When working with chemical compounds, accurately determining their molecular formulas is crucial. One common mistake in this process can arise from the discrepancy between the molecular weight and the empirical formula. For instance, we may encounter a problem where a compound has an empirical formula of C3H3O and a claimed molecular weight of 11 g/mol, leading to confusion. This article explores the potential sources of such errors and provides a solution to arrive at the correct molecular formula.
Understanding the Problem
The empirical formula of a compound, such as C3H3O, represents the simplest whole-number ratio of atoms in the compound. The molecular formula, on the other hand, represents the actual number of atoms in a molecule of the compound. The molecular weight (molecular mass) is calculated from the atomic masses of the elements and the number of atoms of each element in the molecular formula. The relationship between the empirical formula and the molecular formula is a multiplier, which can be determined by dividing the molecular weight by the empirical formula weight.
Theoretical Calculation
The first step in determining the molecular formula from the empirical formula involves calculating the empirical formula weight. For C3H3O:
Weight of C3 3 × 12.01 g/mol (atomic mass of carbon) 36.03 g/mol
Weight of H3 3 × 1.008 g/mol (atomic mass of hydrogen) 3.024 g/mol
Weight of O 16.00 g/mol (atomic mass of oxygen)
Total empirical formula weight 36.03 g/mol 3.024 g/mol 16.00 g/mol 55.054 g/mol
Given the molecular weight of the compound is 11 g/mol, we attempt to find the multiplier:
Multiplier Molecular weight / Empirical formula weight 11 g/mol / 55.054 g/mol ≈ 0.19996
Since the multiplier must be a whole number, it is evident that a molecular weight of 11 g/mol for C3H3O is incorrect. The calculated multiplier (0.19996) is not a whole number, indicating a significant error in the provided molecular weight.
Solving the Error
To resolve this, we should consider a molecular weight that can be a whole-number multiple of the empirical formula weight. A more feasible molecular weight for C3H3O would be significantly higher, such as 110 g/mol:
Multiplier 110 g/mol / 55.054 g/mol ≈ 2
Thus, the correct molecular formula would be:
Molecular formula (C3H3O1)2 C6H6O2
This molecular formula, C6H6O2, represents hydroquinone, a chemical compound with the correct molecular weight of 110 g/mol and the empirical formula C3H3O.
Further Considerations
It is important to note that empirical formulas often represent the skeletal structure of a larger molecule. In the case of hydroquinone (C6H6O2), the empirical formula C3H3O could represent a repeating unit of the structure.
In conclusion, when encountering issues with molecular weights that do not align with empirical formulas, it is essential to re-evaluate the provided data. Ensuring accuracy in the molecular weight is critical for determining the correct molecular formula, which can then be used for a variety of applications, including chemical synthesis, pharmaceuticals, and materials science.
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Conclusion
Through a detailed analysis of the given empirical formula and molecular weight, we have corrected the error in the molecular weight and determined the correct molecular formula. Accurate calculations and verification are crucial in chemistry to ensure the proper identification and application of chemical compounds. Always double-check your data to avoid misleading results and maintain the integrity of your work.