Final answer:
To find the molecular formula of the hydrocarbon, we calculate the empirical formula and use the given range of molecular weights. The empirical formula is CH, and the possible molecular formulas are C2H2 and C3H3. The molecular formula is most likely C2H2.
Step-by-step explanation:
To find the molecular formula of the hydrocarbon, we need to determine the ratio of carbon to hydrogen in the compound. We are given that the hydrocarbon is 7.74% hydrogen. This means that the remaining percentage, 92.26%, must be carbon.
Next, we need to calculate the empirical formula of the hydrocarbon. We can assume a 100 gram sample of the compound, which means that there are 7.74 grams of hydrogen and 92.26 grams of carbon. To find the moles of each element, we divide the mass by the atomic weight:
Moles of hydrogen = 7.74 g / 1 g/mol = 7.74 mol
Moles of carbon = 92.26 g / 12 g/mol = 7.688 mol
To find the smallest whole-number ratio of the elements, we divide the moles of each element by the smallest number of moles, which in this case is 7.688.
Dividing the moles of hydrogen by 7.688 gives us a ratio of 1, and dividing the moles of carbon by 7.688 gives us a ratio of 1.
So, the empirical formula of the hydrocarbon is CH.
To determine the molecular formula, we need to know the molecular mass of the compound. Given that the molecular weight is known to be between 70 and 85 u, we can calculate the possible molecular formulas using the empirical formula and the atomic weights of carbon and hydrogen. The atomic weight of carbon is 12 g/mol and the atomic weight of hydrogen is 1 g/mol.
Using the empirical formula CH, the possible molecular formulas are C2H2 (84 g/mol) and C3H3 (90 g/mol). Since the molecular weight is between 70 and 85 u, the molecular formula of the hydrocarbon is most likely C2H2.