Question

State the number of moles represented by each of the following: (a) \(6.02 \times 10^{23}\) atoms of sulfur, S (b) \(6.02 \times 10^{23}\) molecules of sulfur dioxide, \(\mathrm{SO}_{2}\)

Short answer

(a) 1 mole of sulfur atoms (b) 1 mole of sulfur dioxide molecules

Step-by-step solution

Understand the Problem

The problem asks for the number of moles represented by a given number of atoms or molecules. We are provided with quantities expressed in terms of Avogadro's number, which relates the number of particles to moles.

Apply Avogadro's Number for Part a

Avogadro's number is defined as approximately \(6.02 \times 10^{23}\) particles per mole. For part (a), we have \(6.02 \times 10^{23}\) atoms of sulfur (S). One mole of any substance contains Avogadro's number of particles, so \(6.02 \times 10^{23}\) atoms of sulfur represent 1 mole of sulfur.

Apply Avogadro's Number for Part b

Similarly, for part (b), \(6.02 \times 10^{23}\) molecules of sulfur dioxide (\(\mathrm{SO}_2\)) also represent Avogadro's number of molecules. Thus, this quantity corresponds to 1 mole of sulfur dioxide molecules.

Key concepts

Understanding Moles

A mole is a fundamental concept in chemistry that provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. It is a handy unit for expressing amounts of a chemical substance. Think of a mole like a chemist's dozen, but much larger. Just as a dozen eggs means 12 eggs, a mole means a specific number of particles: Avogadro's number, which is approximately \(6.02 \times 10^{23}\) particles.

• The mole allows chemists to count particles by weighing them. This is crucial because chemical reactions occur at the atomic and molecular levels, but we measure quantities in the lab by mass.
• The specific number \(6.02 \times 10^{23}\) is based on the number of atoms in 12 grams of carbon-12, which is a standard reference.

Understanding moles helps us perform calculations involving masses, volumes, and the number of particles, and it simplifies the complex world of chemistry into something more manageable.

The Nature of Atoms

Atoms are the building blocks of matter, and everything around us is composed of atoms. Each atom consists of a nucleus—made up of protons and neutrons—surrounded by electrons. These particles are incredibly tiny, which is why we use a large number like Avogadro's number to quantify them in terms of moles.

• For example, when chemists talk about 1 mole of sulfur, they're referring to \(6.02 \times 10^{23}\) sulfur atoms.
• This large number makes it feasible to perform experiments and create useful scientific models.

Atoms are distinct and unique for each element, and they determine the properties of the substances they form. The way atoms combine to form molecules defines chemistry itself.

Molecules and Chemical Compounds

A molecule is formed when two or more atoms bond together. Molecules are the smallest units of a chemical compound that can exist while retaining the chemical properties of that compound. For instance, a molecule of sulfur dioxide, \(\mathrm{SO}_2\), consists of one sulfur atom bonded to two oxygen atoms.

• Molecules can be simple, like \(\mathrm{O}_2\), which we breathe, or very complex, like proteins and DNA.
• Understanding the concept of molecules broadens our recognition of how substances interact and change in chemical reactions.

When dealing with amounts of molecules, chemists also use moles. Just as in the example problem, we know that \(6.02 \times 10^{23}\) molecules of \(\mathrm{SO}_2\) equal 1 mole, tying the concept of moles with molecules to simplify and guide chemical calculations.