Question

Explain how Avogadro’s number is used as a conversion factor.

Short answer

Avogadro's number, denoted as \( N_A \), is a fundamental constant in chemistry that represents the number of particles (such as atoms, ions, or molecules) in one mole of any substance, with a value of approximately \( 6.022 \times 10^{23} \) particles per mole. It is used as a conversion factor to convert between the number of particles and the number of moles in a sample. If you have the number of particles and need to find the moles, divide the number of particles by Avogadro's number. Conversely, if you have the number of moles and need to find the number of particles, multiply the number of moles by Avogadro's number.

Step-by-step solution

Understanding Avogadro's number

Avogadro's number, denoted as \( N_A \), is a fundamental constant in chemistry that represents the number of particles (such as atoms, ions, or molecules) in one mole of any substance. It is named after the Italian scientist Amedeo Avogadro and its value is approximately \( 6.022 \times 10^{23} \) particles per mole.

Connection between moles and particles

The relationship between the number of moles and the number of particles in a sample can be established using Avogadro's number. In any chemical reaction, substances react in fixed proportions determined by their molar amounts. So when the amount of a substance is expressed in moles, it means we are referring to the number of particles involved, using Avogadro's number as a conversion factor.

Using Avogadro's number as a conversion factor

To use Avogadro's number as a conversion factor to convert between the number of particles and the number of moles, follow these steps: 1. If you have the number of particles and need to find the moles, divide the number of particles by Avogadro's number. Number of moles = (Number of particles) / \( N_A \) 2. If you have the number of moles and need to find the number of particles, multiply the number of moles by Avogadro's number. Number of particles = (Number of moles) × \( N_A \)

Illustrating with an example

Let's suppose we have a sample containing \( 1.204 \times 10^{24} \) atoms of copper. We want to know how many moles of copper are present. Follow the steps mentioned above: 1. Divide the number of particles by Avogadro's number: Number of moles = (Number of particles) / \( N_A \) = (\( 1.204 \times 10^{24} \)) / (\( 6.022 \times 10^{23} \)) = 2.00 moles So, there are 2.00 moles of copper present in the given sample.

Key concepts

Mole Concept

The mole concept is a bridge between the macroscopic world that we can observe and the microscopic world of atoms and molecules. Simplifying it, a mole represents a specific amount of particles, nearly akin to how a dozen represents twelve items.

In chemistry, the mole is used to express quantities of a substance because counting individual atoms or molecules is impractical. One mole, by definition, contains exactly Avogadro's number of particles, which is about 6.022 x 10^23 particles. This number is as fixed and known as the number 12 in a dozen.

To visualize the scale: if you had a mole of pennies, you could cover the Earth's surface to a depth of several hundred kilometers. It is essential to grasp the vastness of this number to appreciate why moles are necessary to quantify substances in chemical reactions.

Conversion Factor

A conversion factor is a multiplier that allows you to convert a quantity expressed in one set of units into an equivalent quantity in another set of units. In the context of Avogadro's number, it acts as a bridge between the number of discrete particles and the amount of substance in moles.

To perform the conversion, you either divide by Avogadro's number (to go from particles to moles) or multiply by it (from moles to particles), depending on the information you have and what you are trying to find. This conversion factor is fundamental in chemistry because it enables chemists to work with manageable amounts of substances when carrying out experiments and calculations.

Remember, it's just math!

Think of Avogadro's number as you would a dozen: If you have 24 eggs, you know instantly you have 2 dozen because 24 divided by 12 (the conversion factor for dozens) is 2. Similarly, with particles and moles, it's just a matter of dividing or multiplying by 6.022 x 10^23.

Chemical Reaction Stoichiometry

Chemical reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, the amount of products produced is directly related to the amounts of reactants used, and this relationship is quantified using the mole concept.

Stoichiometry allows chemists to predict how much of each reactant is needed to produce a desired amount of product or how much product can be produced from certain amounts of reactants. This balancing act uses the mole concept as its foundation, where each element's moles react according to the coefficients in the balanced chemical equation.

The balanced equation is your recipe!

Just like following a recipe ensures you have the right amount of ingredients for a dish, stoichiometry ensures you have the proper proportion of reactants to get the desired products. Ultimately, without the mole concept and Avogadro's number acting as a conversion factor, stoichiometry would not be possible, highlighting the intertwined nature of these concepts in the study of chemistry.