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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 脳 12.01)+(19 脳 1.008)+(1 脳 14.01)+(3 脳 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 脳 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) 脳 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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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鈥檚 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鈥攖he 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.

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Most popular questions from this chapter

Section 2.9 introduced the idea of structural isomerism, with 1-propanol and 2 -propanol as examples. Determine which of these properties would distinguish these two substances: (a) boiling point; (b) combustion analysis results; (c) molecular weight; (d) density at a given temperature and pressure. You can check on the properties of these two compounds in Wolfram Alpha (http://www.wolframalpha.com/) or the CRC Handbook of Chemistry and Physics.

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Write balanced chemical equations to correspond to each of the following descriptions: (a) When sulfur trioxide gas reacts with water, a solution of sulfuric acid forms. (b) Boron sulfide, \(\mathrm{B}_{2} \mathrm{~S}_{3}(s),\) reacts violently with water to form dissolved boric acid, \(\mathrm{H}_{3} \mathrm{BO}_{3},\) and hydrogen sulfide gas. (c) Phosphine, \(\mathrm{PH}_{3}(g)\), combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide. (d) When solid mercury(II) nitrate is heated, it decomposes to form solid mercury(II) oxide, gaseous nitrogen dioxide, and oxygen. (e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

(a) Determine the chemical formula of the product formed when the metallic element aluminum combines with the nonmetallic element bromine, \(\mathrm{Br}_{2}\). Write the balanced chemical equation for the reaction. (b) What products form when a compound containing \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O}\) is completely combusted in air? Write a balanced chemical equation for the combustion of acetone, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l),\) in air.
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