Question

How many oxygen atoms will be present in \(88 \mathrm{~g}\) of \(\mathrm{CO}_{2} ?\) (a) \(24.08 \times 10^{23}\) (b) \(6.023 \times 10^{23}\) (c) \(44 \times 10^{23}\) (d) \(22 \times 10^{24}\)

Short answer

There will be approximately \(24.08 \times 10^{23}\) oxygen atoms present in 88 g of CO_2.

Step-by-step solution

Calculate the molar mass of \text{CO}_2

First, determine the molar mass of carbon dioxide (CO_2). The molar mass of carbon is approximately 12.01 g/mol, and oxygen is about 16.00 g/mol. Since CO_2 has one carbon atom and two oxygen atoms, its molar mass is: \(12.01\text{ g/mol} + 2 \times 16.00\text{ g/mol} = 44.01\text{ g/mol}.\)

Calculate the number of moles of \text{CO}_2

With the molar mass of CO_2, calculate how many moles are present in 88 g of CO_2 using the formula: \text{moles} = \frac{\text{mass}}{\text{molar mass}}. So the number of moles of CO_2 is: \(\frac{88 \text{ g}}{44.01 \text{ g/mol}} \thickapprox 2\) moles.

Determine the number of oxygen atoms

Since each molecule of CO_2 contains 2 atoms of oxygen, there are 2 moles of oxygen atoms for every mole of CO_2. Hence, for 2 moles of CO_2, there are: \(2 \text{ moles} \times 2 = 4\) moles of oxygen atoms. Using Avogadro's number (approximately \(6.022 \times 10^{23}\) atoms/mol), the total number of oxygen atoms is: \(4 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} = 24.088 \times 10^{23}\) atoms.

Key concepts

Avogadro's number

One of the foundational stones of chemistry is Avogadro's number, which is approximately equal to \(6.022 \times 10^{23}\). This staggering figure represents the quantity of individual entities — usually atoms or molecules — found in one mole of any substance.

Think of Avogadro's number as the chemical equivalent to a dozen. While a dozen indicates \(12\) of something, a mole indicates \(6.022 \times 10^{23}\) based on Avogadro's constant. It is a bridge between the atomic scale and the macroscale that we can observe and measure in the laboratory.

When dealing with substances and their reactions, counting out individual atoms is implausible. Hence, Avogadro's number allows chemists to work with amounts that can be easily handled and measured, translating microscopic properties into macroscopic quantities.

Mole concept

The mole concept is an essential principle in chemistry that enables us to count particles at the atomic and molecular level by relating them to a quantity we can measure: mass.

A mole represents \(6.022 \times 10^{23}\) particles of a substance, be it atoms, molecules, ions, or other entities. The beauty of the mole concept lies in its ability to provide a method for quantifying substances without needing to count every individual particle.

To put it into perspective, if we say we have a mole of carbon atoms, we mean we have \(6.022 \times 10^{23}\) carbon atoms. Each element on the periodic table has a different molar mass, which is the weight of one mole of that element. This mass is usually given in grams per mole and is numerically equivalent to the atomic or molecular weight expressed in atomic mass units (amu).

Stoichiometry

Stoichiometry is the section of chemistry that deals with the measurement and quantitative relationships of the reactants and products in a chemical reaction. It involves using the mole concept to understand the balance of a reaction and predict the amounts of substances consumed and produced.

The term comes from the Greek words 'stoicheion' (element) and 'metron' (measure). In stoichiometry, the balanced chemical equation provides the necessary ratios of reactants and products. For example, the equation \(2H_2 + O_2 \rightarrow 2H_2O\) tells us that two moles of hydrogen gas react with one mole of oxygen gas to produce two moles of water.

In stoichiometric calculations, conserving mass and the number of atoms is crucial. This means that for every atom entering a reaction, it must either be found in the products or accounted for as a byproduct. By following these stoichiometric ratios, chemists can calculate the exact amounts of substances needed to carry out reactions efficiently.