Chemical analysis of a gaseous compound shows its composition to be 36.4% carbon, 57.5% fluorine, and 6.1% hydrogen. A sample of 1.00 L of this gas weighs 2.96 g. What molecular formula do these data suggest for this compound?
I usually know how to do this, but the liter thing threw me off!
To determine the molecular formula of the compound, we first need to find the empirical formula. The empirical formula gives the simplest whole number ratio of atoms in a compound.
Let's assume we have 100g of the compound. This assumption makes it easier to calculate the empirical formula. From the given composition, we know that the compound is 36.4% carbon, 57.5% fluorine, and 6.1% hydrogen.
1. Convert the percentages to grams:
- Carbon: 36.4 g (36.4% of 100g)
- Fluorine: 57.5 g (57.5% of 100g)
- Hydrogen: 6.1 g (6.1% of 100g)
2. Next, calculate the moles of each element:
- Carbon: Moles of carbon = mass of carbon (in grams) / molar mass of carbon
= 36.4 g / 12.01 g/mol (molar mass of carbon)
- Fluorine: Moles of fluorine = mass of fluorine (in grams) / molar mass of fluorine
= 57.5 g / 19.00 g/mol (molar mass of fluorine)
- Hydrogen: Moles of hydrogen = mass of hydrogen (in grams) / molar mass of hydrogen
= 6.1 g / 1.01 g/mol (molar mass of hydrogen)
3. Calculate the mole ratios by dividing each number of moles by the smallest number of moles (carbon in this case):
- Carbon: 36.4 g / 12.01 g/mol = 3.03 moles
- Fluorine: 57.5 g / 19.00 g/mol = 3.03 moles
- Hydrogen: 6.1 g / 1.01 g/mol = 6.04 moles
The mole ratios (to the nearest whole number) are approximately Carbon:Fluorine:Hydrogen = 3:3:6
4. Write the empirical formula using the mole ratios:
The empirical formula is C3F3H6
Now, to find the molecular formula, we need to know the molar mass of the compound. We are given that a sample of 1.00 L of the gas weighs 2.96 g.
5. Calculate the molar mass of the compound using the 1.00 L sample weight:
Molar mass = mass of sample (in grams) / volume of sample (in liters)
= 2.96 g/1.00 L
However, we need to convert the grams to moles. So, divide by the molar mass of the empirical formula (C3F3H6) to get moles:
Number of moles = 2.96 g / (molar mass of C3F3H6)
6. Finally, calculate the molecular formula using the empirical formula and the number of moles of the compound obtained in step 5. The molecular formula will be a multiple of the empirical formula, so multiply each subscript of the empirical formula by the same whole number:
For example, if the number of moles obtained in step 5 is approximately 2, then the molecular formula would be (C3F3H6)2, resulting in C6F6H12.
So, based on the given data, the molecular formula that these data suggest for this compound is C6F6H12.