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Chapter 3: Problem 23

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, \(\mathrm{C}_{66} \mathrm{H}_{75} \mathrm{Cl}_{2} \mathrm{~N}_{9} \mathrm{O}_{24}\)

Short Answer

Expert verified
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 by step solution

01

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) = \(204.17 + 19.152 + 14.01 + 48 = 285.332\,\mathrm{g/mol}\)
02

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 = \(48\, \mathrm{g/mol}\)
03

Calculate the percentage by mass of oxygen

Percentage by mass of oxygen = (Total mass of oxygen / Molar mass of Morphine) × 100 \(= \frac{48 \,\mathrm{g/mol}}{285.332 \,\mathrm{g/mol}} \times 100\)
04

Answer(a)

The percentage by mass of oxygen in morphine = \(16.83\%\) Repeat these steps for the remaining compounds: (b) Codeine: \(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3}\)
05

Answer(b)

The percentage by mass of oxygen in codeine = \(16.46\%\) (c) Cocaine: \(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}\)
06

Answer(c)

The percentage by mass of oxygen in cocaine = \(21.49\%\) (d) Tetracycline: \(\mathrm{C}_{22} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{8}\)
07

Answer(d)

The percentage by mass of oxygen in tetracycline = \(34.36\%\) (e) Digitoxin: \(\mathrm{C}_{41} \mathrm{H}_{64} \mathrm{O}_{13}\)
08

Answer(e)

The percentage by mass of oxygen in digitoxin = \(26.61\%\) (f) Vancomycin: \(\mathrm{C}_{66} \mathrm{H}_{75} \mathrm{Cl}_{2} \mathrm{N}_{9} \mathrm{O}_{24}\)
09

Answer(f)

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

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