An analysis of a compound gave 40% carbon 3.7% hydrogen. the vapour density of the compound is 30. calculate the empirical and molecula fomular.
To calculate the empirical formula and molecular formula of a compound, we need the percentage composition of its elements and the molar mass or the vapor density of the compound.
Given:
- Carbon (C) composition: 40%
- Hydrogen (H) composition: 3.7%
- Vapor density: 30
Step 1: Convert the percentage composition to grams.
Assume we have 100g of the compound, then:
- Carbon (C) mass = 40% of 100g = 40g
- Hydrogen (H) mass = 3.7% of 100g = 3.7g
Step 2: Convert the mass of each element to moles using their molar masses.
- Carbon (C) molar mass = 12.01 g/mol (from the periodic table)
- Hydrogen (H) molar mass = 1.01 g/mol (from the periodic table)
- Moles of Carbon (C) = Carbon mass / Carbon molar mass = 40g / 12.01 g/mol ≈ 3.33 mol
- Moles of Hydrogen (H) = Hydrogen mass / Hydrogen molar mass = 3.7g / 1.01 g/mol ≈ 3.67 mol
Step 3: Find the simplest whole number ratio of the moles.
Divide the number of moles of each element by the smallest number of moles to obtain the simplest ratio:
- Moles of Carbon (C) = 3.33 mol / 3.33 mol ≈ 1
- Moles of Hydrogen (H) = 3.67 mol / 3.33 mol ≈ 1.1
Based on these values, the empirical formula is CH. However, we need to confirm this by finding the molecular formula.
Step 4: Calculate the molar mass of the empirical formula.
The molar mass of CH = [(molar mass of C) x (number of C atoms)] + [(molar mass of H) x (number of H atoms)]
= (12.01 g/mol) + (1.01 g/mol) = 13.02 g/mol
Step 5: Calculate the number of empirical formula units needed to obtain the vapor density.
The vapor density is the ratio of the molar mass of the compound to the molar mass of hydrogen gas (H2). Since hydrogen gas has a molar mass of 2.02 g/mol, we can calculate:
Vapor density = (Molar mass of the compound) / (Molar mass of H2)
30 = (Molar mass of the compound) / 2.02
Molar mass of the compound = 30 x 2.02 ≈ 60.6 g/mol
Step 6: Calculate the ratio of the molar mass of the compound to the molar mass of the empirical formula.
Ratio = (Molar mass of the compound) / (Molar mass of the empirical formula)
= 60.6 g/mol / 13.02 g/mol ≈ 4.66
Step 7: Multiply the subscripts of the empirical formula by this ratio to obtain the molecular formula.
- Empirical formula: CH
- Molecular formula: (CH) x 4.66 = C4.66H4.66
Since we cannot have fractional subscripts in the molecular formula, we can round the values to the nearest whole number: C5H5
Therefore, the empirical formula of the compound is CH, and the molecular formula is C5H5.