In March 2007 a number of pets were sickened or killed by pet food contaminated with the chemical melamine, which is used in the manufacture of certain plastics. It is thought that the melamine was added to make a pet food additive appear to have more protein than it really did. Melamine is 28.57%C, 4.80%H, and 66.63%N by mass. If the molecular weight of melamine is 126.15 g/mol, what is its molecular formula?
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To determine the molecular formula of melamine, we need to know the empirical formula first. The empirical formula represents the simplest, most reduced ratio of atoms in a compound.
Given that melamine is 28.57% carbon (C), 4.80% hydrogen (H), and 66.63% nitrogen (N) by mass, we can assume that we have 100g of the compound. This way, we can convert the percentages into grams.
1. Convert percentages to grams:
- Carbon (C): (28.57 g / 100 g) = 0.2857 g
- Hydrogen (H): (4.80 g / 100 g) = 0.048 g
- Nitrogen (N): (66.63 g / 100 g) = 0.6663 g
2. Convert the grams to moles using the molar mass of each element:
- Carbon (C): 0.2857 g * (1 mol / 12.01 g/mol) = 0.0238 mol
- Hydrogen (H): 0.048 g * (1 mol / 1.01 g/mol) = 0.0475 mol
- Nitrogen (N): 0.6663 g * (1 mol / 14.01 g/mol) = 0.0475 mol
3. Find the smallest whole number ratio of moles by dividing each value by the smallest value:
- Carbon (C): 0.0238 mol / 0.0238 mol = 1
- Hydrogen (H): 0.0475 mol / 0.0238 mol = 2
- Nitrogen (N): 0.0715 mol / 0.0238 mol = 3
Based on our calculations, we have a ratio of 1:2:3 for C:H:N. This means that the empirical formula of melamine is CH2N3.
To find the molecular formula, we need to determine the molecular weight of the empirical formula.
4. Calculate the empirical formula weight:
Empirical formula weight = (Atomic weight of C) + (Atomic weight of H * 2) + (Atomic weight of N * 3)
Empirical formula weight = (12.01 g/mol) + (1.01 g/mol * 2) + (14.01 g/mol * 3)
Empirical formula weight = 27.04 g/mol
5. Finally, find the molecular formula by dividing the molecular weight given in the question (126.15 g/mol) by the empirical formula weight:
Molecular formula = (Molecular weight) / (Empirical formula weight)
Molecular formula = 126.15 g/mol / 27.04 g/mol
Molecular formula = 4.66
Since the result is approximately 4.66, we round this number to the nearest whole number, which is 5. Therefore, the molecular formula of melamine is C5H10N3.