Question

Determine the number of oxygen atoms present in 25.0 g of carbon dioxide.

Short answer

There are approximately $6.835\times {10}^{23}$ oxygen atoms present in 25.0 g of carbon dioxide.

Step-by-step solution

Determine the molar mass of CO2

CO2 is composed of 1 carbon atom and 2 oxygen atoms. The molar mass of carbon is 12.01 g/mol, and the molar mass of oxygen is 16.00 g/mol. To calculate the molar mass of CO2, we add the molar masses of each atom in the molecule: Molar mass of CO2 = (1 × 12.01 g/mol) + (2 × 16.00 g/mol) = 12.01 g/mol + 32.00 g/mol = 44.01 g/mol

Calculate the moles of CO2

To find the moles of CO2, we can use the formula: Moles of CO2 = (mass of CO2) / (molar mass of CO2) So, moles of CO2 = 25.0 g / 44.01 g/mol = 0.568 moles

Determine the moles of oxygen atoms

Since there are 2 oxygen atoms in each CO2 molecule, the moles of oxygen atoms would be twice the moles of CO2. Moles of oxygen atoms = 2 × moles of CO2 = 2 × 0.568 moles = 1.136 moles

Calculate the number of oxygen atoms

To find the number of oxygen atoms, we can use Avogadro's number (6.022 × 10^23 atoms/mol): Number of oxygen atoms = (moles of oxygen atoms) × (Avogadro's number) Number of oxygen atoms = 1.136 moles × 6.022 × 10^23 atoms/mol = 6.835 × 10^23 atoms So, there are approximately 6.835 × 10^23 oxygen atoms present in 25.0 g of carbon dioxide.

Key concepts

Stoichiometry

Stoichiometry is the area of chemistry that pertains to the quantitative relationships among the reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a given reaction. To effectively grasp stoichiometry, it's essential to be comfortable with the mole concept and understand how to use molar mass as a conversion factor.

Consider the example where we determine the number of oxygen atoms in a given mass of carbon dioxide, CO2. Stoichiometry steps in by allowing us to convert between the mass of CO2 and the number of oxygen atoms through several conversions. First, we convert the mass of CO2 to moles, a step crucial because the mole provides a bridge between the atomic scale and the macroscopic scale (a concept we'll delve into later under the mole concept). Then, we use the ratio of oxygen atoms to CO2 molecules to find the moles of oxygen. Finally, Avogadro's number, another pillar of stoichiometry, is used to convert moles of oxygen to the actual number of oxygen atoms.

Through stoichiometry, we systematically break down the problem into manageable steps, each corresponding to a specific conversion, ensuring no detail is overlooked, and that we are working within the confines of balanced chemical relationships.

Avogadro's Number

Avogadro's number, or Avogadro's constant, is a fundamental value in chemistry representing the number of constituent particles, usually atoms or molecules, contained in one mole of a substance. The number is named after the Italian scientist Amedeo Avogadro, and its value is approximately $6.022\times {10}^{23}$ particles per mole.

Understanding Avogadro's number is crucial for translating between the abstract world of atoms and the tangible world of grams and ounces that we can measure physically. In the context of our example problem, Avogadro's number enables the final conversion from moles of oxygen atoms to the actual count of atoms. Once we've determined the moles of oxygen atoms from the mass of CO2, we can multiply by Avogadro's number to arrive at the astounding number of individual atoms present in the sample.

Avogadro's number exemplifies the mole concept in action, giving physical meaning to the concept of a mole by providing a link between a substance's macroscopic properties and its molecular scale – a link without which modern chemistry would be virtually impossible.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a method for quantifying substances. It defines the mole as the unit of measurement for amount of substance in the International System of Units (SI). One mole of any substance contains the same number of particles as there are atoms in exactly 12 grams of carbon-12, which is $6.022\times {10}^{23}$ particles – this is Avogadro's number.

When we talk about moles, we're often talking about counting on an incredibly large scale. In the exercise, we had to first find the number of moles of carbon dioxide based on the given mass and its molar mass. The concept helps us understand that even though substances may have different physical properties or molar masses, one mole of each substance will always contain the same number of entities (atoms, molecules, ions, etc.).

The mole concept serves not only to count particles but also as a hinge that connects mass, which is measurable, to number of particles, which is countable but not directly measurable. This crucial concept in stoichiometry relies on understanding how to calculate molar mass, a skill that converts between grams and moles, allowing us to use stoichiometry to solve chemical problems like the one in our exercise.