Question

Four \(1-1\) flasks are separately filled with the gas hydrogen, helium, oxygen and ozone at the same room temperature and pressure. The ratio of total number of atoms of these gases present in the different flasks would be (a) \(1: 1: 1: 1\) (b) \(1: 2: 2: 3\) (c) \(2: 1: 2: 3\) (d) \(1: 2: 2: 1\)

Short answer

The ratio of the total number of atoms of these gases is (c) 2:1:2:3.

Step-by-step solution

Understand the Molecular Composition

Determine the molecular composition of each gas. Hydrogen (H2) is a diatomic molecule consisting of 2 atoms per molecule. Helium (He) is a monoatomic noble gas with one atom per molecule. Oxygen (O2) is also a diatomic molecule with 2 atoms per molecule. Ozone (O3) consists of 3 oxygen atoms per molecule.

Calculate the Total Number of Atoms per Flask

Since each flask contains the gases at the same conditions of temperature and pressure, they all contain the same number of molecules (Avogadro's Law). To find the total number of atoms for each gas, multiply the number of molecules by the number of atoms per molecule. For hydrogen and oxygen, this is 2 atoms per molecule. For helium, it is 1 atom per molecule, and for ozone, it is 3 atoms per molecule.

Establish the Ratio of Atoms

Using the molecule-to-atom conversion from the previous step, establish the ratios. With the same number of molecules in each flask, the ratio of total atoms is simply the ratio of atoms per molecule: Hydrogen has 2, Helium has 1, Oxygen has 2, and Ozone has 3.

Identify the Correct Option

Matching our ratio of 2:1:2:3 with the given options confirms that option (c) '2:1:2:3' is correct.

Key concepts

Molecular Composition

Understanding molecular composition is foundational to mastering stoichiometry problems in chemistry. In simple terms, molecular composition refers to the kinds and numbers of atoms that make up a molecule. For example, a water molecule (H₂O) is composed of two hydrogen atoms and one oxygen atom.

It's crucial to recognize whether a substance is monoatomic like helium (He), diatomic like hydrogen (H₂) and oxygen (O₂), or triatomic like ozone (O₃). This knowledge helps us to determine how many atoms are present in a sample of gas at given conditions, laying the groundwork for more complex stoichiometry calculations.

When solving problems, a clear understanding of molecular composition enables students to set up proper ratios and conversions, leading to accurate solutions.

Avogadro's Law

Avogadro's Law is a fundamental principle in chemistry that states at the same temperature and pressure, equal volumes of all gases contain the same number of molecules. The number of molecules is always a constant number, known as Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol).

This law holds true regardless of the chemical nature of the gas. Thus, if we have equal volumes of different gases under the same conditions, we can infer that each volume has an equal number of molecules. In terms of stoichiometry, this principle allows us to compare the amounts of substances reacting or produced in a chemical reaction using their volumes as a proxy, assuming the reactions involve gases at constant temperature and pressure.

Gas Laws in Chemistry

The gas laws in chemistry are a set of rules that describe the behavior of gases in response to changes in temperature, pressure, and volume. They include Boyle's Law (pressure and volume), Charles' Law (volume and temperature), and Gay-Lussac's Law (pressure and temperature), among others.

These gas laws are foundational for solving stoichiometry problems involving gas reactions and are often used in conjunction with Avogadro's Law. By understanding how these variables interact, chemists can predict how gases will react under different conditions and calculate unknowns. For instance, if the pressure and temperature conditions are kept constant (as in the original exercise), comparing the number of gas molecules simply becomes a matter of applying Avogadro's Law, thereby sidestepping the complexities introduced by altering temperature or pressure.

Molecules to Atoms Conversion

In chemistry, converting molecules to atoms is an essential skill for understanding the composition of substances and the stoichiometry of reactions. We achieve this by using the molecular formula to determine the number of atoms of each element in a single molecule, then multiplying by the number of molecules.

For example, consider a diatomic molecule such as oxygen (O₂). If we have Avogadro's number of oxygen molecules, we effectively have twice Avogadro's number of oxygen atoms, as each molecule contains two oxygen atoms. This conversion from molecules to atoms is critical for establishing ratios and quantities in chemical equations and when predicting the outcome of reactions, particularly when dealing with gases as in the text problem.