Problem 23 - Chemistry The Central Science

Question

Calculate the percentage by mass of oxygen in the following compounds: (a) morphine, \(\quad \mathrm{C}_{17} \mathrm{H}_{19} \mathrm{NO}_{3}\); (b) codeine, \(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3} \quad\) (c) cocaine, \(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}\); (d) tetracycline, \(\mathrm{C}_{22} \mathrm{H}_{24} \mathrm{~N}_{2} \mathrm{O}_{8} ;\) (e) digitoxin, \(\mathrm{C}_{41} \mathrm{H}_{64} \mathrm{O}_{13} ;\) (f) vancomycin, \(\mathrm{C}_{66} \mathrm{H}_{75} \mathrm{Cl}_{2} \mathrm{~N}_{9} \mathrm{O}_{24}\)

Step-by-Step Solution

Answer

The percentages by mass of oxygen in the given compounds are: (a) morphine: \(16.83\%\), (b) codeine: \(16.46\%\), (c) cocaine: \(21.49\%\), (d) tetracycline: \(34.36\%\), (e) digitoxin: \(26.61\%\), and (f) vancomycin: \(37.88\%\).

Step 1: Calculate the molar mass of the compound

The molar mass of a compound is calculated by adding the molar masses of all the atoms in the compound. Molar mass of Morphine = (17 × 12.01)+(19 × 1.008)+(1 × 14.01)+(3 × 16.00) = \(204.17 + 19.152 + 14.01 + 48 = 285.332\,\mathrm{g/mol}\)

Step 2: Calculate the combined mass of oxygen in the compound

There are 3 oxygen atoms in morphine, with a molar mass of 16.00 g/mol for each oxygen atom. Total mass of oxygen in morphine = 3 × 16.00 = \(48\, \mathrm{g/mol}\)

Step 3: Calculate the percentage by mass of oxygen

Percentage by mass of oxygen = (Total mass of oxygen / Molar mass of Morphine) × 100 \(= \frac{48 \,\mathrm{g/mol}}{285.332 \,\mathrm{g/mol}} \times 100\)

Step 4: Answer(a)

The percentage by mass of oxygen in morphine = \(16.83\%\) Repeat these steps for the remaining compounds: (b) Codeine: \(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3}\)

Step 5: Answer(b)

The percentage by mass of oxygen in codeine = \(16.46\%\) (c) Cocaine: \(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}\)

Step 6: Answer(c)

The percentage by mass of oxygen in cocaine = \(21.49\%\) (d) Tetracycline: \(\mathrm{C}_{22} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{8}\)

Step 7: Answer(d)

The percentage by mass of oxygen in tetracycline = \(34.36\%\) (e) Digitoxin: \(\mathrm{C}_{41} \mathrm{H}_{64} \mathrm{O}_{13}\)

Step 8: Answer(e)

The percentage by mass of oxygen in digitoxin = \(26.61\%\) (f) Vancomycin: \(\mathrm{C}_{66} \mathrm{H}_{75} \mathrm{Cl}_{2} \mathrm{N}_{9} \mathrm{O}_{24}\)

Step 9: Answer(f)

The percentage by mass of oxygen in vancomycin = \(37.88\%\)

Key Concepts

Percentage Composition

Percentage composition in chemistry determines how much of each element exists within a chemical compound.
This helps in understanding the proportions of elements in various substances.
Calculating the percentage composition of an element involves three main steps:

• Find the molar mass of the entire compound. This requires adding the combined atomic weights of all the atoms in the chemical formula.
• Identify the total mass contribution of the element of interest by multiplying its atomic mass by the number of atoms of that element in the formula.
• Divide the element's total mass by the compound’s molar mass, then multiply by 100 to convert it to a percentage.

This calculation provides insight into the predominance of the element in the compound, useful for both practical and theoretical chemistry applications.

Chemical Compounds

Chemical compounds consist of two or more different elements chemically bonded together.
These bonds can be ionic or covalent depending on the nature of the interaction between the atoms.
Each compound displays unique physical and chemical properties determined by its composition.

• Simple compounds include common substances such as water (H\(_2\)O) and carbon dioxide (CO\(_2\)).
• Complex compounds, like proteins and pharmaceuticals, consist of long chains of atoms with more intricate structures.

Understanding chemical compounds is crucial for chemistry and related sciences, allowing predictions about reactivity, stability, and behavior in different conditions.

Oxygen Content Analysis

Oxygen content analysis quantifies the amount of oxygen within compounds, which is important for understanding their reactivity and uses.
For instance, in pharmaceuticals such as morphine or codeine, knowing the oxygen percentage helps in pharmacokinetics—the drug's movement through the body.
The analysis follows a familiar percentage composition method:

• Determine the molar mass of all the oxygen atoms in the compound.
• Compare this mass against the molar mass of the entire molecule.
• Calculate the percentage by dividing and multiplying by 100, which delivers the oxygen's share in the compound.

The oxygen content underscores critical aspects such as oxidation states, potential for combustion, and implications for biological interaction.