Question

Tiwo flasks \(A\) and \(B\) of \(500 \mathrm{~mL}\) each are respectively filled with \(\mathrm{O}_{2}\) and \(\mathrm{SO}_{2}\) at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\). pressure. The flasks will contain: (a) The same number of atoms (b) The same number of molecules (c) More number of moles of molecules in flask \(A\) as compared to flask \(B\) (d) The same amount of gases

Short answer

The flasks contain the same number of molecules (b) and the same amount of gases (d), but they do not contain the same number of atoms nor do they have more moles of molecules in one flask compared to the other.

Step-by-step solution

Understanding the concept of a mole

Know that a mole of any substance contains the same number of molecules (Avogadro's number, which is approximately 6.022 x 10^23). Regardless of the type of molecule, at the same temperature and pressure, equal volumes of all gases contain the same number of molecules (Avogadro's Law).

Relating the gas conditions to moles

Since both flasks are at the same temperature and pressure and have the same volume, they contain equal numbers of moles of gas, according to Avogadro's Law.

Analyzing the type of molecules

Flask A contains O2 (oxygen gas) molecules and Flask B contains SO2 (sulfur dioxide) molecules. Oxygen molecules consist of two atoms, while sulfur dioxide molecules consist of three atoms (one sulfur and two oxygen atoms).

Determining the number of molecules and atoms

Since both flasks contain the same number of moles, they consequently contain an equal number of molecules. However, the number of atoms will differ due to the different number of atoms per molecule in oxygen versus sulfur dioxide.

Making conclusions based on the analyzed data

Option (a) is incorrect because Flask A will have double the number of oxygen atoms compared to the number of sulfur atoms in Flask B, but Flask B will have more total atoms due to the presence of oxygen atoms in SO2. Option (b) is correct because both flasks have the same number of moles and therefore the same number of molecules. Option (c) is incorrect because the number of moles of gas is the same in both flasks. Option (d) is correct because the amount of gas is dependent on the number of moles, and the number of moles is the same in both flasks.

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure in the laboratory. A mole is defined as the amount of a substance that contains as many entities (such as atoms, ions, or molecules) as there are atoms in 12 grams of pure carbon-12. This number is known as Avogadro's number, approximately equal to \(6.022 \times 10^{23}\).

The beauty of the mole concept lies in its universality: one mole of any substance, regardless of its identity, will contain Avogadro's number of entities. For instance, a mole of oxygen molecules (\(O_2\)) and a mole of sulfur dioxide molecules (\(SO_2\)) both contain the same number of molecules. When dealing with gases, the mole concept makes it possible to predict the behavior of the gas in reactions (stoichiometry), relating volumes and combining ratios, and more.

Stoichiometry

Stoichiometry is the section of chemistry concerned with the quantities of substances that come into play in chemical reactions. It deals with the calculation of reactants and products in chemical processes. This quantitative relationship is crucial because it ensures that reactions occur with the correct amounts of substances so none are wasted.

Stoichiometry uses the mole concept to determine the ratios in which chemicals react with each other. It's important in predicting the yields of reactions and in figuring out the optimum proportions to use when combining elements or compounds in a reaction. For instance, in a balanced chemical reaction, the coefficients represent the ratio of moles of each substance involved. By understanding this, you can accurately calculate how much product you'll get from a certain amount of reactant.

Gas Laws

Gas laws describe the behavior of gases in various situations and are crucial for understanding subjects such as chemistry, environmental science, and engineering. Avogadro's Law, one of the fundamental gas laws, states that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. This law is directly related to the mole concept; one mole of any gas at a specified temperature and pressure will occupy the same volume as any other gas.

Other essential gas laws include Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure, Charles's Law, which relates the volume of a gas to its temperature, and the Ideal Gas Law, which combines the previous laws into one equation. The gas laws are vital in understanding how gases will react under different conditions and how to manipulate these conditions to achieve desired outcomes in real-world applications.

Molecular Composition

Molecular composition refers to the types and numbers of atoms that constitute a molecule. The molecular composition determines the characteristics and behaviors of a substance, including its reactivity and physical properties. In the context of our exercise, oxygen gas (\(O_2\)) is composed of two oxygen atoms bonded together, and sulfur dioxide (\(SO_2\)) consists of one sulfur atom and two oxygen atoms bonded together.

The difference in molecular composition means that despite both flasks containing the same number of molecules, they do not contain the same number of atoms. Understanding the molecular composition helps in predicting how different substances will behave in chemical reactions, and it is closely tied to the mole concept and stoichiometry in determining the outcome of chemical processes.