Question

How many \(\mathrm{SO}_{2}\) molecules are in \(1.75\) mol of \(\mathrm{SO}_{2}\) ? How many sulfur atoms and oxygen atoms are there?

Short answer

There are \(1.054 \times 10^{24}\) \(\mathrm{SO}_{2}\) molecules, \(1.054 \times 10^{24}\) Sulfur atoms, and \(2.108 \times 10^{24}\) Oxygen atoms in \(1.75\) mol of \(\mathrm{SO}_{2}\).

Step-by-step solution

Calculate the number of \(\mathrm{SO}_{2}\) molecules

To find how many \(\mathrm{SO}_{2}\) molecules are in \(1.75\) mol of \(\mathrm{SO}_{2}\), multiply the number of moles by Avogadro's number \(6.022 \times 10^{23}\). So, \(1.75 \times 6.022 \times 10^{23} = 1.054 \times 10^{24}\) \(\mathrm{SO}_{2}\) molecules.

Calculate the number of Sulfur atoms

Each molecule of \(\mathrm{SO}_{2}\) contains one sulfur atom. So, the number of sulfur atoms in \(1.75\) mol of \(\mathrm{SO}_{2}\) is equal to the number of \(\mathrm{SO}_{2}\) molecules, \(1.054 \times 10^{24}\).

Calculate the number of Oxygen atoms

Each molecule of \(\mathrm{SO}_{2}\) contains two oxygen atoms, so the number of oxygen atoms is twice the number of \(\mathrm{SO}_{2}\) molecules. \((2\times1.054) \times 10^{24}=2.108\times10^{24}\) oxygen atoms.

Key concepts

Avogadro's Number

Avogadro's Number is a cornerstone concept in chemistry, crucial for understanding the mole concept. Named after the Italian scientist Amedeo Avogadro, it is defined as the number of constitutive particles, typically atoms or molecules, that are contained in one mole of a substance. This number is a constant and is approximately valued at 6.022 x 10^{23}.
This immense number helps chemists count particles at the atomic scale. When you have a mole of any substance, you're effectively holding 6.022 x 10^{23} of its molecules or atoms. So, when given 1.75 moles of sulfur dioxide (SO_2), multiplying by Avogadro's Number reveals that you have 1.054 x 10^{24} molecules of SO_2, providing a bridge from theoretical chemistry to practical, observable quantities.

Sulfur Dioxide Molecule

Sulfur dioxide, or SO_2, is a molecule composed of one sulfur atom and two oxygen atoms. It plays significant roles in both natural and industrial processes. It's a gas at room temperature, known for its pungent smell, often associated with burning sulfur.
When looking at sulfur dioxide in chemical reactions or in stoichiometric calculations, it's essential to note its molecular composition. Each SO_2 molecule includes:

• 1 sulfur atom
• 2 oxygen atoms

Given this composition, if you have a mole of SO_2, you're dealing with the equivalent number of sulfur atoms as molecules, and twice that number of oxygen atoms. Hence, if you have 1.75 moles of SO_2, you directly have 1.054 x 10^{24} sulfur atoms, and twice that count for oxygen atoms, equating to 2.108 x 10^{24}.

Chemical Stoichiometry

Chemical stoichiometry is the aspect of chemistry that deals with the quantitative relationships in chemical reactions. Using stoichiometry allows chemists to predict the amount of product formed or reactants needed in a reaction. It places a particular focus on the ratios of moles and molecules involved.
For sulfur dioxide (SO_2), stoichiometry assists in calculating the exact number of atoms within measurable quantities of the substance. Given a mole quantity of a compound, stoichiometry uses Avogadro's Number to translate that into a molecular count. Then, understanding the molecular makeup of SO_2 lets one break that down further into individual atoms, achieving precision in both theoretical and practical applications. So, when you compute that there are 1.054 x 10^{24} molecules of SO_2 in 1.75 moles, stoichiometry is the vital tool that informs of equal sulfur atoms and double the oxygen atoms at 2.108 x 10^{24} in structural understanding and chemical balanced reactions.