Question

How many atoms are there in 5.10 moles of sulfur (S)?

Short answer

There are approximately \(3.07122 \times 10^{24}\) atoms in 5.10 moles of sulfur.

Step-by-step solution

Understanding Moles in Chemistry

In chemistry, a mole is a unit representing a quantity of substance. One mole contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\) atoms, molecules, or particles.

Applying Avogadro's Number

To find the number of atoms in 5.10 moles of sulfur, use the formula: \[\text{Number of atoms} = \text{moles} \times \text{Avogadro's number} \]Here, moles = 5.10 and Avogadro's number = \(6.022 \times 10^{23}\).

Performing the Calculation

Substitute the values into the formula:\[\text{Number of atoms} = 5.10 \times 6.022 \times 10^{23}\approx 3.07122 \times 10^{24}\text{ atoms}\]Therefore, there are approximately \(3.07122 \times 10^{24}\) atoms in 5.10 moles of sulfur.

Key concepts

Moles in Chemistry

A mole in chemistry is a basic unit that helps scientists to measure large quantities of very small entities like atoms and molecules. Think of a mole as a bridge between the microscopic world that we cannot see, and the macroscopic quantities we can measure and observe.

The idea is similar to a dozen: just as one dozen equals 12 items of anything you count, one mole represents approximately 6.022 x 10²³ atoms, molecules, or particles. This number is known as Avogadro's number, and it enables chemists to count particles in a single mole in the same way we count items in groups of twelve with a dozen.

When you're dealing with grams, moles help to convert these into an actual number of particles. This is because the mass of a substance and the number of moles can be easily related by the substance's molar mass, which is the mass of one mole of that substance expressed in grams per mole. This characteristic makes moles particularly indispensable in chemical equations and reactions where precise amounts are crucial.

Avogadro's Number

Avogadro's number, which is approximately 6.022 x 10²³, is a fundamental constant in chemistry. It denotes the number of atoms, molecules, or particles contained in one mole of a substance.

The history of Avogadro’s number dates back to the early 19th century when Amedeo Avogadro hypothesized that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This idea laid the groundwork for this critical constant that links the micro and macro aspects of chemistry.

Avogadro's number is incredibly large, illustrating how small atoms and molecules actually are. It allows chemists to work comfortably with laboratory-sized quantities and gives them the ability to convert between the mass of a sample and the number of constituent particles. It acts as a pivotal factor in the calculation of atoms, molecules, or ions within a given substance, such as our task of calculating atoms in moles of sulfur.

Sulfur Atoms Calculation

To calculate the number of sulfur atoms in a given number of moles, such as 5.10 moles, start by understanding that each mole contains Avogadro's number of atoms.

Next, multiply the number of moles by Avogadro's number to determine the total number of atoms:

• Start with: 5.10 moles of sulfur
• Multiply by: 6.022 x 10²³ atoms/mole
• The formula: Number of atoms = 5.10 x 6.022 x 10²³

By performing the multiplication, you will find that:

• Number of atoms ≈ 3.07122 x 10²⁴ atoms

This result illustrates that in 5.10 moles of sulfur, there are approximately 3.07122 x 10²⁴ sulfur atoms. This kind of calculation is a vital skill for chemists when it comes to understanding how much of a substance they are dealing with in terms of particles.