Question

Determine the number of moles of oxygen atoms in each sample. $$ \begin{array}{l}{\text { a. } 4.88 \text { mol } \mathrm{H}_{2} \mathrm{O}_{2}} \\ {\text { b. } 2.15 \text { mol } \mathrm{N}_{2} \mathrm{O}_{2}} \\ {\text { c. } 0.0237 \mathrm{mol} \mathrm{H}_{2} \mathrm{CO}_{3}} \\ {\text { d. } 24.1 \mathrm{mol} \mathrm{CO}_{2}}\end{array} $$

Short answer

a. 9.76 mol O, b. 8.60 mol O, c. 0.0711 mol O, d. 48.2 mol O

Step-by-step solution

- Calculate Moles of Oxygen in Hydrogen Peroxide

Determine the number of oxygen atoms in one molecule of hydrogen peroxide (H2O2). There are 2 oxygen atoms per molecule. Multiply the moles of H2O2 by 2 to find the moles of oxygen atoms. 4.88 mol H2O2 * 2 = 9.76 mol O

- Calculate Moles of Oxygen in Dinitrogen Tetroxide

Determine the number of oxygen atoms in one molecule of dinitrogen tetroxide (N2O4). There are 4 oxygen atoms per molecule. Multiply the moles of N2O4 by 4 to find the moles of oxygen atoms. 2.15 mol N2O4 * 4 = 8.60 mol O

- Calculate Moles of Oxygen in Carbonic Acid

Determine the number of oxygen atoms in one molecule of carbonic acid (H2CO3). There are 3 oxygen atoms per molecule. Multiply the moles of H2CO3 by 3 to find the moles of oxygen atoms. 0.0237 mol H2CO3 * 3 = 0.0711 mol O

- Calculate Moles of Oxygen in Carbon Dioxide

Determine the number of oxygen atoms in one molecule of carbon dioxide (CO2). There are 2 oxygen atoms per molecule. Multiply the moles of CO2 by 2 to find the moles of oxygen atoms. 24.1 mol CO2 * 2 = 48.2 mol O

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. Simply put, it's the math behind the science. It allows a chemist to predict how much of a reactant is needed to create a certain amount of product, or vice versa. At the heart of stoichiometry is the mole concept, which provides a universal measuring unit for counting atoms, molecules, ions, or other chemical entities.

To perform stoichiometric calculations, you first need to understand the balanced chemical equation involved in the reaction. This equation shows the ratio in which reactants combine to form products. However, in our textbook exercise, we aren't looking at whole reactions, but rather, individual compounds and the number of specific atoms within them. By using the ratios presented by the chemical formula of each compound, we can determine the moles of oxygen atoms present, which is a fundamental stoichiometric calculation.

Chemical Formula

A chemical formula provides significant information about the composition of a compound. It indicates the elements present and the number of atoms of each element in a molecule. For instance, the formula for water, H2O, tells us that each molecule consists of 2 hydrogen atoms and 1 oxygen atom.

In the case of our exercise, the chemical formulas given are H2O2, N2O4, H2CO3, and CO2. These formulas are the key to unlocking the number of oxygen atoms present; they tell us that hydrogen peroxide (H2O2) contains 2 oxygen atoms, dinitrogen tetroxide (N2O4) has 4, carbonic acid (H2CO3) has 3, and carbon dioxide (CO2) includes 2. By understanding how to read chemical formulas, students can easily progress to calculating the moles of each element within a compound.

Mole Concept

The mole concept is a fundamental principle in chemistry that defines the amount of substance. One mole is Avogadro's number, or approximately 6.022 x 10^23 particles, whether they be atoms, molecules, electrons, or other particles.

The beautiful thing about the mole is that it lets chemists talk about the microscopic world of atoms in terms of grams, which is much more practical for laboratory work. When we say that a sample contains a certain amount of moles of a substance, we are actually referring to a very specific number of particles. In our exercise, when we talk about, for example, 4.88 moles of H2O2, we mean 4.88 times Avogadro's number of H2O2 molecules. The mole provides a bridge from the microscale to the macroscale.

Molecular Composition

Molecular composition refers to the types and quantities of atoms that make up a molecule. With the molecular composition and the mole concept in hand, we can determine how much of a specific element is in a mole of a compound. A balanced chemical formula is our guide to understanding the molecular composition.

For example, carbon dioxide's composition is captured by its formula, CO2, meaning each molecule consists of one carbon and two oxygen atoms. Knowing this formula, we can deduce that in a mole of carbon dioxide, there will be twice as many moles of oxygen atoms as there are moles of carbon dioxide. The textbook exercise demonstrates this by taking the moles of each compound and multiplying by the number of oxygen atoms indicated by the molecular composition to find the moles of oxygen.