Question

Diphenhydramine hydrochloride, a drug used commonly as an antihistamine, has the formula \(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO} \cdot \mathrm{HCl}\). What is the percent composition of each element in this compound?

Short answer

C: 70.09%, H: 7.63%, N: 4.81%, O: 5.49%, Cl: 12.17%

Step-by-step solution

- Determine the Molar Mass

Calculate the molar mass of each element in the formula. Sum the masses of all atoms in the compound. For diphenhydramine hydrochloride \(\text{C}_{17} \text{H}_{21} \text{NO} \text{HCl}\), the molar mass is calculated as follows: \(17 \times 12.01 + 21 \times 1.01 + 1 \times 14.01 + 1 \times 16.00 + 1 \times 1.01 + 1 \times 35.45 = 291.36 \text{g/mol}\).

- Calculate Individual Masses

Find the total mass of each element in the compound. \( \text{C: } 17 \times 12.01 = 204.17 \text{g}ewline \text{H: } 21 \times 1.01 + 1 \times 1.01 = 22.22 \text{g}ewline \text{N: } 1 \times 14.01 = 14.01 \text{g}ewline \text{O: } 1 \times 16.00 = 16.00 \text{g}ewline \text{Cl: } 1 \times 35.45 = 35.45 \text{g} \)

- Calculate Percent Composition

Determine the percent composition of each element by dividing the total mass of the element by the molar mass of the compound and multiplying by 100. \( \text{Percent Carbon (} \text{C} \text{): } \frac{204.17}{291.36} \times 100 = 70.09\text{\text{%}}ewline \text{Percent Hydrogen (} \text{H} \text{): } \frac{22.22}{291.36} \times 100 = 7.63\text{\text{%}}ewline \text{Percent Nitrogen (} \text{N} \text{): } \frac{14.01}{291.36} \times 100 = 4.81\text{\text{%}}ewline \text{Percent Oxygen (} \text{O} \text{): } \frac{16.00}{291.36} \times 100 = 5.49\text{\text{%}}ewline \text{Percent Chlorine (} \text{Cl} \text{): } \frac{35.45}{291.36} \times 100 = 12.17\text{\text{%}} \)

Key concepts

molar mass calculation

To understand the percent composition of a compound, we first need to calculate its molar mass. The molar mass is the sum of the atomic masses of all the atoms in the chemical formula. For diphenhydramine hydrochloride, which has the formula \(\text{C}_{17} \text{H}_{21} \text{NO} \cdot \text{HCl}\), we break it down by element:

For carbon (C), we have 17 atoms. Multiply 17 by the atomic mass of carbon, which is 12.01 g/mol:
\(17 \times 12.01 = 204.17 \text{g/mol}\)

For hydrogen (H), we have 21 atoms in diphenhydramine and 1 atom in HCl, making a total of 22 atoms:
\(22 \times 1.01 = 22.22 \text{g/mol}\)

Nitrogen (N) has 1 atom:
\(1 \times 14.01 = 14.01 \text{g/mol}\)

Oxygen (O) also has 1 atom:
\(1 \times 16.00 = 16.00 \text{g/mol}\)

Chlorine (Cl) in HCl has 1 atom:
\(1 \times 35.45 = 35.45 \text{g/mol}\)

Adding up all these values gives us the molar mass of the compound:
\(204.17 + 22.22 + 14.01 + 16.00 + 35.45 = 291.36 \text{g/mol}\)

chemical formula analysis

Chemical formula analysis helps us understand how many of each type of atom are present in a compound. For diphenhydramine hydrochloride, the formula is \(\text{C}_{17} \text{H}_{21} \text{NO} \cdot \text{HCl}\). Breaking it down, we interpret the formula as follows:

• \text{C}_{17} means there are 17 carbon atoms.
• \text{H}_{21} indicates there are 21 hydrogen atoms in the diphenhydramine portion of the compound.
• \text{NO} denotes that there is 1 nitrogen atom and 1 oxygen atom.
• \text{HCl} means there is 1 extra hydrogen atom and 1 chlorine atom.

Summing up the hydrogen atoms, we have a total of 22 hydrogen atoms (21 from diphenhydramine and 1 from HCl). This analysis helps set the stage for calculating both the molar mass and the percent composition of each element in the compound.

elemental analysis

Elemental analysis involves calculating what percentage of the total compound's mass is made up by each element. The percent composition is found by dividing the mass of each element by the total molar mass of the compound and then multiplying by 100.

The general formula is:
\(\text{Percent of Element} = \frac{\text{Mass of Element}}{\text{Molar Mass of Compound}} \times 100 \)

For each element in diphenhydramine hydrochloride, we use their calculated masses from earlier:

• Carbon (C): \(\frac{204.17}{291.36} \times 100 = 70.09\%\)
• Hydrogen (H): \(\frac{22.22}{291.36} \times 100 = 7.63\%\)
• Nitrogen (N): \(\frac{14.01}{291.36} \times 100 = 4.81\%\)
• Oxygen (O): \(\frac{16.00}{291.36} \times 100 = 5.49\%\)
• Chlorine (Cl): \(\frac{35.45}{291.36} \times 100 = 12.17\%\)

This process allows scientists to determine how much of each element is present relative to the whole compound, which is essential in various fields such as chemistry, pharmacology, and environmental science.