The empirical mass of ethane (C₂H₆) is half its molecular mass, representing the simplified whole number ratio of its constituent atoms.
To understand the difference, let's break down the concepts:
Molecular Mass
The molecular mass is the sum of the atomic masses of all atoms present in a molecule. Ethane has the molecular formula C₂H₆.
- Atomic mass of Carbon (C) ≈ 12 amu
- Atomic mass of Hydrogen (H) ≈ 1 amu
Therefore, the molecular mass of ethane (C₂H₆) = (2 12 amu) + (6 1 amu) = 24 amu + 6 amu = 30 amu.
Empirical Mass
The empirical formula represents the simplest whole number ratio of atoms in a compound. For ethane (C₂H₆), the ratio of carbon to hydrogen is 2:6, which simplifies to 1:3. Therefore, the empirical formula of ethane is CH₃.
The empirical mass is the sum of the atomic masses of the atoms in the empirical formula.
- Atomic mass of Carbon (C) ≈ 12 amu
- Atomic mass of Hydrogen (H) ≈ 1 amu
Therefore, the empirical mass of ethane (CH₃) = (1 12 amu) + (3 1 amu) = 12 amu + 3 amu = 15 amu.
Summary of the Difference
Here's a table summarizing the difference:
| Feature | Molecular Mass | Empirical Mass |
|---|---|---|
| Formula | C₂H₆ | CH₃ |
| Definition | Mass of the molecule | Mass of empirical formula |
| Calculation | (2 12) + (6 1) | (1 12) + (3 1) |
| Value | 30 amu | 15 amu |
| Represents | Actual molecule | Simplest ratio |
Conclusion
The molecular mass of ethane is 30 amu, based on its molecular formula C₂H₆, while its empirical mass is 15 amu, based on its simplified empirical formula CH₃. The empirical mass is half the molecular mass in this case because the molecular formula is a multiple of the empirical formula.
