Problem 23 - General Chemistry: Principles and Modern Applications

Question

Determine the mass percent of each of the elements in the antimalarial drug quinine, \(\mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{2}\)

Step-by-Step Solution

Answer

The percentage composition by mass of each element in quinine, \(\mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{2}\), is computed by the formulas given. The exact values will require calculator usage to complete these calculations.

Step 1: Compute the Molar Mass of Quinine

The molar mass of quinine is calculated by adding the molar masses of all the atoms in one molecule. Given that Carbon (C) has an atomic weight of approximately 12.01 g/mol, Hydrogen (H) has an approximate atomic weight of 1.008 g/mol, Nitrogen (N) has an atomic weight of approximately 14.01 g/mol, and Oxygen (O) weighs about 16 g/mol yields: \( \text{Molar mass of quinine} = (20 \times 12.01 \, \text{g/mol}) + (24 \times 1.008 \, \text{g/mol}) + (2 \times 14.01 \, \text{g/mol}) + (2 \times 16 \, \text{g/mol}) \)

Step 2: Determine the Molar Mass of Each Element in Quinine

Calculate the molar mass contributed by each element by multiplying the atomic weight of each element by the number of atoms of that element in the molecule. For example, for Carbon: \( \text{Molar mass of C in quinine} = 20 \times 12.01 \, g/mol \). Repeat this for Hydrogen, Nitrogen, and Oxygen.

Step 3: Use the Formula to Calculate Percent Composition

To find the percent composition, divide the molar mass of each element by the molar mass of quinine, and then multiply the result by 100%. For example, for Carbon: \( \text{Percent composition of C} = \left(\frac{\text{Molar mass of C in quinine}}{\text{Molar mass of quinine}}\right) \times 100\% \). Compute this for every element.

Key Concepts

Molar Mass

The concept of molar mass is pivotal in chemistry as it represents the mass of one mole of a given substance. It is measured in grams per mole (g/mol) and is calculated by summing up the atomic masses of all atoms in the molecule present in the chemical formula. For a compound like quinine (\(\text{C}_{20}\text{H}_{24}\text{N}_{2}\text{O}_{2}\), the molar mass is found by adding the individual atomic weights of carbon, hydrogen, nitrogen, and oxygen accordingly:

• Carbon (C): 20 atoms with an atomic mass of approximately 12.01 g/mol.
• Hydrogen (H): 24 atoms each weighing about 1.008 g/mol.
• Nitrogen (N): 2 atoms, each having an atomic weight of 14.01 g/mol.
• Oxygen (O): 2 atoms with an atomic mass of 16 g/mol.

To obtain the total molar mass of quinine, we calculate: \[(20 \times 12.01) + (24 \times 1.008) + (2 \times 14.01) + (2 \times 16)\]This results in the molar mass value which is essential in assessing other chemical properties such as the percent composition.

Percent Composition

Percent composition is a vital concept that helps to elucidate how much of each element makes up a compound. It indicates the proportion, expressed in percentage, of each element present in the compound based on its molar mass. For quinine, determining the percent composition involves several calculation steps:

• Firstly, compute the molar mass of each element within the quinine molecule as previously determined.
• Then, divide the molar mass of each element by the total molar mass of the compound.
• Multiply each result by 100 to convert the ratio into a percentage.

For example, the percent composition of carbon in quinine is calculated by:\[\left(\frac{\text{Molar mass of Carbon in quinine}}{\text{Total molar mass of quinine}}\right) \times 100\%\]Using this formula consistently will provide the percent composition for Hydrogen, Nitrogen, and Oxygen in the molecule as well.

Antimalarial drug quinine

Quinine is a well-known antimalarial drug derived from the bark of the cinchona tree. It has been used historically to treat malaria, a disease caused by parasites transmitted through the bites of infected mosquitoes.
Quinine's chemical significance in medicine lies in its ability to effectively target and eradicate the malaria parasite, therefore preventing the disease's proliferation in the human body.
The chemical structure of quinine is quite complex:

• Quinine is represented with the chemical formula \(\text{C}_{20}\text{H}_{24}\text{N}_{2}\text{O}_{2}\).
• This formula reveals the presence of 20 carbon, 24 hydrogen, 2 nitrogen, and 2 oxygen atoms.

Understanding the composition and chemical structure of quinine aids chemists and pharmacologists in exploring its reactions and therapeutic behaviors in biological settings.

Chemical Formula Analysis

Chemical formula analysis involves evaluating the specific arrangement and quantity of atoms within a molecule. This helps in comprehending the compound's characteristics and chemical behavior.
Analyzing quinine's formula \(\text{C}_{20}\text{H}_{24}\text{N}_{2}\text{O}_{2}\):

• It is evident that quinine is a complex molecule laden with different types of elements in varying numbers.
• This formula is interpreted by discerning how many atoms of each element are present in one molecule of quinine.

The detailed analysis also assists in performing activities such as determining molar mass or percent composition. Additionally, studying its chemical formula provides insight into potential molecular interactions and its medicines or drugs' role, such as preventing malaria in the case of quinine. Understanding this allows scientific exploration into broader applications beyond its current uses.