Question

How many moles of \(\mathrm{O}\) atoms are in \(4.25 \mathrm{~mol}\) of calcium carbonate, \(\mathrm{CaCO}_{3}\), the chief constituent of seashells?

Short answer

There are 12.75 moles of oxygen atoms in 4.25 moles of calcium carbonate.

Step-by-step solution

Determine the molecular formula of calcium carbonate

Identify calcium carbonate by its chemical formula, which is \( \text{CaCO}_3 \). This indicates that each molecule has one calcium atom (Ca), one carbon atom (C), and three oxygen atoms (O).

Calculate the total number of oxygen atoms per molecule of calcium carbonate

Since there are three oxygen atoms in each molecule of calcium carbonate, to find the total number of moles of oxygen atoms, multiply the moles of calcium carbonate by 3.

Calculate the number of moles of oxygen atoms

Multiply the given amount of calcium carbonate in moles (4.25 mol) by the number of oxygen atoms per molecule (3) to find the total moles of oxygen atoms: \( 4.25 \text{ mol CaCO}_3 \times 3 \text{ mol O atoms/mol CaCO}_3 = 12.75 \text{ mol O atoms}\).

Key concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is a fundamental concept in chemistry that allows us to predict the amounts of substances consumed and produced in a given reaction. When dealing with stoichiometry, it is vital to understand the mole ratio, which is the proportion of reactants to products based on the balanced chemical equation.

To solve stoichiometric problems, such as determining the amount of reactants needed or products formed, we use the coefficients in the balanced chemical equation. In our example involving calcium carbonate, \( \text{CaCO}_3 \), there is no chemical reaction per se, but the concept still applies when breaking down the compound into its constituent elements. Since the molecular formula indicates a 1:3 ratio of calcium to oxygen atoms, we know that for every mole of calcium carbonate, there are three moles of oxygen atoms. Understanding this ratio is fundamental to solving the given problem.

Molecular Formula

The molecular formula represents the actual number of atoms of each element in a molecule. In the case of calcium carbonate, the molecular formula is \( \text{CaCO}_3 \), denoting it contains one atom of calcium (Ca), one atom of carbon (C), and three atoms of oxygen (O). Knowing this is crucial because it gives us the specifics needed to calculate the amount of each element in a given sample.

The formula showcases that these elements are in a fixed ratio, which is constant and does not change regardless of the quantity of the substance we have. So, if we need to know the moles of oxygen in a sample, we look at the ratio indicated by the formula. For every single molecule of calcium carbonate, there will always be precisely three oxygen atoms, a fact that is essential to the resolution of stoichiometric problems.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic realm that we can measure in the laboratory. One mole is defined as exactly \(6.022 \times 10^{23}\) entities, be it atoms, molecules, ions, or other particles. This number is known as Avogadro's number.

When working with moles, we can translate between the count of particles and the mass using molar mass, but in the context of our problem, we are concerned with the mole ratio. As we know, the molecular formula of calcium carbonate informs us that for every mole of this compound, we have three moles of oxygen atoms. This direct relationship allows us to scale our calculations up from the molecular to the molar level, as demonstrated in the exercise, where \(4.25 \text{ mol}\) of calcium carbonate equate to \(4.25 \times 3 = 12.75 \text{ mol}\) of oxygen atoms, making complex quantitative analysis of compounds accessible and manageable.