Question

Quinine, \(\mathrm{C}_{20} \mathrm{H}_{24} \mathrm{~N}_{2} \mathrm{O}_{2}\), is a component of tonic water and bitter lemon. a. How many moles of hydrogen are in \(1.0\) mole of quinine? b. How many moles of carbon are in \(5.0\) moles of quinine? c. How many moles of nitrogen are in \(0.020\) mole of quinine?

Short answer

a) 24 moles H, b) 100 moles C, c) 0.040 moles N

Step-by-step solution

- Identify the number of atoms per molecule

Quinine has the chemical formula \(\text{C}_{20}\text{H}_{24}\text{N}_{2}\text{O}_{2}\). This indicates that each molecule of quinine contains 20 carbon atoms, 24 hydrogen atoms, 2 nitrogen atoms, and 2 oxygen atoms.

- Calculate moles of hydrogen in 1.0 mole of quinine

Since there are 24 hydrogen atoms in one molecule of quinine, there will be 24 times the number of moles of hydrogen atoms per mole of quinine. \[ n(\text{H}) = 1.0 \text{ mole quinine} \times 24 \frac{\text{moles H}}{\text{mole quinine}} = 24 \text{ moles H} \]

- Calculate moles of carbon in 5.0 moles of quinine

Since there are 20 carbon atoms in one molecule of quinine, there will be 20 times the number of moles of carbon atoms per mole of quinine. \[ n(\text{C}) = 5.0 \text{ moles quinine} \times 20 \frac{\text{moles C}}{\text{mole quinine}} = 100 \text{ moles C} \]

- Calculate moles of nitrogen in 0.020 mole of quinine

Since there are 2 nitrogen atoms in one molecule of quinine, there will be 2 times the number of moles of nitrogen atoms per mole of quinine. \[ n(\text{N}) = 0.020 \text{ mole quinine} \times 2 \frac{\text{moles N}}{\text{mole quinine}} = 0.040 \text{ moles N} \]

Key concepts

Mole concept

The mole concept is fundamental in chemistry. It helps in quantifying substances based on their number of particles. One mole represents Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles.
This number links the microscopic world of atoms to the macroscopic world we experience. For instance, when we say we have one mole of hydrogen atoms, we know we have \(6.022 \times 10^{23}\) hydrogen atoms.
This unit conversion is extremely useful in chemistry calculations because it allows chemists to work with manageable amounts of substances.
In the given exercise, the mole concept is used to determine the number of moles of different atoms in the compound quinine. For example:

• 1 mole of quinine has 24 moles of hydrogen atoms.
• 5 moles of quinine has 100 moles of carbon atoms.
• 0.020 moles of quinine has 0.040 moles of nitrogen atoms.

Chemical formula

A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound. It uses symbols for the chemical elements and subscripts to indicate the number of each type of atom.
In our example, quinine has the chemical formula \( \text{C}_{20}\text{H}_{24}\text{N}_{2}\text{O}_{2} \). This tells us several important things:

• There are 20 carbon (\text{C}) atoms.
• There are 24 hydrogen (\text{H}) atoms.
• There are 2 nitrogen (\text{N}) atoms.
• There are 2 oxygen (\text{O}) atoms.

The chemical formula is essential to understanding how substances are composed on a molecular level. It forms the basis for calculating the moles of each element present in a compound. By knowing the formula, we can analyze the composition and reactions of that substance more efficiently.

Molecular composition

Molecular composition refers to the types and numbers of atoms present in a molecule of a substance. Understanding a molecule's composition helps predict its properties and reactions.
For quinine, the chemical formula \( \text{C}_{20}\text{H}_{24}\text{N}_{2}\text{O}_{2} \) provides a complete picture of its molecular composition. We understand that each quinine molecule is built from:

• 20 carbon atoms
• 24 hydrogen atoms
• 2 nitrogen atoms
• 2 oxygen atoms

Each element's specific number allows us to determine the total quantity of each element when handling multiple moles of the compound. For example, when calculating the moles of a particular element in multiple moles of quinine:

• Multiply the number of moles of quinine by the number of atoms of that element in one molecule of quinine.

By knowing the molecular composition, we can also infer other properties like molecular weight and how the molecule might interact in chemical reactions. For instance, quinine’s composition suggests it’s a complex organic molecule, contributing to its unique properties in medicinal chemistry.