Question

State the number of moles represented by each of the following: (a) \(6.02 \times 10^{23}\) atoms of lithium, \(\mathrm{Li}\) (b) \(6.02 \times 10^{23}\) molecules of bromine, \(\mathrm{Br}_{2}\)

Short answer

(a) 1 mole of lithium atoms, (b) 1 mole of bromine molecules.

Step-by-step solution

Understanding Avogadro's number

Avogadro's number is a constant that tells us how many particles, such as atoms or molecules, are present in one mole of a substance. This number is approximately \(6.02 \times 10^{23}\).

Calculating moles of lithium atoms

To convert from atoms to moles, use Avogadro’s number. For lithium (\(\mathrm{Li}\), part (a)): If you have \(6.02 \times 10^{23}\) atoms of lithium, you can directly equate this to 1 mole because by definition \(1\) mole \(= 6.02 \times 10^{23}\) particles.

Calculating moles of bromine molecules

Similarly, for bromine molecules (\(\mathrm{Br}_2\), part (b)): \(6.02 \times 10^{23}\) molecules of bromine also correspond to 1 mole, using the definition of Avogadro's number.

Key concepts

Understanding Moles

A mole is a fundamental unit in chemistry used to express the quantity of a chemical substance. Think of it like a dozen, which represents 12 items. When chemists talk about a mole, they are talking about Avogadro's number of particles, which is approximately \(6.02 \times 10^{23}\). This could be atoms, molecules, or any other basic unit. Why \(6.02 \times 10^{23}\) ? It’s a scaling factor that allows chemists to count out elements and compounds in laboratory-sized quantities. Instead of dealing with the tiny masses of atoms individually, the mole allows us to convert this small scale into something more palpable.

• 1 mole of any substance contains \(6.02 \times 10^{23}\) of its respective particles.
• This concept is universal, meaning it applies to atoms, molecules, ions, and other particles alike.

This makes moles a very convenient way to relate mass to the number of particles, allowing chemists to use balance scales effectively in the lab.

Counting Lithium Atoms

Lithium, represented by its symbol \(\mathrm{Li}\), is a commonly studied element in chemistry due to its simple atomic structure. When we talk about \(6.02 \times 10^{23}\) atoms of lithium, we are talking about exactly one mole of lithium. Here’s how it works:

• If you have \(6.02 \times 10^{23}\) lithium atoms, you directly have 1 mole of lithium.
• This is because the definition of a mole is tied to Avogadro's number, so these quantities are always equivalent by definition.
• This relationship makes it incredibly straightforward to calculate the number of moles when given the number of atoms.

This straightforward conversion is one reason Avogadro's number is so pivotal in chemistry—making it easier to work with atoms on a human scale.

Working with Bromine Molecules

Bromine, denoted as \(\mathrm{Br}_2\), often exists as diatomic molecules, meaning each molecule contains two bromine atoms. When you are given \(6.02 \times 10^{23}\) bromine molecules, you again have 1 mole. Here's why:

• Just like with atoms, molecules follow the rule of Avogadro's number.
• \(6.02 \times 10^{23}\) molecules of bromine equates to 1 mole of bromine molecules.
• Although a single \(\mathrm{Br}_2\) molecule consists of two atoms, when considering molecules for moles, it’s these units of \(\mathrm{Br}_2\) that are counted.

This is crucial for reactions and stoichiometry in chemistry, where knowing how many molecules react or form helps predict the outcomes and quantities accurately.