Question

Which has a higher percentage of oxygen: morphine \(\left(\mathrm{C}_{17} \mathrm{H}_{19} \mathrm{NO}_{3}\right)\) or heroin \(\left(\mathrm{C}_{21} \mathrm{H}_{23} \mathrm{NO}_{5}\right) ?\)

Short answer

Heroin (\text{C}_{21} \text{H}_{23} \text{NO}_{5}) has a higher percentage of oxygen.

Step-by-step solution

Determine the molar mass of morphine

Calculate the molar mass of morphine \(\mathrm{C}_{17} \mathrm{H}_{19} NO_{3}\) by summing the molar masses of all the atoms in the formula. The molar masses are approximately 12 g/mol for carbon (C), 1 g/mol for hydrogen (H), 14 g/mol for nitrogen (N), and 16 g/mol for oxygen (O). The molar mass of morphine is \(17 \times 12 + 19 \times 1 + 14 + 3 \times 16\) g/mol.

Calculate the percentage of oxygen in morphine

The total mass of oxygen in morphine is the product of the number of oxygen atoms and the molar mass of oxygen. Hence, the mass of oxygen in morphine is \(3 \times 16\) g. Divide this by the molar mass of morphine obtained from Step 1 and multiply by 100 to get the percentage of oxygen in morphine.

Determine the molar mass of heroin

Calculate the molar mass of heroin \(\mathrm{C}_{21} \mathrm{H}_{23} NO_{5}\) by summing the molar masses of all the atoms in the formula. The molar mass of heroin is \(21 \times 12 + 23 \times 1 + 14 + 5 \times 16\) g/mol.

Calculate the percentage of oxygen in heroin

The total mass of oxygen in heroin is the product of the number of oxygen atoms and the molar mass of oxygen. Hence, the mass of oxygen in heroin is \(5 \times 16\) g. Divide this by the molar mass of heroin obtained from Step 3 and multiply by 100 to get the percentage of oxygen in heroin.

Compare the percentages

Compare the percentage of oxygen in morphine from Step 2 with that of heroin from Step 4 to determine which compound has a higher percentage of oxygen.

Key concepts

Molar Mass Calculation

Understanding molar mass is a crucial part of chemistry that deals with quantifying the mass of chemical compounds. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). A mole is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other particles.

The calculation is straightforward. Each element has a standard atomic weight, which can be found on the periodic table. For example, the molar mass of carbon (C) is roughly 12 g/mol. To calculate the molar mass of a compound, you sum the molar masses of each element multiplied by the number of times the element appears in the compound. For morphine, with the formula \(C_{17}H_{19}NO_{3}\), we calculate it as (17 atoms of C times 12 g/mol) + (19 atoms of H times 1 g/mol) + (1 atom of N times 14 g/mol) + (3 atoms of O times 16 g/mol).

This calculation is essential for understanding the composition of the compound and is used in further calculations such as determining the percentage of an element within a compound.

Stoichiometry

When we speak of stoichiometry, we refer to the quantitative relationships between the reactants and products in a chemical reaction. It's like a recipe that tells you how much of each ingredient you'll need to produce a certain amount of product.

In the context of our problem, stoichiometry allows us to calculate the percentage of oxygen in a compound by using the molar mass and the number of oxygen atoms. It is the stoichiometric relationship between oxygen atoms and the entire compound that determines what fraction of the compound's mass is due to oxygen. By understanding stoichiometry, we can make accurate calculations about the proportions of elements in compounds and predict how much of a substance will be needed or produced in a chemical reaction.

Chemical Composition

The chemical composition of a substance tells us which elements are present and in what proportions. When we analyze the chemical composition, we are essentially dissecting a compound into its elemental parts.

For the compounds in question, morphine and heroin, analyzing the chemical composition involves identifying the presence and quantity of carbon, hydrogen, nitrogen, and oxygen. By calculating the percentage of oxygen in these substances, we are examining a specific aspect of their chemical composition, which sheds light on how much oxygen contributes to the total mass of the compound. This analysis gives us valuable insights into the properties and behavior of the compound, such as its reactivity and how it might interact with other substances.

Empirical Formula

An empirical formula represents the simplest whole-number ratio of the elements in a compound. It’s different from the molecular formula, which shows the exact number of atoms of each element in a molecule.

For instance, if a compound's molecular formula is \(C_{2}H_{6}O\), its empirical formula would be \(CH_{3}O\), simplifying the ratio of the atoms to the smallest whole numbers. Although the molecular formulas for morphine and heroin are much more complex than this simple example, the approach to ascertain the empirical formula remains consistent. The empirical formula is particularly useful for determining the percentage composition of a compound because it provides the fundamental ratio of the elements present, which can then be related back to their molar masses to perform precise calculations.