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)
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
Explanation of Solution
Given that,
Mass percent of carbon is
Mass percent of hydrogen is
Mass percent of oxygen is
The atomic mass of carbon is
The atomic mass of hydrogen is
The atomic mass of oxygen is
The number of moles is calculated using the formula (assuming the sample to be
Substituting the values of given mass and the molar mass in the above expression,
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
For hydrogen
For oxygen
The calculated value of the number of moles is multiplied by a common multiple
Therefore, the empirical formula obtained is
Now, to determine the molecular formula of ibuprofen:
Given that,
Empirical formula is
Molar mass of the compound is
The atomic mass of carbon is
The atomic mass of hydrogen is
The atomic mass of oxygen is
The empirical formula mass of
The given molar mass value is divided by the calculated empirical formula mass value to obtain a whole number multiple,
The subscripts of the empirical formula are multiplied by the whole number multiple obtained to get the molecular formula of the given compound,
(b)
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
Explanation of Solution
Given that,
Mass percent of carbon is
Mass percent of hydrogen is
Mass percent of nitrogen is
The atomic mass of carbon is
The atomic mass of hydrogen is
The atomic mass of nitrogen is
The number of moles is calculated using the formula (assuming the sample to be
Substituting the values of given mass and the molar mass in the above expression,
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
For hydrogen
For nitrogen
The calculated value of the number of moles is multiplied by a common multiple
Therefore, the empirical formula obtained is
Now, to determine the molecular formula of cadaverine:
Given that,
Empirical formula is
Molar mass of the compound is
The atomic mass of carbon is
The atomic mass of hydrogen is
The atomic mass of nitrogen is
The empirical formula mass of
The given molar mass value is divided by the calculate empirical formula mass value to obtain a whole number multiple,
The subscripts of the empirical formula are multiplied by the whole number multiple obtained to get the molecular formula of the given compound,
(c)
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
Explanation of Solution
Given that,
Mass percent of carbon is
Mass percent of hydrogen is
Mass percent of nitrogen is
Mass percent of oxygen is
The atomic mass of carbon is
The atomic mass of hydrogen is
The atomic mass of nitrogen is
The atomic mass of oxygen is
The number of moles is calculated using the formula (assuming the sample to be
Substituting the values of given mass and the molar mass in the above expression,
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
For hydrogen
For nitrogen
For oxygen
Therefore, the empirical formula obtained is
Now, to determine the molecular formula of epinephrine:
Given that,
Empirical formula is
Molar mass of the compound is
The atomic mass of carbon is
The atomic mass of hydrogen is
The atomic mass of nitrogen is
The atomic mass of oxygen is
The empirical formula mass of
The given molar mass value is divided by the calculate empirical formula mass value to obtain a whole number multiple,
The subscripts of the empirical formula are multiplied by the whole number multiple obtained to get the molecular formula of the given compound,
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Chapter 12 Solutions
Chemistry: The Central Science (13th Edition)
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