
41 x factor(n) = 82.
factor(n) = ?
molecular formula = (C3H5)n
To determine the molecular formula of the compound, we need to know the molar masses of carbon and hydrogen, as well as the actual number of carbon and hydrogen atoms in the molecule.
The molar mass of carbon (C) is approximately 12 g/mol, while the molar mass of hydrogen (H) is approximately 1 g/mol.
Let's start by assuming a 100 g sample of this compound.
From the given percent composition, we know that within this 100 g sample:
- 87.8 g is carbon (C) and
- 12.2 g is hydrogen (H).
Next, let's convert the mass of each element to moles using its molar mass.
For carbon (C):
- Moles of carbon = Mass of carbon (g) / Molar mass of carbon (g/mol)
- Moles of carbon = 87.8 g / 12 g/mol ≈ 7.316 moles
For hydrogen (H):
- Moles of hydrogen = Mass of hydrogen (g) / Molar mass of hydrogen (g/mol)
- Moles of hydrogen = 12.2 g / 1 g/mol = 12.2 moles
The ratio of moles of carbon to moles of hydrogen can give us a clue about the molecular formula. In this case, we have approximately 7.316 moles of carbon to 12.2 moles of hydrogen.
To find a whole number ratio, we can divide both values by the smaller number (in this case, 7.316) and then round to the nearest whole number:
- Moles of carbon ≈ 7.316 / 7.316 ≈ 1
- Moles of hydrogen ≈ 12.2 / 7.316 ≈ 1.67
Now, we have approximately 1 mole of carbon to 1.67 moles of hydrogen. To simplify the ratio, we need to multiply each value by a whole number to make the hydrogen mole ratio a whole number.
In this case, we multiply both values by 3 to approximate the nearest whole number ratio:
- Moles of carbon ≈ 1 x 3 = 3
- Moles of hydrogen ≈ 1.67 x 3 ≈ 5
So, the approximate whole number ratio of carbon to hydrogen atoms in the molecule is 3:5.
Finally, to determine the molecular formula, we need to find the empirical formula. The empirical formula represents the simplest, whole-number ratio of atoms in a compound.
The empirical formula of this compound is CH₃.
To find the molecular formula, we need to compare the empirical formula mass to the given molecular mass.
The empirical formula mass can be calculated using the molar masses of each element:
- Empirical formula mass = (Molar mass of carbon x number of carbon atoms) + (Molar mass of hydrogen x number of hydrogen atoms)
- Empirical formula mass = (12 g/mol x 1) + (1 g/mol x 3) = 12 g/mol + 3 g/mol = 15 g/mol
Now, we can determine the molecular formula by dividing the given molecular mass by the empirical formula mass:
- Molecular formula = Molecular mass / Empirical formula mass
- Molecular formula = 82 g/mol / 15 g/mol ≈ 5.47
Since the molecular formula should be a whole number, we round 5.47 to the nearest whole number, which is 5.
Therefore, the molecular formula of the compound is C₅H₅.