Chemistry: The Central Science (13th Edition)
Chemistry: The Central Science (13th Edition)
13th Edition
ISBN: 9780321910417
Author: Theodore E. Brown, H. Eugene LeMay, Bruce E. Bursten, Catherine Murphy, Patrick Woodward, Matthew E. Stoltzfus
Publisher: PEARSON
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Chapter 12, Problem 1DE

Determine the empirical and molecular formulas of each of the following substances:

a. Ibuprofen, a headache remedy, contains 75.69% C, 8.80% H, and 15.51% 0 by mass and has a molar mass of 206 g/mol.
b. Cadaverine, a foul-smelling substance produced by the action of bacteria on meat, contains 58.55% C, 13.81% H, and 27.40% N by mass; its molar mass is 102.2 g/mol.
c. Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains 59.0% C, 7.1% H, 262% 0, and 7.7% N by mass; its molar mass is about 180 amu.

(a)

Expert Solution
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Interpretation Introduction

Interpretation: The empirical and molecular formula of ibuprofen.

Concept introduction:
A formula that depicts the simplest ratio of the constituent elements in a compound is known as the empirical formula.
The empirical formula mass of a given compound is the total of the atomic masses of the constituent atoms.
The steps to determine the molecular formula from the empirical formula are,

  • The empirical formula mass is calculated.
  • The gram molecular mass of the compound is divided by the empirical formula mass.
  • The subscripts within the empirical formula are multiplied by the number obtained in the previous step.
  • The chemical formula obtained having new subscript values is the molecular formula of the compound.

Answer to Problem 1DE

Solution: The empirical formula of ibuprofen is C13H18O2 and its molecular formula is C13H18O2 .

Explanation of Solution


Given that,
Mass percent of carbon is 75.69% .
Mass percent of hydrogen is 8.80% .
Mass percent of oxygen is 15.51% .

The atomic mass of carbon is 12g .
The atomic mass of hydrogen is 1g .
The atomic mass of oxygen is 16g .

The number of moles is calculated using the formula (assuming the sample to be 100g ),
Numberofmoles=GivenmasspercentAtomicmassofthesubstance

Substituting the values of given mass and the molar mass in the above expression,

  Numberofmolesofcarbon=75.69g12g=6.3moles

  Numberofmolesofhydrogen=8.80g1g=8.8moles

  Numberofmolesofoxygen=15.51g16g0.97mole

The calculated values are divided by the smallest number of moles to determine the simplest whole number ratio of moles of each constituent,

For carbon (C) ,
  C=6.3mol0.97mol=6.5

For hydrogen (H) ,
  H=8.8mol0.97mol=9

For oxygen (O) ,
  O=0.97mol0.97mol=1

The calculated value of the number of moles is multiplied by a common multiple 2 to obtain the simplest whole number values for the same.
Therefore, the empirical formula obtained is C13H18O2 .

Now, to determine the molecular formula of ibuprofen:
Given that,
Empirical formula is C13H18O2 .
Molar mass of the compound is 206g/mol .

The atomic mass of carbon is 12g .
The atomic mass of hydrogen is 1g .
The atomic mass of oxygen is 16g .

The empirical formula mass of C13H18O2 =(( 13×12)+( 1×18)+( 2×16))g=206g

The given molar mass value is divided by the calculated empirical formula mass value to obtain a whole number multiple,
Wholenumbermultiple=206g/mol206g/mol=1

The subscripts of the empirical formula are multiplied by the whole number multiple obtained to get the molecular formula of the given compound,

  Molecular formula=( C 13 H 18 O 2)1=C13H18O2

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The empirical and molecular formula of cadeverine.

Concept introduction:
A formula that depicts the simplest ratio of the constituent elements in a compound is known as the empirical formula.
The empirical formula mass of a given compound is the total of the atomic masses of the constituent atoms.
The steps to determine the molecular formula from the empirical formula are,

  • The empirical formula mass is calculated.
  • The gram molecular mass of the compound is divided by the empirical formula mass.
  • The subscripts within the empirical formula are multiplied by the number obtained in the previous step.
  • The chemical formula obtained having new subscript values is the molecular formula of the compound.

Answer to Problem 1DE

Solution: The empirical formula of cadeverine is C5H14N2 and its molecular formula is C5H14N2 .

Explanation of Solution


Given that,
Mass percent of carbon is 58.55% .
Mass percent of hydrogen is 13.81% .
Mass percent of nitrogen is 27.40% .

The atomic mass of carbon is 12g .
The atomic mass of hydrogen is 1g .
The atomic mass of nitrogen is 14g .

The number of moles is calculated using the formula (assuming the sample to be 100g ),
Numberofmoles=GivenmasspercentAtomicmassofthesubstance

Substituting the values of given mass and the molar mass in the above expression,

  Numberofmolesofcarbon=58.55g12g=4.87moles4.9moles

  Numberofmolesofhydrogen=13.81g1g=13.81moles

  Numberofmolesofnitrogen=27.40g14g=1.95moles2moles

The calculated values are divided by the smallest number of moles to determine the simplest whole number ratio of moles of each constituent,

For carbon (C) ,
  C=4.9mol2mol2.5

For hydrogen (H) ,
  H=13.81mol2mol7

For nitrogen (N) ,
  N=2mol2mol=1

The calculated value of the number of moles is multiplied by a common multiple 2 to obtain the simplest whole number values for the same.
Therefore, the empirical formula obtained is C5H14N2 .

Now, to determine the molecular formula of cadaverine:

Given that,
Empirical formula is C5H14N2 .
Molar mass of the compound is 102.2g/mol .

The atomic mass of carbon is 12g .
The atomic mass of hydrogen is 1g .
The atomic mass of nitrogen is 14g .

The empirical formula mass of C5H14N2 =(( 5×12)+( 14×1)+( 2×14))g=102g

The given molar mass value is divided by the calculate empirical formula mass value to obtain a whole number multiple,

  Wholenumbermultiple=102.2g/mol102g/mol1

The subscripts of the empirical formula are multiplied by the whole number multiple obtained to get the molecular formula of the given compound,

  Molecular formula=( C 5 H 14 N 2)1=C5H14N2

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The empirical and molecular formula of epinephrine.

Concept introduction:
A formula that depicts the simplest ratio of the constituent elements in a compound is known as the empirical formula.
The empirical formula mass of a given compound is the total of the atomic masses of the constituent atoms.
The steps to determine the molecular formula from the empirical formula are,

  • The empirical formula mass is calculated.
  • The gram molecular mass of the compound is divided by the empirical formula mass.
  • The subscripts within the empirical formula are multiplied by the number obtained in the previous step.
  • The chemical formula obtained having new subscript values is the molecular formula of the compound.

Answer to Problem 1DE

Solution: The empirical formula of epinephrine is C9H13O3N and its molecular formula is C9H13O3N .

Explanation of Solution


Given that,
Mass percent of carbon is 59.0% .
Mass percent of hydrogen is 7.1% .
Mass percent of nitrogen is 7.7% .
Mass percent of oxygen is 26.2% .

The atomic mass of carbon is 12g .
The atomic mass of hydrogen is 1g .
The atomic mass of nitrogen is 14g .
The atomic mass of oxygen is 16g .

The number of moles is calculated using the formula (assuming the sample to be 100g ),

Numberofmoles=GivenmasspercentAtomicmassofthesubstance

Substituting the values of given mass and the molar mass in the above expression,

  Numberofmolesofcarbon=59.0g12g=4.91moles5moles

  Numberofmolesofhydrogen=7.1g1g=7.1moles

  Numberofmolesofnitrogen=7.7g14g=0.55moles

  Numberofmolesofoxygen=26.2g16g=1.64moles

The calculated values are divided by the smallest number of moles to determine the simplest whole number ratio of moles of each constituent,

For carbon (C) ,
C=5mol0.55mol9

For hydrogen (H) ,
  H=7.1mol0.55mol13

For nitrogen (N) ,
  N=0.55mol0.55mol=1

For oxygen (O) ,
  O=1.64mol0.55mol3

Therefore, the empirical formula obtained is C9H13O3N .

Now, to determine the molecular formula of epinephrine:
Given that,
Empirical formula is C9H13O3N .
Molar mass of the compound is 180amu .

The atomic mass of carbon is 12amu .
The atomic mass of hydrogen is 1amu .
The atomic mass of nitrogen is 14amu .
The atomic mass of oxygen is 16amu .

The empirical formula mass of C9H13O3N =(( 9×12)+( 13×1)+( 3×16)+14)amu=183amu

The given molar mass value is divided by the calculate empirical formula mass value to obtain a whole number multiple,

Wholenumbermultiple=180g/mol183g/mol1

The subscripts of the empirical formula are multiplied by the whole number multiple obtained to get the molecular formula of the given compound,

  Molecular formula=( C 9 H 13 O 3N)1=C9H13O3N

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Chapter 12 Solutions

Chemistry: The Central Science (13th Edition)

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