Question

Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing number of atoms: \(9.0 \times 10^{23}\) molecules of \(\mathrm{H}_{2} \mathrm{O}_{2}, 2.0 \mathrm{~mol} \mathrm{CH}_{4}, 16 \mathrm{~g} \mathrm{O}_{2}\)

Short answer

The order of increasing number of atoms for the given samples, without doing detailed calculations, is: O2 < H2O2 < CH4.

Step-by-step solution

Identify atomic weights

Refer to the periodic table to find the atomic weights of the elements involved in the samples: - Hydrogen (H): 1 g/mol - Oxygen (O): 16 g/mol - Carbon (C): 12 g/mol

Calculating number of atoms in sample 1

Given: - \(9.0 \times 10^{23}\) molecules of H2O2 Each molecule of H2O2 contains 2 hydrogen atoms and 2 oxygen atoms: - Number of H atoms = \(9.0 \times 10^{23} \times 2\) - Number of O atoms = \(9.0 \times 10^{23} \times 2\) Total number of atoms in H2O2 = H atoms + O atoms

Calculating number of atoms in sample 2

Given: - 2.0 moles of CH4 Each molecule of CH4 contains 1 carbon atom and 4 hydrogen atoms. We know the number of atoms in a mole = Avogadro's Number (6.022 x 10^23). So, for 2 moles of CH4, atoms: - Number of H atoms = \(2 \times 4 \times (6.022 \times 10^{23})\) - Number of C atoms = \(2 \times 1 \times (6.022 \times 10^{23})\) Total number of atoms in CH4 = H atoms + C atoms

Calculating number of atoms in sample 3

Given: - 16 g of O2 Each molecule of O2 has 2 oxygen atoms. Oxygen has a molar mass of 16 g/mol. To find the number of moles in 16 g of O2, we can use the formula: Moles (O2) = (Mass of O2) / (Molar mass of O2) = \(16/32\) = 0.5 moles Now we can find the number of atoms: - Number of O atoms = \(0.5 \times 2 \times (6.022 \times 10^{23})\) Total number of atoms in O2 = O atoms

Rank the samples

Now, we'll compare the number of atoms in each sample: 1. H2O2: atoms = \(9.0 \times 10^{23} \times 2\) 2. CH4: atoms = \(2 \times 5 \times (6.022 \times 10^{23})\) 3. O2: atoms = \(0.5 \times 2 \times (6.022 \times 10^{23})\) The order of increasing number of atoms: O2 < H2O2 < CH4

Key concepts

Molecular Composition

Molecular composition refers to the types and numbers of atoms in a molecule. Different molecules have unique compositions, which determine their chemical properties. For example, hydrogen peroxide (H2O2) is composed of two hydrogen atoms and two oxygen atoms. This composition defines its chemical behavior, like being a bleaching agent. Methane (CH4), on the other hand, is made up of one carbon atom and four hydrogen atoms, making it a primary component of natural gas.

When analyzing molecular composition, it’s crucial to consider both the types of atoms present and their quantities. These factors directly influence the molecule’s mass and properties. In stoichiometry, understanding molecular composition is vital to calculate numbers of atoms or molecules in chemical reactions and equations. Keep in mind, a molecule's reactivity and physical properties depend largely on its molecular structure.

Periodic Table

The periodic table is a tabular display of chemical elements arranged by atomic number, electron configuration, and recurring chemical properties. It serves as a useful reference for understanding an element's properties and its interactions with other elements.

Each element in the periodic table has a unique atomic weight or molar mass, usually expressed in grams per mole. This is crucial when dealing with stoichiometry because it allows you to convert between mass and moles, a fundamental stoichiometric skill. For instance, oxygen has an atomic weight of 16 g/mol, which means one mole of oxygen atoms weighs 16 grams.

• The periodic table is divided into metals, non-metals, and metalloids.
• Groups/families on the table show elements with similar chemical properties.
• Periods are rows that indicate the number of electron shells.

Memorizing how to quickly locate an element and understand its basic properties from the periodic table can save time in more complex calculations.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is a fundamental constant used in chemistry. It represents the number of atoms, ions, or molecules in one mole of a substance. This number is crucial for converting between atoms/molecules and moles in chemical equations.

Understanding Avogadro's number is key to grasping the concept of the mole. For example, in one mole of carbon atoms, there are 6.022 x 10^23 carbon atoms. This standardized quantity helps chemists quantify elements and compounds at the atomic level universally.

• Avogadro's number allows chemists to work with the microscopic world using macroscopic measurements.
• It links the atomic scale to everyday quantities.
• Using this number, chemists can equate masses of substances to their quantities in terms of atoms or molecules.

Mastering Avogadro's number is essential for anyone studying chemistry and sets the foundation for more advanced topics in stoichiometry.