Question

If \(1.00 \mathrm{~mol}\) of \(\mathrm{LiCl}\) has a mass of \(42.394 \mathrm{~g}\), what is the average mass of \(1 \mathrm{LiCl}\) formula unit in atomic mass units?

Short answer

The average mass of one \(\mathrm{LiCl}\) formula unit is \(70.91 \mathrm{amu}\).

Step-by-step solution

Understanding the Problem

The problem provides that \(1.00 \mathrm{~mol}\) of \(\mathrm{LiCl}\) has a mass of \(42.394 \mathrm{~g}\). The task is to find out the average mass of one \(\mathrm{LiCl}\) formula unit in atomic mass units (amu).

From grams to AMU

Firstly, you need to convert the mass of one mole \(42.394 \mathrm{~g}\) to atomic mass units. Given that \(1 \mathrm{g}\) is equivalent to \(6.022 \times 10^{23} \mathrm{amu}\), you multiply \(42.394 \mathrm{~g}\) by \(6.022 \times 10^{23} \mathrm{amu/g}\) to get the total mass in atomic mass units.

Divide total AMU by Avogadro's number

Then, to find the average mass of \(1 \mathrm{LiCl}\) formula unit, divide the total mass in atomic mass units by Avogadro's number (\(6.022 \times 10^{23}\) formula units/mol). This gives the average mass of a single formula unit of \(\mathrm{LiCl}\) in atomic mass units (amu).

Key concepts

Avogadro's number

Avogadro's number is a fundamental concept in chemistry. It represents the number of particles, typically atoms or molecules, in one mole of a substance. This value is an astonishingly large number: \(6.022 \times 10^{23}\). It's named after the scientist Amedeo Avogadro, who made significant contributions to understanding molecular theory.
When we talk about a mole of something, whether it’s atoms, molecules, or formula units, we're referring to \(6.022 \times 10^{23}\) of those entities. For example, one mole of carbon atoms means there are \(6.022 \times 10^{23}\) atoms of carbon. This immense number helps bridge the gap between the atomic scale and the everyday macroscopic world we interact with.
In the problem above, Avogadro’s number is used to calculate the average mass of one \(\text{LiCl}\) formula unit. It demonstrates how this large number aids in scaling down a bulk measurement (like grams) to an individual unit on the atomic scale.

LiCl formula unit

A formula unit in chemistry is the simplest ratio of ions in an ionic compound that results in a neutral charge. For \(\text{LiCl}\), this unit consists of one lithium ion \(\text{Li}^+\) and one chloride ion \(\text{Cl}^-\). Together, these ions form the compound lithium chloride.
Ionic compounds do not consist of discrete molecules but rather collections of ions arranged in lattice structures. The formula unit is the smallest repeatable unit within this structure that maintains overall charge neutrality. This concept is essential in understanding how ions combine to form compounds and in calculating masses at the atomic scale.
When we talk about the average mass of a \(\text{LiCl}\) formula unit in the problem, we are considering the combined atomic masses of lithium and chlorine in one simple and complete collection. This unit allows us to use the mole concept to relate mass in grams to atomic mass units.

Mole concept

The mole concept is a central idea in chemistry that simplifies the counting of atoms and molecules by relating mass to the number of particles. This is crucial because atoms and molecules are incredibly tiny and individually counting them is impractical. Instead, chemists use the mole to express amounts of a chemical substance.
One mole of any substance contains \(6.022 \times 10^{23}\) entities, which is Avogadro's number. This standard measurement allows for consistency in chemical reactions and calculations. For example, when determining the mass of one formula unit in amu, as in the provided problem, the mole concept helps convert between mass at the macroscopic level and atomic level.
The mole also facilitates calculations by connecting measurable quantities like mass (in grams) to the microscopic world of atoms and molecules. It provides a bridge between the scale of the chemical world and the lengths, masses, and volumes we measure directly.