Question

The koala dines exclusively on eucalyptus leaves. Its digestive system detoxifies the eucalyptus oil, a poison to other animals. The chief constituent in eucalyptus oil is a substance called eucalyptol, which contains \(77.87 \% \mathrm{C}\). \(11.76 \% \mathrm{H}\), and the remainder \(\mathrm{O}\). (a) What is the empirical formula for this substance? (b) A mass spectrum of eucalyptol shows a peak at about 154 amu. What is the molecular formula of the substance?

Short answer

The empirical formula of the substance eucalyptol is C10H18O, and its molecular formula is the same as the empirical formula, which is C10H18O.

Step-by-step solution

Calculate moles of each element

Assume we have 100 grams of the compound, so the mass of each element in grams can be written directly from the given percentages: - Mass of carbon (C): 77.87 g - Mass of hydrogen (H): 11.76 g Since the remainder is oxygen (O), we can subtract the other percentages from 100 to find oxygen's percentage: - Mass of oxygen (O): 100 - 77.87 - 11.76 = 10.37 g Now, we will convert the mass of each element into moles using their molar masses: - Moles of C: 77.87 g / 12.01 g/mol = 6.484 mol - Moles of H: 11.76 g / 1.008 g/mol = 11.67 mol - Moles of O: 10.37 g / 16.00 g/mol = 0.648 mol

Find the ratio of moles

To find the ratio, divide the moles of each element by the smallest value among them (which is O, 0.648 mol): - C: 6.484 mol / 0.648 mol = 10 - H: 11.67 mol / 0.648 mol = 18 - O: 0.648 mol / 0.648 mol = 1 The ratio of moles of C, H, and O in the compound is 10:18:1.

Determine the empirical formula

Since the ratio is 10:18:1, the empirical formula of this substance is C10H18O.

Find the molecular formula

We are given that the mass spectrum of eucalyptol shows a peak at about 154 amu (atomic mass units). To find the molecular formula, first, we need to calculate the molecular weight of the empirical formula: Molecular weight of C10H18O = (10 × 12.01) + (18 × 1.008) + (1 × 16) = 154.24 g/mol Since the molecular weight of the empirical formula (154.24 g/mol) is equal to the given peak value of the mass spectrum (154 amu), the molecular formula is the same as the empirical formula: Molecular formula = C10H18O

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that relates to measuring the proportions of elements within compounds and the relationships between reactants and products in chemical reactions. In the context of empirical and molecular formulas, stoichiometry provides the framework to balance the elements and deduce the simplest ratio of atoms within a compound. For instance, if a koala digests eucalyptus oil consisting of carbon (C), hydrogen (H), and oxygen (O), stoichiometry assists in quantifying how these elements combine to form the actual compound.

Understanding stoichiometry involves mastering the concepts of moles and molar ratios. Moles measure the number of particles, such as atoms or molecules, providing a bridge between the microscopic particles and a quantity that can be observed and measured in the lab. With this knowledge, solving for empirical and molecular formulas becomes more manageable, as one can correlate the mass of the elements consumed to their respective number of moles and ultimately to the ratio of atoms in the formula.

Mass Percent Composition

The mass percent composition of an element in a compound describes the fraction of the total mass of the compound that is attributable to that element. It is calculated by dividing the mass of the element by the total mass of the compound and then multiplying by 100 to get a percentage.

This is crucial when starting with the composition of a substance, such as eucalyptol, when only the mass percentages are provided for each element. For better comprehension of mass percent composition, the calculation can be visualized as if one had 100 grams of a substance: the percentages would directly represent the mass in grams of each constituent element. In eucalyptol's case, the mass percent composition can tell us there are 77.87 grams of carbon, 11.76 grams of hydrogen, and the remainder being oxygen, in a 100-gram sample of the substance. This sets the stage for converting these masses into moles, which can then help in the determination of the empirical formula.

Molar Mass

Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a way to convert between the mass of a substance and the number of moles, making it a foundational concept in stoichiometry and in chemistry as a whole.

The molar mass of an element is numerically equivalent to its relative atomic mass but given in units of g/mol. For compounds, the molar mass is the sum of the molar masses of its constituent elements, multiplied by the number of atoms of each element in the formula. For example, to find the molar mass of eucalyptol, you would take the molar masses of carbon (12.01 g/mol), hydrogen (1.008 g/mol), and oxygen (16.00 g/mol), and then add them together according to the number of each atom present in the compound's molecular formula.

Molecular Weight Calculations

Molecular weight calculations are performed to determine the weight of a molecule based on its atomic composition. This weight, typically measured in atomic mass units (amu), is critical when comparing the empirical formula's mass to data from mass spectrometry or other analytical techniques.

The process involves adding the atomic weights of all atoms in a molecule—if each atom's weight is considered as the molar mass, then the resulting molecular weight corresponds to one mole of that molecule. As seen in the eucalyptol example, the calculated molecular weight of its empirical formula, C10H18O, can be compared with the mass spectrum data to determine if the substance's empirical formula also represents its molecular formula. When the calculated molecular weight matches the observed data, it indicates that the empirical formula is indeed correct for the molecular formula.