Question

How many oxygen atoms are in \(0.2 \mathrm{~mol}\) of \(\mathrm{SO}_{2}\) ?

Short answer

There are \(2.4088 \times 10^{23}\) oxygen atoms in \(0.2 \mathrm{~mol}\) of \(\mathrm{SO}_{2}\).

Step-by-step solution

Understanding the molecule

A molecule of \(\mathrm{SO}_{2}\) consists of one atom of sulfur (S) and two atoms of oxygen (O). Therefore, in one molecule of \(\mathrm{SO}_{2}\), there are 2 oxygen atoms.

Identify the number of moles

The problem gives us that we have \(0.2\) moles of \(\mathrm{SO}_{2}\).

Apply Avogadro's number

We know that one mole of particles contains \(6.022 \times 10^{23}\) particles (atoms, molecules) according to Avogadro's number. Therefore, \(0.2\) moles of \(\mathrm{SO}_{2}\) molecules will contain \(0.2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{23}\) molecules of \(\mathrm{SO}_{2}\).

Calculate the number of Oxygen atoms

Since there are 2 oxygen atoms in one molecule of \(\mathrm{SO}_{2}\), \(1.2044 \times 10^{23}\) molecules of \(\mathrm{SO}_{2}\) will contain \(2 \times 1.2044 \times 10^{23} = 2.4088 \times 10^{23}\) oxygen atoms.

Key concepts

Moles

Moles are a fundamental concept in chemistry that help us count particles at a molecular level. When dealing with chemical substances, atoms, and molecules, we often work with quantities so small that using the term "mole" allows for a more practical approach. A mole is essentially a count of particles, similar to how a dozen refers to twelve units of something. Specifically, one mole is defined as exactly 6.022 x 10^23 particles of a substance. This magical number, known as Avogadro's number, makes it easier to perform calculations in chemistry.

For example, when we say we have 0.2 moles of SO2, we're expressing a specific quantity of SO2 molecules, allowing us to predict and calculate further properties of the substance, such as how many sulfur or oxygen atoms are present.

Avogadro's Number

Avogadro's number, named after the Italian scientist Amedeo Avogadro, is crucial for understanding the mole concept. This constant, 6.022 x 10^23, represents the number of particles (atoms or molecules) in one mole of a substance. It allows chemists to convert between the mass of a substance and the number of atoms or molecules present.

This gigantic number is key in bridging the gap between the macroscopic world that we can see and measure and the microscopic world of atoms and molecules. When calculating the total number of particles in any given number of moles, Avogadro's number is the multiplier. For example, when you have 0.2 moles of SO2, you multiply 0.2 by Avogadro's number to find the number of SO2 molecules, which is 1.204 x 10^23 molecules. Then, we can use this to determine the number of individual atoms or specific elements, like oxygen in a compound.

SO2 Molecule

The SO2 molecule, known as sulfur dioxide, comprises one sulfur atom and two oxygen atoms. This simple composition is important to understand when counting atoms in a chemical problem.

In the context of moles, when we say we have a certain number of moles of SO2, we're referring to these molecules in bulk. When working with a volume of 0.2 moles of SO2, for instance, applying Avogadro's number as a conversion factor tells us how many molecules of SO2 are present, and subsequently, how many oxygen atoms are included, due to the fixed ratio of two oxygen atoms per SO2 molecule.

By understanding the structure of the SO2 molecule, it becomes much easier to transition from calculating moles, using Avogadro's number, to determining the specific quantity of oxygen or any other atom in a compound. This understanding forms the basis of many chemical calculations required in academia and industry.