Question

Determine the number of moles of oxygen atoms in each sample. a. \(4.88 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}_{2}\) b. \(2.15 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}\) c. \(0.0237 \mathrm{~mol} \mathrm{H}_{2} \mathrm{CO}_{3}\) d. \(24.1 \mathrm{~mol} \mathrm{CO}_{2}\)

Short answer

a. 9.76 mol O atoms, b. 2.15 mol O atoms, c. 0.0711 mol O atoms, d. 48.2 mol O atoms

Step-by-step solution

Relate moles of substance to moles of oxygen atoms

Understand that the number of moles of oxygen atoms in a compound can be found by multiplying the number of moles of the compound by the number of oxygen atoms in one molecule of that compound. For example, in one molecule of water (H2O), there are two hydrogen atoms and one oxygen atom.

Calculate moles of oxygen in \(4.88 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}_{2}\)

Hydrogen peroxide (\(\mathrm{H}_{2} \mathrm{O}_{2}\)) has two oxygen atoms per molecule. Multiply the moles of \(\mathrm{H}_{2} \mathrm{O}_{2}\) by 2 to find the moles of oxygen atoms: \(4.88 \mathrm{~mol} \times 2 = 9.76 \mathrm{~mol}\) oxygen atoms.

Calculate moles of oxygen in \(2.15 \mathrm{~mol} \mathrm{N}_{2} \mathrm{O}\)

Dinitrogen monoxide (\(\mathrm{N}_{2} \mathrm{O}\)) has one oxygen atom per molecule. Multiply the moles of \(\mathrm{N}_{2} \mathrm{O}\) by 1 to find the moles of oxygen atoms: \(2.15 \mathrm{~mol} \times 1 = 2.15 \mathrm{~mol}\) oxygen atoms.

Calculate moles of oxygen in \(0.0237 \mathrm{~mol} \mathrm{H}_{2} \mathrm{CO}_{3}\)

Carbonic acid (\(\mathrm{H}_{2} \mathrm{CO}_{3}\)) has three oxygen atoms per molecule. Multiply the moles of \(\mathrm{H}_{2} \mathrm{CO}_{3}\) by 3 to find the moles of oxygen atoms: \(0.0237 \mathrm{~mol} \times 3 = 0.0711 \mathrm{~mol}\) oxygen atoms.

Calculate moles of oxygen in \(24.1 \mathrm{~mol} \mathrm{CO}_{2}\)

Carbon dioxide (\(\mathrm{CO}_{2}\)) has two oxygen atoms per molecule. Multiply the moles of \(\mathrm{CO}_{2}\) by 2 to find the moles of oxygen atoms: \(24.1 \mathrm{~mol} \times 2 = 48.2 \mathrm{~mol}\) oxygen atoms.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the reactants and products in chemical reactions. In practice, stoichiometry is all about the balance of elements in chemical equations. For students, understanding stoichiometry starts with the basic concept that matter is conserved in chemical reactions – atoms aren't lost, they're rearranged.

When you're given an amount of a chemical substance, such as moles, stoichiometry allows you to predict how much of another substance is involved in the reaction, whether it be reactants or products. One of the fundamental stoichiometric relationships is based on the chemical formula of substances, where the coefficients in the balanced equation indicate the relative number of moles of each substance involved.

Applying stoichiometry to a problem where we determine moles of oxygen atoms in a compound involves counting the number of oxygen atoms per molecule of the substance (given by its chemical formula) and multiplying by the total moles of the substance you have. This is precisely the approach taken in the exercise example provided.

Molar Mass Calculation

The concept of molar mass is vital in stoichiometry as it links the mass of a substance to the number of moles, which is a counting unit similar to 'dozen' for eggs, but for atoms and molecules. By definition, the molar mass is the mass of one mole of a substance, and it can be calculated from the chemical formula by summing the atomic masses of all atoms in the molecule.

Molar mass calculation often serves as an intermediate step in stoichiometry problems, especially when converting between mass and moles of a substance. It's not directly asked for in the exercise provided, but it's crucial to understand the concept as it may play a role in more complex scenarios, where you might need to convert grams to moles or vice versa before finding the number of moles of a particular atom within the compound.

Chemical Formula

Chemical formulas represent the types and numbers of atoms that make up a molecule. For example, the formula for water, H2O, means each molecule has two hydrogen atoms and one oxygen atom. Understanding chemical formulas is critical for stoichiometry since it provides the ratio of each kind of atom in a molecule, directly impacting the mole calculations.

When calculating the moles of an atom in a sample, as in the exercise, the chemical formula tells you how many atoms of each element are in one molecule of the compound. Using the formula, you can then relate this to the amount of the substance, often given in moles, to find out the total number of moles of the desired atom. In this way, the chemical formula is like a recipe that tells you how many of each ingredient you have when you know how many batches of the recipe (or moles of the compound) you have.